Personal Tutor Final.doc

8/17/2019 Personal Tutor Final.doc

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Personal Tutorto accompany

Chemistrya project of the

American Chemical Society

W.H. Freeman and Company

Wayne Morgan

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Table of Contents

0.0 Introduction to the Personal Tutor (pg.2)

1.0 nderstandin! the ses of "umbers (pg.3)

1.1 Measurement and the Metric System (pg. 3)1.2 Derived Units (pg. )

1.3 Dimensiona! "na!ysis (pg. #)1.$ %recision and "ccuracy in Measurement (pg. 1&)

1.' %ercent rror (pg. 12)

1. Significant igures (pg. 13)

1.* Using Significant igures in +a!cu!ations (pg. 1)1.# Scientific ,otation (pg. 1#)

#.0 nderstandin! and Interpretin! $raphs and Tables (pg. 2&)

2.1 -ypes of raphs (pg. 2&)

2.1.1 %ie +harts (pg. 2&)2.1.2 /ar raphs (pg. 21)2.1.3 Mu!tip!e /ar raphs (pg. 22)

2.1.$ 0ine raphs (pg. 2$)

2.1.' y %!otsraphs (pg. 2')

2.2 /asic raphing 4u!es (!ine and y graphs) (pg. 31)

2.3 5nterpreting -a6!es (pg. 32)

%.0 nderstandin! the &ole (pg. 3')

3.1 What is a mo!e7 (pg. 3')

3.2 Mo!ar Mass (pg. 3')

3.3 Mass−Mo!e +onversions (pg. 3*)3.$ 8o!ume−Mo!e +onversions (pg. $&)

'.0 nderstandin! &ass (elationships in Chemical (eactions (pg. $2)

$.1 Understanding +hemica! 9uations (pg. $2)

$.2 /a!ancing +hemica! 9uations (pg. $3)

$.3 Stoichiometry (pg. $')$.$ 0imiting 4eactants (pg. $)

).0 nderstandin! *e+is ,ot and Structural Formulas (pg. '&)

'.1 Steps in Writing the 0e:is Structure (pg. '&)

'.2 Structura! ormu!as (pg. '$)

'.3 /onding %atterns in Many ;ydrocar6on Mo!ecu!es (pg. '')

'.$ orma! +harge (pg. '*)

-.0 nderstandin! $as *a+ Problems (pg. '


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Introduction

" chemistry tet6oo= is a va!ua6!e resource. 5t can he!p you in deve!oping a deeper understanding of themateria! you discuss in c!ass. 5t can i!!ustrate the most common types of pro6!ems you :i!! face and give

eamp!es of ho: to approach those pro6!ems. -he tet6oo= cannot anticipate :hich students :i!! havedifficu!ty :ith computations. ven the most comprehensive tet6oo= cannot possi6!y sho: every type of

pro6!em that might 6e encountered. -he %ersona! -utor is a supp!ement to the tet6oo= to give you moreguidance and practice :ith pro6!ems and computations. Using the %ersona! -utor is much !i=e visiting the

professor during office hours or going to a human tutor. >ou may need to ta=e advantage of it fre9uent!y or

you may on!y need its assistance a fe: times during the course. -he 9uestions can 6e a good revie: :hen

preparing for the test even if you are confident that you =no: ho: to so!ve the pro6!ems or do thecomputations.

ven the %ersona! -utor is not a comprehensive set of pro6!ems. ;o:ever? the types of pro6!ems sho:n

here shou!d he!p you get a good foundation in so!ving pro6!ems. 5t is important to remem6er that aneamination :ou!d not tru!y test your understanding of concepts and your a6i!ity to so!ve pro6!ems if the

professor mere!y put on the pro6!ems you had a!ready seen. 5f you use your tet6oo=? the %ersona! -utor?

and any other sources avai!a6!e you can 6e successfu! in this chemistry course.

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nderstandin! the ses of "umbers

+hemists re!y on data in order to test theories? so!ve pro6!ems and ma=e decisions. Most of the data is

numerica! data accumu!ated from carefu! measurements in the !a6oratory. "n important part of !earning

chemistry is !earning ho: to interpret and use numerica! data.

&AS(&"T A", TH &T(IC S2ST&

Metric units :ere first introduced in rance more than 1&& years ago. " moderni@ed form of the metricsystem :as internationa!!y adopted in 1


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>ou may me more fami!iar :ith the typica! ng!ish units of measurement that :e use in everyday !ife.

;ere are some comparisons that may he!p you visua!i@e the metric units.

1 :ilo!ram is a !itt!e over 2 pounds (1 =i!ogram 2.2 !6s)

1 meter is a !itt!e over 1 yard (1 meter 3< inches)

1. :ilometer is a6out 1 mi!e (1&& meters ≈ 1 mi!e)#% ; is the free@ing point of :ater (& o+ or 32 o)

%% ; is the 6oi!ing point of :ater (1&& o+ or 212 o)

#ou can use the

meanings from igure 2 to he!p you.

More than one unit conversion factor may 6e used in a sing!e pro6!em. Sometimes it is easier to ma=e a

conversion in more than one step. -here is no rea! !imit to the num6er of unit conversions that may 6e put

together. ;o:ever? never use any more unit conversions that are rea!!y necessary to move from the unityou are given to the unit you desire. -he net eamp!e sho:s ho: to use more than one step to ma=e a unitconversion.

'

ample= Con7ert 1')- ! to :ilo!rams.

5n igure 2 the meaning of =i!o te!!s that 1 =i!ogram :ou!d 6e e9ua! to 1&3 grams.

9uiva!anceG 1 =i!ogram (=g) 1 E 1&3 grams (g)

-he e9uiva!ence 6et:een =i!ograms and grams can 6e used to create a conversion factor. " conversion

factor? often ca!!ed a unit conversion factor? is one :here the numerator is a 9uantity e9ua! to the

9uantity in the denominator. -he on!y difference 6et:een the numerator and denominator is the units.-his means that a unit conversion factor is rea!!y e9ua! to one. Mu!tip!ication 6y a unit conversion

factor is !i=e mu!tip!ying 6y one. 5t :i!! resu!t in the units changing 6ut not the va!ue of the

measurement.

Unit +onversion actorG g X

kg 31&1

1or

kg

g X

1

1&1 3

Since :e are given a mass in grams it :i!! 6e necessary to choose the conversion factor that :i!! a!!o:

grams to 6e cance!!ed and to have =i!ograms !eft.

Unit +onversionG kg kg g X

kg grams $.1$'.1

1&1

11$'

3 ===


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,eri7ed nits

re9uent!y :e :ish to measure 9uantities that cannot 6e epressed using one of the 6asic S5 units. 5n these

situations t:o or more units are com6ined to create a ne: unit. -hese units are ca!!ed deri7ed units. oreamp!e? speed is defined as the ratio of distance to time. -o measure speed? t:o unitsHdistance and time

Hare com6ined. or eamp!e? the speed of your car :ou!d 6e epressed in the units of =i!ometers per

hour (=m hr −1

).

">T= >ou may 6e more fami!iar :ith seeing an epression !i=e =i!ometers per hour :ritten as=mhr. 5n chemistry the community of scientists has esta6!ished ru!es te!!ing ho: num6ers? names? and

other information shou!d 6e :ritten for pu6!ication. -he accepted :ay to :rite the AperB epression is to

:rite the term in the denominator :ith a −1 eponent. -his is the :ay these mied units :i!! 6e :rittenthroughout the persona! tutor.

" derived unit fre9uent!y used in chemistry is vo!ume. 0et us see ho: these derived unit for vo!ume isre!ated to fundamenta! S5 units. -he vo!ume of a cu6e is determined 6y mu!tip!ying (!ength E :idth E

height). " cu6e :ith sides of 1& cm? has a vo!ume of 1&&& cm3 (1&cm E 1&cm E 1&cm)? :hich is defined

as a !iter.

1000 cm% ≡ 1 liter 81*9

5n the !a6oratory the most common unit of vo!ume :i!! !i=e!y 6e the mi!!i!iter. -he metric prefies used for the fundamenta! units may a!so 6e app!ied to the derived unit? the 0iter. 1&&& m0 1 0.

Since 1&&& cm3 ≡ 1 0 and 1&&& m0 1 0? a usefu! e9uiva!ence can 6e stated. 1 cm3 1 m0. -hisre!ationship can 6e very usefu! in so!ving chemistry pro6!ems and :i!! often 6e a usefu! conversion in thechemistry !a6oratory.

Density is an important property for determining the identity of a samp!e of matter. 5t is defined as the

ratio of mass to vo!ume (Volume

Mass Density = ). 5t is a com6ination of severa! of the fundamenta! units

so it too is a derived unit. -:o units are com6inedHa mass unit and a vo!ume unit. -he density of so!idsand !i9uids is usua!!y epressed as g cm−3 and the density of gases as g 0−1.

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-here are other units that you :i!! encounter as you go through your chemistry course. -he calorie and

the ?oule are units used in epressing energy. -he ca!orie :as defined as the amount of energy necessary to

raise the temperature of eact!y one gram of :ater one degree +e!sius. -he jou!e comes from physics and

re!ates energy to forces at :or=. 5n chemistry :e use jou!es as our unit of energy measure. 5n 6io!ogy theca!orie or the =i!oca!orie ( 1 =ca! 1&&& ca!ories) is sti!! used. 1 ca!orie $.1# I. -he nutritiona! +a!orie

(+a!) given on food !a6e!s is actua! 1 =ca! or 1&&& ca!ories.

5n chemistry there are severa! units that are used to epress the pressure of gases. -he norma! atmospheric pressure at sea !eve! is defined as 6eing 1 atmosphere (atm) of pressure. Fne historica! unit for pressure is

the Torr? named for -orrece!!i :ho invented the 6arometer. -raditiona!!y 6arometers had a co!umn of

mercury that :ou!d rise and fa!! :ith changing air pressure. -he height of the mercury :as measured to

give the pressure in millimeters of mercury (mm ;g). -orr and mm;g of mercury are numerica!!yidentica! measurements. 1 atmosphere *& -orr *& mm ;g. >ou :i!! find a!! three of these units for

measuring pressure in many chemistry tet6oo=s and !a6oratory manua!s. -he S5 unit of pressure?

ho:ever? is the pascal (%a). 1 atmosphere 1&1? 32' %a Since this is such a !arge num6er it is often the

case that tet6oo=s :i!! give pressure in =i!opasca!s (=%a). 1 atm 1&1.32' =%a.

#

Practice Problems

1. -he average person in the United States uses 3$& 0 of :ater dai!y. +onvert this to

mi!!i!iters.

2. " 9uart is approimate!y e9ua! to


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,I&"SI>"A* A"A*2SIS

Dimensiona! ana!ysis? a!so ca!!ed the factor!a6e! method? is :ide!y used 6y

scientists to so!ve a :ide variety of pro6!ems. >ou have a!ready used this method to convert one type ofmetric unit to another. -he method is he!pfu! in setting up pro6!ems and a!so in chec=ing :or= 6ecause if

the unit !a6e! is incorrect? the numeric ans:er to the pro6!em is !i=e!y to 6e incorrect. -he use of

dimensiona! ana!ysis consists of three 6asic stepsG

1. Identify e@ui7alence relationships in order to create unit con7ersion

factors.

#. Identify the !i7en unit and the ne+ unit desired.

%. Arran!e the con7ersion factor so !i7en units cancel/ lea7in! the ne+

desired unit. Perform the calculation.

-he fo!!o:ing eamp!e i!!ustrates the use of dimensiona! ana!ysis.

re9uent!y in chemistry more than one conversion factor :i!! 6e necessary in order to so!ve a particu!ar

pro6!em. -he net eamp!e sho:s ho: more than one factor can 6e used to so!ve the pro6!em.

<

ample= In an eercise your laboratory partner measured the len!th of an ob?ect to be

1#.# inches. All other measurements +ere in centimeters and the ans+er +as to

be reported in cm%. 2our lab partner could measure the ob?ect a!ain this time in

centimeters/ or 1#.# inches could be con7erted to centimeters. Since you

already put a+ay the ruler you decide to con7ert inches to centimeters.

Step 1G ind the e9uiva!ence re!ating centimeters and inches.

,F-G +onversions factors are fre9uent!y found inside the 6ac= covers of science

tet6oo=s. Sometimes they can 6e found in the appendices of the tet. 5f you

cannot find the unit conversions you need in this? or any other tet? you can do an

internet search and find them at the many encyc!opedia or reference :e6 sites.

2.'$ cm 1 in

Step 2G 5dentify the given unit and the AdesiredB unit

iven unitG inchesADesiredB unitG cm

Step 3G +hoose the fraction :ith the AgivenB 9uantity in the denominator and the AdesiredB

9uantity in the numerator.

cm

in

cm X in &.3&

1

'$.22.12 =

-he units of inches (in) cance! !eaving the desired unit of centimeters (cm).


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Practice Problems

1. -he distance 6et:een ,e: >or= and San rancisco is $ ?*$1?&&& m. ,o:? that may sound

impressive? 6ut to put a!! those digits on a car odometer is s!ight!y inconvenient. (Ff course? in

the United States the odometer measures mi!es? 6ut that is another story.) 5n this case?=i!ometers are a 6etter choice for measuring distance. +hange the distance to =i!ometers.

2. +onvert *?2' m0 to 0.

3. -he 1'&& meter race is sometimes ca!!ed the Ametric mi!e.B +onvert 1'&& m to mi!es. (1 m

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P(CISI>" A", ACC(AC2 I" &AS(&"T

+hemistry eperiments often re9uire a num6er of different measurements? and there is a!:ays some error in

measurement. ;o: much error depends on severa! factors? such as the s=i!! of the eperimenter? the 9ua!ityof the instrument? and the design of the eperiment. -he re!ia6i!ity of the measurement has t:o

componentsG precision and accuracy. %recision refers to ho: c!ose!y measurements of the same 9uantity

agree. " highprecision measurement is one that produces very near!y the same resu!t each time it ismeasured. "ccuracy is ho: :e!! measurements agree :ith the accepted or true va!ue.

5t is possi6!e for a set of measurements to 6e precise :ithout 6eing accurate. igure 3

demonstrates different possi6!e com6inations of precision and accuracy in an eperiment designed to hit the

center of the target.

igure 3 %recision and "ccuracy

" second eamp!e of accuracy and precision is given in igure $. -he ta6!e !ists the resu!ts of temperature

measurements from a 6ea=er of 6oi!ing :ater. -he standard temperature of 6oi!ing :ater is 1&& J+. -he

data in the ta6!e i!!ustrates the different possi6!e com6inations of precision and accuracy in an eperiment.

Trial

Temperature (eadin!s

8oC9

Thermometer

1

Thermometer

#

Thermometer

%

Thermometer

'

1


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Practice Problems

roups of students determined the density of an un=no:n !i9uid in the !a6oratory. +a!cu!ate theaverage and range for each groupKs measurements.

1. roup 1 o6tained the fo!!o:ing va!uesG 1.3$ g m0−1? 1.32 g m0−1 ? 1.3 g m0−1. -he actua!

va!ue is 1.3$ g m0−1.

2. roup 2 o6tained the same resu!ts? 6ut the actua! va!ue is 1.$& g m0−1 .

3. roup 3 o6tained the fo!!o:ing va!uesG 1. g m0−1? 1.2# g m0−1? 1.1# g m0−1. -he actua!

va!ue is 1.3$ g m0−1.

$. roup $ o6tained the fo!!o:ing va!uesG 1.& g m0−1? 1.*& g m0−1? 1.$& g m0−1. -he actua!

va!ue is 1.$& g m0−1.

-he average va!ue for each set is usua!!y the va!ue compared to the accepted 6oi!ing point of :ater.

"ccuracy :i!! 6e judged 6y ho: c!ose the average is to the accepted va!ue. -he rangeHthe difference

6et:een the !argest and sma!!est va!uesHis the measure of the agreement among the individua!

measurements and :i!! 6e used to judge precision.

-he data ta=en :ith -hermometer 1 is accurate and precise? since the average agrees :ith the accepted

va!ue and the range is sma!!. -hermometer 2 provided data that is accurate 6ut not precise since the range is

re!ative!y !arge. -he data from -hermometer 3 is precise 6ut not accurate. -he range is sma!! enough that itis possi6!e that -hermometer 3 may not have 6een ca!i6rated proper!y. -hermometer $ provides data that is

neither precise nor accurate.

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Percent rror

Percent error is a measurement of the accuracy of the measurement. 5t is ca!cu!ated using the fo!!o:ing

formu!aG

L1&& X

Value Accepted

Value Accepted Valueal Experiment Error Percent

−=

"ote= %ercent error is a positive num6er :hen the eperimenta! va!ue is too high and is a negative

num6er :hen the eperimenta! va!ue is too !o:. Fften? though? percent error is reported as a positive

num6er regard!ess of :hether the eperimenta! va!ue is too high or !o:. re9uent!y the a6so!ute va!ue of

the difference 6et:een the eperimenta! and accepted va!ues is used. perimenta! 8a!ue − "ccepted8a!ue

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Practice Problems

+a!cu!ate the percent error for a!! four groups in the previous set of practice pro6!ems. Use the

average for each group as the eperimenta! va!ue. -he actua! va!ues are your accepted va!ues.

;ere are the data sets you need.

roups of students determined the density of an un=no:n !i9uid in the !a6oratory. +a!cu!ate the

average and range for each groupKs measurements.

1. roup 1 o6tained the fo!!o:ing va!uesG 1.3$ g m0−1? 1.32 g m0−1 ? 1.3 g m0−1. -he actua!

va!ue is 1.3$ g m0−1.

2. roup 2 o6tained the same resu!ts? 6ut the actua! va!ue is 1.$& g m0−1 .

3. roup 3 o6tained the fo!!o:ing va!uesG 1. g m0−1? 1.2# g m0−1? 1.1# g m0−1. -he actua!va!ue is 1.3$ g m0−1.

$. roup $ o6tained the fo!!o:ing va!uesG 1.& g m0−1? 1.*& g m0−1? 1.$& g m0−1. -he actua!

va!ue is 1.$& g m0−1.


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SI$"IFICA"T FI$(S

"s discussed ear!ier? measurements are an integra! part of most chemica! eperimentation. ;o:ever? the

numerica! measurements that resu!t have some inherent uncertainty. -his uncertainty is a resu!t of themeasurement device as :e!! as the fact that a human 6eing ma=es the measurement. ,o measurement is

a6so!ute!y eact. When you use a piece of !a6oratory e9uipment? read and record the measurement to one

decima! p!ace 6eyond the sma!!est mar=ing on the piece of e9uipment.

-he !ength of the arro: p!aced a!ong the centimeter stic= is $.*' cm !ong. -here are no graduation

mar=ings to he!p you read the !ast measurement as '. -his is an estimate. "s a resu!t this digit is uncertain."nother person may read this as $.* cm. -his is accepta6!e since it is an estimation. -here is error

(uncertainty) 6ui!t into each measurement and cannot 6e avoided.

5f the measurement is reported as $.*' cm? scientists accept the princip!e that the !ast digit has an

uncertainty of ±&.&1 cm. 5n other :ords the !ength might 6e as sma!! as $.*$ cm or as !arge as $.* cm. 5t isunderstood 6y scientists that the !ast digit recorded is an estimation and is uncertain. 5t is important tofo!!o: this convention.

-here are three processes invo!ving significant figures that :e :i!! mention here. -he first process is

estimation in measurement. >ou :i!! encounter this most fre9uent!y in the !a6oratory :hen measuringvo!umes :ith a graduated cy!inder? a 6uret or perhaps a pipette. stimation :i!! a!so 6e important :hen

measuring !ength :ith a ru!er. -he process of estimating the !ast digit :i!! 6e very simi!ar to the process

descri6ed at the 6eginning of this section.

"nother process is eamining measurements or data a!ready ta=en 6y you or someone e!se and determining

the num6er of significant figures in the measurement. -he net section provides you :ith si guide!ines for

determining the num6er of significant figures in a recorded measurement.

-he third process is reporting a ca!cu!ated ans:er to the proper num6er of significant figures. -he ru!es for

assigning the appropriate num6er of significant figures to an ans:er are covered in the section that 6egins

on page 1.

Significant figures :i!! 6e of concern any time you perform a mathematica! computation 6ased on data. 5t

is important to present an ans:er that ref!ects the precision of the instruments used to co!!ect the data.

1$


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$uidelines for ,eterminin! Si!nificant ,i!its

1. All di!its recorded from a laboratory measurement are called si!nificant fi!ures 8or

di!its9.

-he measurement of $.*' cm has three (3) significant figures.

"ote= 5f you use an e!ectronic piece of e9uipment? such as a 6a!ance? you shou!d record themeasurement eact!y as it appears on the disp!ay.

#. All nonBero di!its are considered si!nificant.

-here are specia! ru!es for @eros. eros in a measurement fa!! into three typesG !eading

@eros? trai!ing @eros? and midd!e @eros (@eroes 6et:een non@ero digits).

%. A middle ero is al+ays si!nificant.

3&3 mm has 3 significant figuresG a midd!e @eroHa!:ays significant

'. A leadin! ero is ne7er si!nificant. 5t is on!y a p!aceho!derN not a part of the actua!measurement.

&.&123 =g has 3 significant figuresG a !eading @eroHnever significant

). A trailin! ero is si!nificant +hen it is to the ri!ht of a decimal point. -his is not a

p!aceho!der. 5t is a part of the actua! measurement.

23.2& m0 has $ significant figuresG a trai!ing @eroHsignificant to the right of a decima!

point

22& m0 has on!y 2 significant figuresG a trai!ing @eroHthere is no decima! point so this@ero is ,F- significant

-. All si!nificant fi!ures include units since they are a result of a measurement. "

num6er :ithout units has !itt!e significance.

&easurement "umber of Si!nificant Fi!ures

123 g 3

$.'$ m0 $

&.33 cm 2

*2.# mm;g $

&.&33 3igure ' Significant igures

1'

-he most common errors concerning significant figures are (1) recording a!!

digits on the ca!cu!ator readout? (2) fai!ing to inc!ude significant trai!ing @eroes

(e.g.? 1$.1'& g)? and (3) considering !eading @eroes to 6e significant (e.g.?&.&&2 gG on!y 1 significant figure? not three).


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Practice Problems

1. ;o: many significant figures are in each of the fo!!o:ing7

a. $'1 &&& m

6. .2 E 1&−3$

I O sc. &.&&' gd. $&' 8

e. &.&'$& m0

2. or the centimeter ru!ers 6e!o: record the !ength of the arro: sho:n.

a.

6.

1


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SI"$ SI$"IFICA"T FI$(S I" CA*C*ATI>"S

When performing ca!cu!ations in chemistry you :i!! ta=e measurements and app!y some mathematica!

operation. >ou might 6e adding masses or finding a difference in masses. >ou might 6e so!ving a pro6!emthrough mu!tip!ication or division. 5t is easy to p!ug the num6ers into the ca!cu!ator and get a disp!ay that

may have up to ten digits. ,ot a!! of those digits can 6e =ept in the fina! ans:erP +hemists? and chemistry

students? have to 6e honest at the end of every ca!cu!ation and ref!ect the !eve! of precision in the data.;ere are some ru!es to he!p you determine ho: many digits to =eep at the end of a mathematica! operation.

Addition and Subtraction

-he num6er of decima! p!aces in the ans:er shou!d 6e the same as in the measured 9uantity :ith the least

precision. -he easiest :ay to determine this is 6y eamining the num6er of p!aces? e.g.? hundreds? tens?

ones? tenths? hundredths? thousandths? in the measurement. -he ans:er can have as many p!aces in the

ans:er as the term :ith the fe:est p!aces.

12'


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Practice Problems

1. "ns:er the fo!!o:ing pro6!ems using the correct num6er of significant figures.

a. 1.2* Q &.$3 Q 32.1

6. $2.&' − 3.

c. 1'.1 &.&32

d. 13.3 ÷ &.&$#

e.$2$.1

.12)&$.&3.13( x+

2. 5n the !a6oratory a group of students :as assigned to determine the density of an un=no:n

!i9uid. -hey used a 6uret to measure the !i9uid and found a vo!ume of 2.&$ m0. -he mass

:as determined on an ana!ytica! 6a!ance to 6e 2.2& g. ;o: shou!d they report the densityof the !i9uid7

3. 5n the first !a6oratory activity of the year? students :ere assigned to find the tota! area of

three ta6!etops in the room. -o save time? each of the three students gra66ed a ru!er andmeasured the dimensions. -hey then ca!cu!ated the area for each ta6!etop and added them

together. igure presents the studentsK measurements. What is the tota! area of the three

ta6!etops7

Student *en!th Width

A 12* cm *$ cm

D 1.3& m &.#& m

C '&.& in 2


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SCI"TIFIC ">TATI>"

5n chemistry :e dea! :ith very sma!! and very !arge num6ers. 5t is a:=:ard to use many @eros to epress

very !arge or very sma!! num6ers? so scientific notation is used. -he num6er is re:ritten as the product of anum6er 6et:een 1 and 1& and an eponentia! termH1&n? :here n is a :ho!e num6er.

5t is easier to assess the magnitude and to perform operations :ith num6ers :ritten in scientific notation. 5t

is a!so easier to identify the proper num6er of significant figures.

AdditionESubtraction sin! Scientific "otation

1. +onvert the num6ers to the same po:er of ten.

2. "dd (su6tract) the noneponentia! portion of the num6ers.

3. -he po:er of ten remains the same.

amp!eG 1.&& E 1&$

Q 2.3& E 1&'

" good ru!e to fo!!o: is to epress a!! num6ers in the pro6!em to the highest po:er of ten.

+onvert 1.&& E 1&$ to &.1&& E 1&'.

&.1&& E 1&' Q 2.3& E 1&' 2.$& E 1&'

&ultiplication sin! Scientific "otation

1. -he num6ers (inc!uding decima!s) are mu!tip!ied.

2. -he eponents are added.

3. -he ans:er is converted to proper scientific notationHthe product of a num6er 6et:een

1 and 1& and an eponentia! term.

1<

ample= 8'.#' 10#9 8).G 10'9

($.2$ '.*#) E (1&2Q$) 2$.' E 1&

+onvert to proper scientific notation 2.$' E 1&*

amples

1. The distance bet+een "e+ 2or: City and San Francisco '/'1/000

meters=

$?*$1?&&& m ($.*$1 E 1?&&&?&&&) m? or $.*$1 E 1& m

#. The mass of #) +ater molecules 0.000 000 000 000 000 000 000 'G

!rams=

&.&&& &&& &&& &&& &&& &&& &&& *$# grams *.$# E &.&&& &&& &&& &&& &&& &&& &&& 1 g

*.$# E 1&−22 grams


20/100

,i7ision sin! Scientific "otation

1. Divide the decima! parts of the num6er.

2. Su6tract the eponents.3. press the ans:er in scientific notation.

2&

ample= 8%.G 10)9 ÷ 8-.# 10G9

(3.*# ÷ .2) E (1&'R#) &.1 E 1&−3

+onvert to proper scientific notation .1 E 1&−$

Practice Problems

1. +onvert the fo!!o:ing num6ers to eponentia! notation.

a. &.&&&&3< 6.1&&&

3

c. &.&$'2

d. $ '2& &&& e. 3' &&&

2. +arry out the fo!!o:ing operationsG

a. (1.2 E 1&3) Q (3.$ E 1&2) d. (.&2 E 1&23) (2.& E 1&2)

6. (1.*' E 1&−1) − ($. E 1&−2) e. (.&2 E 1&23) ÷ (12.&)c. (1'.1 E 1&2) (3.2 E 1&−2)


21/100

nderstandin! and Interpretin! $raphs and Tables

-he a6i!ity to interpret graphs and ta6!es is a necessary s=i!! in science 6ut a!so finds use in everyday !ife.

5n artic!es or tet6oo=s you are !i=e!y to find graphs and ta6!es. Understanding the artic!eKs message

depends heavi!y on 6eing a6!e to interpret many different types of graphs and ta6!es.

5n science ta6!es are used to provide information. re9uent!y one 9uantity in a ta6!e depends upon or isre!ated to another. Data from ta6!es can 6e graphed to aid interpretation. raphs give a visua! representation

of the data that he!ps to revea! regu!arities and patterns.

T2PS >F $(APHS

raphs are of four 6asic typesG pie charts? 6ar graphs? !ine graphs? and E>p!ots. -he type chosen depends

on the characteristics of the data disp!ayed.

Pie Charts

%ie charts sho: the re!ationship of parts to a :ho!e. -he pie chart in igure #

disp!ays the !argest contri6utions to the composition of the human 6ody. -his presentation he!ps the readerto visua!i@e the magnitude of the differences 6et:een various e!ements :hich ma=e up the 6ody. %ie charts

are used infre9uent!y in the ana!ysis of data from the chemistry !a6oratory. -here are times :hen you :i!!

see scientific information presented in a pie chart and :i!! need to interpret it.

igure *G !ementa! +omposition of the ;uman /ody

21

Composition of the Human Body

61%23%

10% 6%

Fygen

+ar6on

;ydrogen

"!! Fther !ements


22/100

Dar $raphs

/ar graphs can 6e usefu! to study trends and compare re!ative va!ues. 5n this ta6!e atomic num6er and si@e

are compared.

"tomic ,um6er "tomic 4adius

(nm)1 *.<

2 $.<

3 2&&'

$ 1$

' 11.*


23/100

Practice Problems

Use igure < to ans:er these 9uestions.

1. What happens to atomic radius as you go across a series on the periodic ta6!e from !eft to

right7

2. What e!ement(s) have the sma!!est atomic radius among these 1


24/100

Practice Problems

1. What happens to the first ioni@ation energy as you go from !eft to right across the second period of the periodic ta6!e7 ;o: does this compare to the trend you found for atomic

radius7

2. Does the trend for first ioni@ation energy ho!d for the third period e!ements as :e!!7

3. Which of the first nineteen e!ements has the !argest first ioni@ation energy7

$. What is the re!ationship 6et:een atomic radius and first ioni@ation energy7

Comparison of Atomic Radius and First Ionization ner!y

0

5

10

1520

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Atomic Number

A t o m i c R a d

i u s

( n m )

I o n i z a t i o n n

e r ! y

( e " )

Atomic Radius Ionization Energy

Figure 11: Comparison of Atomic Radius and First Ionization for the First Nineteen Elements

2$


25/100

*ine $raphs

+onstructing a !ine graph is another :ay to sho: the re!ationship 6et:een t:o varia6!es. +onsider the data

co!!ected from the titration of 1'.&& m0 of &.1&& M ;+! :ith &.1&& M ,aF;. 5n this !a6oratory eercisethe 1'.&& m0 of hydroch!oric acid is p!aced into a f!as= and the p; of the so!ution is recorded after the

addition of each 1.&& m0 of sodium hydroide. " !ine graph of this data :i!! a!!o: you to visua!i@e :hat is

happening at various points in the titration.

olume of "a>H

8m*9

pH olume of "a>H

8m*9

pH

&.&& 1.&& 1.&& 11.'1

1.&& 1.& 1*.&& 11.#&

2.&& 1.12 1#.&& 11.


26/100

Practice Problems

"!=anes are compounds of car6on and hydrogen :ith the genera! formu!a? +n;2nQ2. Suppose that you

did an eperiment to determine the heat of com6ustion of severa! a!=anes and noticed that the heat of

com6ustionmo!e increased as the num6er of car6ons in the a!=ane increased. -he data ta=en are sho:nin igure 1$.

"!=ane ,um6er of +ar6on "toms ;eat of +om6ustion

(=I mo!−1)

Methane? +;$ 1 #


27/100

,ugget Mass

(grams)

8o!ume

(m0)

1 &.11 &.&&

2 &.2'1 &.&12

3 &.2


28/100

ample= Find the slope of the trend line dra+n on the &assEolume !raph.

-o find the s!ope? choose t:o points on the !ine. -hese points do not need to 6e

ones you p!otted. Determine the and y coordinates of each point.

+a!cu!ate the s!ope using the formu!aG12

12

x x

y y slope

−

−=

Step 1G %ic= out t:o points from the !ine

5t is usua!!y 6est to pic= points that have one ais va!ue that fa!!s on the grid !ine.-:o p!aces are mar=ed on the graph :here the trend !ine crosses a grid mar= on

the y ais. 5f :e use these t:o :e :i!! =no: the y va!ue :ith good precision and

on!y have to estimate the va!ue.

-he y va!ue of the first point is .2& grams (y1) and the va!ue of the first point is

a6out .&1& m0 (1). -he y va!ue of the second point is .3& grams (y2) and the

va!ue of the second point is a6out .&1'' m0 (2).

Step 2G Su6stitute into the s!ope formu!a and so!ve

12

12

x x

y y slope

−−

=

11#&&''.

1.

&1&.&1''.

2.3. −==−

−= mL g

mL

g

mLmL

g g Slope

-he y graph is often used :hen you are !oo=ing to esta6!ish a mathematica! re!ationship 6et:een t:o

varia6!es. 5t is a!so fre9uent!y used to assist in predicting the va!ues of one varia6!e 6ased on the va!ue of

the other.

2#


29/100

&ass+"o'ume Ratio

R2 ! 09882

y ! 17973" # 001920

01

02

0304

05

0 0005 001 0015 002 0025

"o'ume (m*)

& a s s

( ! )

Figure 18: Mass/Volume Ration Graph with Trend Line, Equation and R2 Value

5f you !oo= at the !ast graph of the go!d nugget data you :i!! see t:o specia! features. Many types of

graphing soft:are :i!! not on!y give you the 6est fit trend !ine for your data it :i!! a!so do some ana!ysis of

ho: :e!! the !ine fits the data. 5n this case the re!ationship 6et:een mass and vo!ume :as !inear? i.e.? thedata points gave a straight !ine 6est fit curve. -he soft:are :as a6!e to give the e9uation for that straight

!ine ( y 1*.


30/100

#he ,ependence of "o'ume on -ressure

0

2

4

6

8

10

0 50 100 150 200 250 300

-ressure (atm)

" o

' u m e ( m

* )

igure 2&G raph of %ressure8o!ume 4e!ationship

5t is o6vious from this graph that the vo!ume is not re!ated to pressure 6y a !inear? straight !ine? re!ationship

!i=e :e say :ith the graph of mass and vo!ume for the go!d nugget samp!es. >ou can sti!! do a 6est fitcurve and trend !ine. 5f you use graphing soft:are you can eperiment :ith possi6i!ities unti! you find the

trend !ine that gives the 6est fit. Using ce! the 6est trend !ine comes from the Apo:erB choice.

#he ,ependence of "o'ume on

-ressure

R2 ! 1

0

5

10

0 100 200 300

-ressure (atm)

" o ' u

m e

( m * )

igure 21G -he ffect of %ressure on the 8o!ume of "mmonia as :ith -rend 0ine

Since 4 2 is e9ua! to 1 this is a very good fit 6et:een the data points and the trend !ine. >ou cannot get a

6etter fitP -his :i!! a!most never 6e the case :ith data you gather in the !a6oratory. -he data points for thiseamp!e :ere actua!!y ca!cu!ated from the mathematica! re!ationship 6et:een vo!ume and pressure. -here

are a!:ays things that ma=e the data you co!!ect in the !a6oratory !ess precise than the ca!cu!ated va!ues. 5n

other :ords? do not epect to get such a marve!ous fit :hen you ana!y@e your !a6oratory data.

When the 6est smooth curve is not a straight !ine? the data can 6e manipu!ated to see if another

mathematica! re!ationship is possi6!e. 5n this case it appears that as the pressure increases the vo!ume

decreases. So :e can ca!cu!ate the va!ue of 18? add another co!umn to the ta6!e (igure 1


31/100

olume

8m*9

1Eolume

8m*9

Pressure

8atm9

2$$.' &.&&$&< &.1&&&

122.2 &.& &.2&&&

1.&2 &.&1$ &.$&&&

3&.$$ &.&32< &.#&&&12.1* &. 2.&&&&

'.


32/100

DASIC $(APHI"$ (*S 8line and By !raphs9

1. irst decide :here the information :i!! 6e graphed. -he hori@onta! ais (ais) is used for the

9uantity that can 6e contro!!ed or adjusted. -his is ca!!ed the independent varia6!e. -he vertica!ais (yais) is used for the 9uantity that responds to the changes in the 9uantity on the ais.

-his is ca!!ed the dependent varia6!e.

2. +hoose the sca!e so the graph 6ecomes !arge enough to fi!! most of the avai!a6!e space on the paper.

3. ach regu!ar!y spaced division on the graph paper shou!d e9ua! some convenient? constant va!ue.

5n genera!? each interva! shou!d have a va!ue that can 6e easi!y divided visua!!y such as 1? 2? '? or1&? rather than a va!ue such as 3? ? *? or


33/100

ample= Find t+o compounds in the table +ith similar molar masses. Compare their meltin!

points. Which of the characteristics listed appears to correlate +ith the differences

in meltin! point

Sodium ch!oride (MM '#.' g mo!−1) and magnesium f!uoride (MM 2 g mo!−1) have

very simi!ar mo!ar masses. -here me!ting points are 6oth much higher than other

su6stances !isted on the ta6!e. -hey are a!so significant!y different from each other? #&&

and 12$# o+ respective!y.

/oth have ionic structures so this cannot account for the difference in me!ting point. -he on!y other factorfrom the ta6!e is the formu!a. -here must 6e something a6out their composition that ep!ains the

difference in me!ting point. ,a+! is made up of t:o ionsG ,aQ and +!−. Mg2 is made up of three ionsG

Mg2Q and 2−. We !earned ear!y in chapter one that charge :as responsi6!e for interaction 6et:eensu6stances. +harge is a!so important in the interaction 6et:een ions in an ionic su6stance. +ou!om6Ks !a:

te!!s us that the !arger the charge? the greater the force of attraction or repu!sion. -he magnesium f!uoride

has a !arger force of attraction :ith the Mg2Q ion than there is :ith the ,aQ ion in the sodium ch!oride.

-his ep!ains the difference in me!ting points for the t:o su6stances. 5n chapter 2 there is a greaterep!anation of the interaction of ions in an ionic so!id.

ample= Compare the molecular compounds +ith the ionic compounds and ma:e a

!eneraliation about structure and meltin! point.

-he t:o ionic compounds have me!ting points of #&& o+ and 12$# o+. -he mo!ecu!ar

su6stances have me!ting points that range from −1#3 o+ to Q#& o+. 5t is a!:aysdangerous to ma=e genera!i@ations from sma!! amounts of data. ;o:ever? it appears that

ionic compounds? in genera!? have much higher me!ting points than mo!ecu!arsu6stances. -he forces that ho!d ionic so!ids together must 6e much stronger than the

forces that ho!d mo!ecu!ar su6stances together. -hese forces are discussed in chapters

one and t:o of the tet6oo=.

I"T(P(TI"$ TAD*S

-a6!es can 6e as simp!e as !isting the va!ue for a sing!e property of a su6stance or as comp!e as the one in

igure 2'. -he unshaded portion !ists the me!ting points for severa! su6stances. -he shaded portion of thechart suggests some additiona! information to aid in interpretation. >ou may 6e as=ed to !oo= for

re!ationships in the data.

Substance Formula &eltin! Point

8oC9

&olar &ass

8! mol 19

Stucture Polarity of

&olecule

Water ;2F & 1# Mo!ecu!ar %o!ar

/en@ene +; ' *# Mo!ecu!ar ,onpo!ar

,aphtha!ene +1&;# #& 12# Mo!ecu!ar ,onpo!ar

Sodium ch!oride ,a+! #&& '#.' 5onic ,ot app!ica6!e

Methane +;$ −1#3 1 Mo!ecu!ar ,onpo!ar

Magnesium f!uoride Mg2 12$# 2 5onic ,ot app!ica6!e

Methano! +;3F; −


34/100

Practice Problems

1. +ompare the characteristics of methane? 6en@ene? and naphtha!ene. What factor seems to

6e responsi6!e for differences in the me!ting points of these three su6stances7

2 -he previous three 9uestions use on!y some of the information avai!a6!e in the ta6!e. Writet:o more 9uestions that might 6e as=ed a6out the ta6!e.

3. 5t is important to use a!! of the information avai!a6!e in a ta6!e. ;o:ever? you shou!d not

ma=e s:eeping genera!i@ations that are supported 6y on!y a sma!! num6er of facts. 0oo= atyour ans:er to uestion 1 and state :hat other information you might :ish to !oo= up to

support your statement.

Additional Practice Problems

1. -he graph in igure 2 sho:s the approimate !eve! of +F2 in the atmosphere from 1


35/100

2. raphica!!y determine the density of ethy!ene g!yco! for the fo!!o:ing data co!!ected in the

!a6oratory. -he density :i!! 6e the s!ope of the straight !ine 6est fit curve for the data points.

&ass

8!9

olume

8m*9

11.2& 1&.&

1.*2 1'.&

22.1$ 2&.&

1*.*# 2'.&

33.$2 3&.&igure 2*G thy!ene !yco! Density Data

3. -he data 6e!o: :as co!!ected :hen :ater :as heated to its 6oi!ing point. Decide :hich type of

graph to use and graph this data. "ns:er the 9uestions that fo!!o: 6ased upon your graph.

Time

8minutes9

Temperature

8oC9

& 23.&

&.' 2*.&

1.& 3$.&

1.' $3.&

2.& '#.&

2.'


36/100

nderstandin! the &ole

WHAT IS A &>*

The mole is the S5 unit of amount. 5t is used as a counting num6er in chemistry. %air? do@en and ream are

other eamp!es of counting num6ers. 5t is un!i=e!y that you :ou!d ever purchase computer paper 6y thesheet. 5nstead you :ou!d pro6a6!y purchase a ream? or pac=age of '&& sheets? of paper. "t the grocery store

you 6uy eggs 6y the do@en. 5t is convenient to 6uy groups of things !i=e paper and eggs. When you 6uy a pac=age of a do@en? you =no: you :i!! get t:e!ve o6jects. When you 6y a ream it is consistent!y '&&

sheets. " gross is a do@en do@en? 1$$ o6jects. 5n the same :ay? a mo!e e9ua!s .&2 E 1&23 o6jectsP Most

often things that are counted in units of mo!es are very sma!! in si@e? e.g.? atoms? mo!ecu!es? or e!ectrons.

+ounting individua! chemica! units :ou!d 6e impossi6!e since there are 6i!!ions of 6i!!ions of units in evena re!ative!y sma!! amount of matter. 5t is much easier to count them in groups of mo!es. -he mo!e :i!! 6e

the common unit of amount in chemistry. 5t is used in many ca!cu!ations since 1 mo!e of anything :i!!

a!:ays contain .&2 E 1&23 chemica! units.

/ecause it :ou!d ta=e an impossi6!y !ong time to count .&2 E 1&23 o6jects? an indirect method is used. "n

ana!ogy may 6e he!pfu!. 5f you go into a home improvement store you may find nuts and 6o!ts in 6ins that

can 6e 6ought in 6u!=. 5t :ou!d 6e very tedious to count out every sing!e nut if you :anted a !arge num6er.

5nstead you cou!d :eigh out a 6ag containing a num6er of nuts. Suppose it :eighs 1?&&&. grams. 5f you=no: ho: much a sing!e nut :eighs :e can ca!cu!ate the num6er of nuts in the 6ag. Suppose each nut

:eighs 1&. grams. 5f :e divide 1?&&&. grams 6y 1&. grams per nut :e find that there are 1&& nuts in the

6ag. We can do the same thing :ith chemica!s. 5f :e =no: the mass of a samp!e :e can divide 6y the

mass of one mo!e to ca!cu!ate the num6er mo!es in the samp!e. -he mass of one mo!e is ca!!ed the molar

mass of a su6stance and is discussed in the net section.

&olar &ass

-he modern definition of a mo!e is the num6er of atoms in eact!y 12 grams of the car6on12 (+12)

isotope. -his num6er itse!f is named after "medeo "vogadro? :ho investigated re!ated concepts 6ut never

determined the num6er. "t !east four different types of eperiments have determined that the num6er is

.&2 E 1&23. "vogadroKs num6er is =no:n to ten significant figures? 6ut three :i!! 6e enough for most of

your ca!cu!ations.

1 mole -.0##1#-%- 10#% particles

-he modern atomic:eight sca!e is a!so 6ased on +12. -he re!ative mass of a hydrogen atom compared to

a car6on atom is 1.&. -herefore? one mo!e of hydrogen atoms has a mass of 1.& g? and one mo!e of

oygen atoms is 1'.


37/100

-he num6er of grams in one mo!e? or molar mass? of a compound is found 6y adding the re!ative atomic

masses of the atoms in the formu!a.

3*

ample= What is the molar mass of methanol/ CH%>H

Step 1G 5dentify the e!ements in the compound.

+ar6on? ;ydrogen? and Fygen

Step2G 4ead the atomic :eights of the e!ements from the periodic ta6!e

+ar6onG 12.&1 amu per atom 12.&1 g per mo!e of atoms

;ydrogenG 1.&1 amu per atom 1.&1 g per mo!e of atomsFygenG 1.&& amu per atom 1.&& g per mo!e of atoms

">T= Since :e are usua!!y interested in mo!es of atoms? mo!ecu!es? ions or formu!a units

it is common practice to use the grams per mo!e va!ues. -hese are numerica!!y e9uiva!ent tothe amu from the atomic :eights given on the periodic ta6!e.

">T= "s= your instructor if they have a preference on :hether to use the entire atomic:eight given or ho: many decima! p!aces they prefer you have for your atomic :eights.

Step3G Mu!tip!y the num6er of mo!es of atoms of each e!ement 6y the mo!ar mass of each e!ement

+ar6onG 1mo!e 12.&1g mo!e−1 12.&1 g

;ydrogen $ mo!es 1.&1 g mo!e−1 $.&$ g

Fygen 1 mo!es 1.&& g mo!e−1 1.&& g

Step $G "dd together the mo!ar mass contri6utions of a!! the e!ements

12.&1 g Q $.&$ gQ 1.&& g 32.&' g for one mo!e of methano!

Methano! has a mo!ar mass of 32.&' g mo!−1

. -his means that in every 32.&' grams of methano! thereare 1 mo!e or .&2 E 1&23 mo!ecu!es of methano!.

Practice Problems

ind the mo!ar mass (grams in one mo!e) of each of the fo!!o:ingG

1. thanoic acid (acetic acid)? +;3+FF;

2. Methana!? (forma!dehyde)? ;+;F

3. 2Dodecano!? +;3(+;2)


38/100

&assB&ole Con7ersions

Unit conversions? dimensiona! ana!ysis? can 6e used to convert 6et:een mass and mo!es.

Amoles A grams gramsmole

→

A grams Amoles moles grams

→


→

3#

ample= Ho+ many moles are there in 100.0 !rams of +ater

Step 1G +a!cu!ate the mo!ar mass of :ater

;G 1.&1 g mo!e−1 2 mo!es 2.&2 g

FG 1.&& g mo!e−1 1 mo!e 1.&& g

2.&2 g Q 1.&& g 1#.&2 g 1#.&2 g mo!e−1

Step 2G +hoose the appropriate conversion factor

1 mo!e 1#.&2 g so g

mole

&2.1#

1 or

mole

g

1

&2.1#


→

Since you are given grams and want moles you will choose g

mole

&2.1#

1

Step 3: Multiple the grams given by the conversion factor

O H molesO H grams

O H mole X O H grams 2

2

2

2 '$


39/100

A grams Amoles moles grams

→

3<

ample= Ho+ many !rams in ).)0 moles of +ater

Step 1G +a!cu!ate the mo!ar mass

-he mo!ar mass of :ater? ;2F :as ca!cu!ated 6efore and found to 6e 1#.&2 g mo!e−1

Step 2G +hoose the appropriate conversion factor

mole

g

1

&2.1# A grams Amoles moles

grams

→

Step 3: Multiple the moles given by the conversion factor

O H gramsO H mole

O H grams X O H moles 2

2

22 1.


40/100

Practice Problems

1. "cetic acid? +;3+FF;? and sa!icy!ic acid? +*;F3? com6ine to form aspirin. 5f a chemist uses'.&& g sa!icy!ic acid and 1&.'3 g acetic acid? ca!cu!ate the num6er of mo!es of each compound

used.

2. 2Dodecano!? +;3(+;2)H

Step 1G +a!cu!ate the mo!ar mass

+G 12.&1 g mo!e−1 2 mo!es 2$.&2 g

;G 1.&1 g mo!e−1 mo!es .& g

FG 1.&& g mo!e−1 1 mo!es 1.&& g

2$.&2 g Q .& g Q 1.&& g $. g $. g mo!e−1

Step 2G +hoose the appropriate conversion factors

-he first conversion is from =i!ograms to gramsGOH CH CH kg

OH CH CH grams23

23

11&&&

The second conversion is from grams to moles:OH CH CH grams

OH CH CH mole

23

23

.$

1

Step 3: Multiple by the appropriate conversion factors

C moleOH CH CH g

OH CH CH mole X

OH CH CH kg

OH CH CH g X OH CH CH kg

23

23

23

23

23 1.2*.$

1

1

1&&&2'.1 =


41/100

olume J &ole Con7ersions

uite often in the chemistry !a6oratory you :i!! 6e using so!ution :ith concentrations !a6e!ed :ith the

sym6o! M. -he M represents concentration in mo!arity? mo!es 0−1. -his is a very convenient unit since it

a!!o:s us to ca!cu!ate mo!es if :e =no: the vo!ume of the so!ution in !iters.

)( L solution Ao !olume Amoles moleliters

→

Amoles Lin solution Ao !olume liter mole

→ )(

5f you =no: the desired amount of mo!es you can ca!cu!ate the vo!ume of so!ution that :i!! contain thatmany mo!es

>ou can even use mo!arity as a conversion factor a!ong :ith the mo!ar mass to convert from vo!ume to

mass.

$1

ample= Ho+ many moles are there in #).00 m* of a 0.0)00 & solution of "aCl

Step 1G +onvert vo!ume to !iters

1 0 1&&& m0 so LmL

L X mL &2'&&.&

1&&&

1&&.2' =

Step 2G Use the mo!arity as a conversion factor to so!ve for mo!es

Amoles Lin solution Ao !olume liter mole

→ )(

"aCl moles L

moles X L &&12'.&

1

&'&&.&&2'&&.& =

ample= Ho+ many milliliters of 0.#)0 & potassium dichromate are needed to supply

0.0'0 moles of potassium dichromate

Use conversion factors to convert from mo!es to !iters and then to mi!!i!iters. ,otice that the chemica!

used ma=es no difference in these ca!cu!ations. 4emem6er one mo!e of any su6stance contains the

same num6er of mo!ecu!es as one mo!e of any other su6stance. ;o:ever? it is a!:ays 6est to inc!udethe chemica! identity :ith the unitsP

dichromate potassiummL L

mL X

moles

L X moles 1&&

1

1&&&

2'&.&

1&$&.& =


42/100

Practice Problems

1. ;o: many mo!es are there inG

". 12' m0 of &.&11/ are there in )00.0 m* of a 0.1)0 &

solution

-here are t:o conversion factors needed for this ca!cu!ationG mo!arity and mo!ar mass.

-he mo!arity isG L

moles

1

1'&.&. -he mo!ar mass isG mole

grams

1

3$.3$2.

sucrose gramsmole

grams X

L

moles X L *.2

1

3$.3$2

1

1'&.&'&&.& =


43/100

nderstandin! &ass (elationships in Chemical (eactions

9uations are the !anguage of chemistry? and they are important in he!ping us understand ho: atoms and

mo!ecu!es form ne: su6stances. 5t has 6een said many times that chemistry is a 9uantitative science.

+hemistry is a!so a very precise science. "toms com6ine to form mo!ecu!es in definite ratios. Su6stancesreact in definite ratios to form ne: materia!s. "toms and mo!ecu!es are very sma!! and difficu!t to count

individua!!y? so the idea of a mo!e :as deve!oped.

",(STA",I"$ CH&ICA* 6ATI>"S

Fne :ay to descri6e a chemica! reaction can 6e descri6ed 6y :riting an ng!ish sentence.

When ethano! 6urns in the presence of sufficient oygen? the products are car6on dioide and :ater.

"nother :ay is to :rite a :ord e9uation using the chemica! names of the reactants and products. -he arro:here is often read Ayie!ds?B 6ut it can a!so 6e thought of as an e9ua! sign.

thano! Q oygen car6on dioide Q :ater

Whi!e a :ord e9uation does provide us :ith additiona! information? rep!acing the chemica! names :ithformu!as and indicating the physica! states of each su6stance is even more descriptive and specific.

+;3+;2F;(!) Q F2(g) +F2(g) Q ;2F(!)

;o:ever? a chemica! sentence is not an e9uation unti! it is 6a!anced. -he la+ of conser7ation of matter

states that in a chemica! reaction? matter is neither created nor destroyed. -hat means the num6er of atoms

of each type must 6e the same on 6oth sides of the e9uation. -he fo!!o:ing chemica! e9uation sho:s a

6a!anced chemica! e9uation. +ount the num6er of car6on atoms? hydrogen atoms? and oygen atoms to 6esure.

+;3+;2F;(!) Q F2(g) +F2(g) Q ;2F(!)

(eactant Side Product Side2 car6on atoms 2 car6on atoms

hydrogen atoms hydrogen atoms

* oygen atoms * oygen atoms

$3


44/100

DA*A"CI"$ CH&ICA* 6ATI>"S

-here are t:o =ey ingredients to :riting chemica! e9uations. irst and foremost? you must :rite the correct

formu!a for each su6stance in the e9uation. -he second ingredient is satisfying the !a: of conservation ofmass. 5n chemica! e9uations this means that there must 6e the same num6er of atoms of each e!ement in the

reactants as there are in the products. ,o atoms may 6e !ost and none may 6e created in a chemica!

reactionP

+onsider the reactionG hydrogen gas reacts :ith oygen gas to form gaseous :ater

Step 1G Write the formu!as for each reactant and product correct!y.

;ydrogen gasG ;2 (g)

Fygen gasG F2 (g)

WaterG ;2F (g)

Step 2G Write out the e9uation and see if it is 6a!anced

;2 (g) Q F2 (g) ;2F (g)

(eactants Side Products Side

2 hydrogen atoms 2 hydrogen atoms

2 oygen atoms 1 oygen atom

-he num6er of oygen atoms is not the same on 6oth sides of the e9uation.

Step 3G %!ace coefficients in front of formu!as unti! the e9uation is 6a!anced

We cou!d p!ace a 2 in front of the formu!a for :ater to give more :ater mo!ecu!es since :e founda deficit of oygen on the product side 6efore

;2 (g) Q F2 (g) 2;2F (g)


2 hydrogen atoms $ hydrogen atoms


-he oygen atoms are no: e9ua! on 6oth sides. ;o:ever? there are more hydrogen atoms on the product side than the reactant side. ,o: :e need to p!ace a coefficient in front of the hydrogen

gas formu!a to he!p 6a!ance the e9uation. %!ace a 2 in front of the ;2 and see if the e9uation is

6a!anced.

2;2 (g) Q F2 (g) 2;2F (g)


$ hydrogen atoms $ hydrogen atoms


,o: the e9uation is 6a!anced and the !a: of conservation of mass is satisfied.

$$


45/100

Practice Problems

/a!ance these mo!ecu!ar e9uations

1. n (s)Q ;+! (a9) n+!2 (a9) Q ;2 (g)

2. "! (s) Q F2 (g) "!2F3 (s)

3. +$;1& (g) Q F2 (g) +F2 (g) Q ;2F (g)

$. C+!F3 (s)

C+! (s) Q F2 (g)

'. e (s) Q ;2F (!) e3F$ (s) Q ;2 (g)

. +a+2 (s) Q ;2F (!) +2;2 (g) Q +a(F;)2 (a9)

*. MnF2 (s) Q ;+! (a9) Mn+!2 (a9) Q ;2F (!) Q +!2 (g)

#. e2F3 (s) Q +F (g) e (s) Q +F2 (g)


46/100

Stoichiometry

5f the num6er of atoms is conserved in a chemica! reaction? the mass must a!so 6e conserved as epected

from the 0a: of +onservation of Mass. 5n the e9uation for the formation of :aterH2 ;2(g) Q F2(g) 2

;2F(!)H2 mo!ecu!es of hydrogen and 1 mo!ecu!e of oygen com6ine to form 2 mo!ecu!es of :ater. We

cou!d a!so say that 2 mo!es of hydrogen mo!ecu!es react :ith 1 mo!e of oygen mo!ecu!es to form 2 mo!es

of :ater mo!ecu!es. Using the num6er of grams in a mo!e of each su6stance? the mass re!ationships in theta6!e can 6e determined. -he ratio of mo!es of hydrogen to mo!es of oygen to form :ater :i!! 6e 2G1. 5f 1&

mo!es of hydrogen are avai!a6!e? ' mo!es of oygen are re9uired.

# H# 8!9 K ># 8!9 # H#> 8l9

2 mo!ecu!es 1 mo!ecu!e 2 mo!ecu!es

2 mo!es 1 mo!e 2 mo!es

(2 mo!)(2.&2 g mo!−1) (1 mo!)(32.&& g mo!−1) (2 mo!)(1#.&2 g mo!−1)

$.&$ g 32.&& g 3.&$ g

So!ving pro6!ems invo!ving the masses of products and or reactants is convenient!y accomp!ished 6y

dimensiona! ana!ysis. "!! numerica! pro6!ems invo!ving chemica! reactions 6egin :ith a 6a!anced e9uation.

$

ample Find the mass of +ater produced +hen 10.0 !rams hydro!en

reacts +ith ecess oy!en.

2 ;2(g) Q F2(g) 2 ;2F(!)

Step 1G +onvert grams of a given su6stance to mo!es of a given su6stance.


→

22

2

2


47/100

enera!!y? you :i!! :ant to put these three steps together in one pro6!em. 5f you have the conversion

factors set up proper!y the units :i!! cance! out and !eave you :ith the units you need for the fina! ans:er.

O H g O H mol

O H g

H mol

O H mol

H g

H mol H g 2

2

2

2

2

2

2

2 2.#<1

&2.1#

2

2

&2.2

1)&.1&( =

,F-G -his is the theoretical yield of this reaction. 5t represent the amount of product that can 6e made if

the reaction :or=s perfect!y. 5n practice the yie!d of product :ou!d 6e something !ess than this amount.

.

$*

Practice Problems

1. "cety!ene 6urns in air to form car6on dioide and :aterG

' +2;2(g) Q 2 F2(g) $ +F2(g) Q 2 ;2F(!)

;o: many mo!es of +F2 are formed from 2'.& mo!es +2;27

2. 5f insufficient oygen is avai!a6!e? car6on monoide can 6e a product of the com6ustion of

6utaneG

< +$;1&(!) Q 2 F2(g) # +F(g) Q1& ;2F(!).

What mass of +F cou!d 6e produced from '.& g 6utane7

3. 1'.& g ,a,;2 is re9uired for an eperiment. Using the fo!!o:ing reaction? :hat mass ofsodium meta! is re9uired to produce the ,a,;27

2 ,a(s) Q 2 ,;3(g) 2 ,a,;2(s) Q ;2(g)7

$. thano! and acetic acid react to produce ethy! acetate according to the reaction +2;'F; Q

+;3+(F)F; +;3+(F)F+2;' Q ;2F. 5f the reaction is on!y 3'L efficient at the conditions

used? :hat mass of +;3+(F)F; :i!! 6e necessary to produce 1&&. g +;3+(F)F+2;'7

"ssume that sufficient ethano! is avai!a6!e.

'. ;eating +a+F3 yie!ds +aF and +F2. Write the 6a!anced e9uation. +a!cu!ate the mass of

+a+F3 consumed :hen $.' g of +aF forms


48/100

nderstandin! *imitin! (eactants

5f a com6ustion pro6!em states that ecess oygen is avai!a6!e? :e need not concern ourse!ves :ith the

oygento:ater ratio. -he mass of :ater produced is predicted from (and !imited 6y) the mass of hydrogenavai!a6!e. Ff course in the !a6oratory :e often dea! :ith specified masses of each reactant? 6ut that re9uires

an enhanced pro6!emso!ving method.

Suppose a fami!y :ants to ma=e severa! chi!e re!!eno cassero!es to serve at a neigh6orhood party. -herecipe !ists re9uired ingredients? :hich are itemi@ed in the !eft co!umn of the ta6!e that fo!!o:s. -he right

co!umn represents a survey of pantry and refrigerator contents.

4e9uired 5ngredients "vai!a6!e 5ngredients %ossi6!e +assero!es

1 2*o@ can :ho!e green chi!es 2 2*o@ cans :ho!e green chi!es 2

1 !6 Monterrey Iac= cheese 3 !6 Monterrey Iac= cheese 3

1 !6 +heddar cheese 3 !6 +heddar cheese 3

3 eggs 1 do@ eggs $

3 -6sp f!our ' !6 f!our Many

'o@ canned evaporated mi!= $ 'o@ cans evaporated mi!= $

;o: many cassero!es can 6e made7 "!though four cassero!es can 6e made from the avai!a6!e eggs or mi!=?there are on!y enough cans of green chi!es for t:o cassero!es. 5n other :ords? the num6er of cans of green

chi!es can 6e ca!!ed the !imiting factor. "fter the t:o cassero!es are prepared? cheese? eggs? f!our? and mi!=

:i!! remain? 6ut a!! the green chi!es :i!! 6e used. -herefore? no more than t:o cassero!es can 6e made.5n this eamp!e? the green chi!es are the !imiting reactant. -he !imiting reactant is the reactant that is

consumed first and !imits the amount of product that can 6e made. -he same princip!e app!ies in

determining the 9uantity of product that can 6e produced in a chemica! reaction. 0etKs ta=e another !oo= at

the reaction of hydrogen and oygen to produce :ater? then consider :hat :ou!d happen if 2.&& mo!hydrogen and 2.&& mo! oygen :ere avai!a6!e. ;o: many mo!es of :ater can 6e produced7 What is the

!imiting reactant7 Which reactant :i!! 6e in ecess and 6y ho: much7

2 ;2(g) Q F2(g) 2 ;2F(!)

-he 6a!anced chemica! e9uation states that 2.&& mo! hydrogen react :ith 1.&& mo! oygen. When thereaction is comp!ete? 2.&& mo! :ater are produced and 1.&& mo! oygen remains unreacted. -his pro6!em iseasy to so!ve 6y inspection. Many times it :i!! not 6e so easy to judge :hich is the !imiting reactant

through inspection. -his is especia!!y true :hen you are given grams of the reactants instead of mo!es.

Fne method that is easy and :i!! a!:ays he!p you determine the !imiting reactant is to set up the three steps(grams of given mo!es of given? mo!es of given mo!es of :anted? mo!es of :anted grams of

:anted) for 6oth reactants as if the other one :as present in ecess. -he reactant that gives the sma!!er

amount of product :i!! 6e the !imiting reactant. 5t is the reactant that !imits the amount of product that can 6e made.

$#


49/100

$<

ample Ho+ many !rams of +ater can be made if ).00 ! of H# 8!9 and ).00 ! of ># 8!9

are allo+ed to react What is the limitin! reactant

Set up the conversion factors for each one and so!ve.

( ) O H g O H mol

O H g

H mol

O H mol

H g

H mol H g 2

2

2

2

2

2

22 .$$

1

&2.1#

2

2

&2.2

1&&.' =

( ) O H g O H mol

O H g

Omol

O H mol

O g

Omol O g 2

2

2

2

2

2

22 3.'

1

&2.1#

1

2

&&.32

1&&.' =

Since the oygen gas produces the sma!!er amount of :ater it must 6e the !imiting reactant. -hatmeans that :hen '.&& g of hydrogen and oygen gases react a tota! of '.3 g of :ater can 6e produced.

Fnce :e have identified the !imiting reactant :e can ca!cu!ate the mass of the ecess reactant that

remains unused at the end of the reaction.

irst? ca!cu!ate ho: much of the ecess reactant is used up in the reaction. Start :ith the !imiting

reactant and so!ve for the mass of the ecess reactant.

( ) used H g H mol

H g

Omol

H mol

O g

Omol O g 2

2

2

2

2

2

22 31.

1

&2.2

1

2

&&.32

1&&.' =

5t on!y ta=es &.31 g of hydrogen gas to react :ith the '.&& grams of oygen gas. We started out :ith

'.&& grams of oygen gas and used up &.31 grams. -hat means that $.3* grams of hydrogen remain

unused at the end of the reaction ('.&& g R &.31 g $.3* g ;2).


50/100

'&


51/100

Practice Problems

1. 5n the synthesis of sodium amide ( ,a,;2)? :hat is the maimum mass of ,a,;2 possi6!eif '&.& g of ,a and '&.& g ,;3 :ere used7

2 ,a(!) Q 2 ,;3(g) 2 ,a,;2(s) Q;2(g)

2. -he fue! methano!? +;3F;? can 6e made direct!y from car6on monoide (+F) andhydrogen (;2).

a. Write a 6a!anced e9uation for the reaction.

6. +a!cu!ate the maimum mass of methano! if one starts :ith '.*' g +F

and 1&.& g ;2.

c. Which reactant is the !imiting reactant7d. ;o: much of the ecess reactant remains7

3. "spirin (+


52/100

ample= Ho+ many 7alence electrons in +ater/ H#>

;G (1 va!ence e!ectron) E (2 hydrogen atoms) 2 va!ence e!ectrons

FG ( va!ence e!ectrons) E (1 oygen atom) va!ence e!ectrons

-he sum of the va!ence e!ectrons is #.

ample= Ho+ many 7alence electrons in the sulfate ion/ S>'#

SG ( va!ence e!ectrons) E (1 su!fur atom) va!ence e!ectrons

FG ( va!ence e!ectrons) E ($ oygen atoms) 2$ va!ence e!ectrons

-he sum of the va!ence e!ectrons is 3&.

Since this is a negative!y charged ion :e need to add in e!ectrons e9ua! to itscharge.

-he tota! va!ence e!ectrons :i!! 6e 3& Q 2 32.

ample= Ho+ many 7alence electrons in the hydronium ion/ H%>K

;G (1 va!ence e!ectron) E (3 hydrogen atoms) 3 va!ence e!ectronsFG ( va!ence e!ectrons) E (1 oygen atom) va!ence e!ectrons

-he sum of the va!ence e!ectrons is


53/100

,F-G 5t is usua!!y good to start 6y putting the e!ement :ith the fe:est atoms in the formu!a in

the center and arranging the other e!ements around it. >ou :ou!d not choose hydrogen as

a centra! atom for any of the three eamp!es here.

; F ; F ;

F S F F ;

F ;

Step %= ,istribute electrons to the atoms that are not in the center until they ha7e G 7alence electrons

8' pairs of electrons9. This is called an octet. ">T= The pair in the bond is counted as one

of the ' pairs of the octet. Hydro!en +ill not !et an octet. It +ill only ha7e one pair of

7alence electrons.

; F ; F ;

F S F F ;

F ;

Step '= If there are any 7alence electrons remainin! they may be placed around the atom in the

center until it has an octet or all the a7ailable electrons are used up.

; F ; F ;

F S F F ;

F ;

">T= 5ons are :ritten :ith 6rac=ets around them and the charge noted at the upper right hand

corner. -his assists in the e!ectron counting process. -he 6rac=ets and charge identify :hy there

are etra or missing e!ectrons. >ou can :ait unti! you have comp!eted the 0e:is structure to puton the 6rac=ets and charge if you :ish.

'3

1Q2−


54/100

Step )= Chec: to see if each atom has an octet of electrons. If the central atom does not ha7e an

octet it may be necessary to share more than one pair of electrons +ith one of the other

atoms/ i.e./ form a double or triple bond.

,F-G +? F? S? ,? and % are a!! capa6!e of sharing t:o pairs of e!ectrons in a 6ond? i.e.? forming

dou6!e 6onds. + and , are capa6!e of sharing three pairs of e!ectrons in a 6ond? i.e.?

forming a trip!e 6ond.

;ydrogen and the ha!ogens :i!! not routine!y form dou6!e or trip!e 6onds.

"!! three of the compounds sho:n in the eamp!es for Step $ have octets around a!! the atoms

ecept hydrogen. -herefore? no dou6!e 6onds are needed and a!! three 0e:is structures are fine as:ritten.

ample= Write the *e+is structure for the nitrite ion/ "># .

Step 1G -ota! va!ence e!ectrons

,G (' va!ence e!ectrons) E (1 nitrogen atom) ' va!ence e!ectrons

FG ( va!ence e!ectrons) E (2 oygen atoms) 12 va!ence e!ectrons

-he sum of the va!ence e!ectrons is 1*. ;o:ever? since it has a 1− charge :e have to add 1 moreto the 1* to get a grand tota! of 1# va!ence e!ectrons avai!a6!e in the nitrite ion.

Step 2G /ond atoms :ith a pair of e!ectrons

F , F

Step 3G +omp!ete octets of e!ectron on outer atoms

F , F

Step $G %!ace any remaining e!ectrons around the centra! atom

F , F ,itrogen does not have an octet after adding the remaining e!ectrons.

Step 'G +omp!ete the octet around the centra! atom 6y forming dou6!e or trip!e 6onds if possi6!e

F , F Sharing t:o pairs of e!ectrons :ith the oygen gives nitrogen an octet.

F , F "!! three atoms no: have an octet of e!ectrons.

'$

2−

2−


55/100

ample= Write the *e+is structure for methane/ CH'

Step 1G +G $ va!ence e!ectronsN ;G 1 E $ $N tota! is # va!ence e!ectrons

Step 2G ;

; + ; Steps 3 R ' :i!! not resu!t in any changes to the structure.

;

ample= Write the *e+is structure for methanal/ HC8>9H

Step 1G ;G 1 E 2 2N +G $ E 1 $N FG E 1 N tota! va!ence e!ectrons is 12.

Step 2G

F

; + ;

,F-G >ou may :onder :hy the car6on atom is p!aced in the center since there are one atom

each of car6on and oygen. 5t :ou!d 6e possi6!e to :rite a 0e:is structure :ith oygen as the

centra! atom. 5n a !ater section the concept of forma! charge :i!! 6e introduced as a :ay to he!pdetermine :hich of severa! possi6!e 0e:is structures :ou!d 6e more !i=e!y to occur. 4ight no:

you cou!d app!y the 6onding patterns for hydrocar6ons and :ou!d see that the 0e:is structure

:ith oygen in the center :i!! not 6e consistent :ith the 6onding patterns.

Step 3G

F

; + ; "!! 12 va!ence e!ectrons have 6een used.

Step $G -here are no va!ence e!ectrons remaining to p!ace on the car6on atom.

Step 'G

F

H C H

-:o pairs of e!ectrons must 6e shared in order for car6on to have an octet.

''


56/100

ample= Write the *e+is structure for carbon dioide/ C>#

Step 1G +G $ E 1 $N FG E 2 12N tota! va!ence e!ectrons is 1

Step 2G

F + F

Step 3G

F + F

Step $G -here are no !eft over va!ence e!ectrons to 6e p!aced around the car6on atom. 5t does not have an

octet so it :i!! 6e necessary to share more than one e!ectron :ith each oygen.

Step 'G

F + F

-here :i!! not 6e a trip!e 6ond :ith one oygen and a sing!e 6ond :ith the other since oygen is

not one of the t:o e!ements !i=e!y to form trip!e 6onds. Fygen does ma=e dou6!e 6onds.

Structural Formulas

Sometimes you :i!! see the 0e:is structure a66reviated 6y rep!acing the dots representing shared pairs ofe!ectrons? i.e.? 6onds? :ith dashes.

"># = F , F

CH'= ;

; + ;

;

HC8>9H= F

; + ;

C>#= F + F

'

1−


57/100

Dondin! Patterns in &any Hydrocarbon &olecules

5n the tet6oo= a num6er of 6io!ogica!!y important mo!ecu!es are descri6ed. -here are some simp!e

6onding patterns that can 6e app!ied to many of the hydrocar6on mo!ecu!es that you :i!! encounter in thetet so that it :i!! 6e easier to :rite structura! or 0e:is formu!as. >ou cannot app!y these patterns 6eyond

hydrocar6on mo!ecu!es composed of car6on? hydrogen and oygen :ithout the ris= of the patterns 6rea=ing

do:n.

5n these hydrocar6on mo!ecu!es car6on :i!! ma=e four 6onds. -his cou!d 6e four sing!e (sigma 6onds) or

any com6ination of sing!e? dou6!e or trip!e 6onds that add up to four tota! 6onds. Fygen :i!! ma=e t:o

6onds. -his cou!d 6e from t:o sing!e 6onds (sigma 6onds) or from a dou6!e 6ond (a sigma 6ond Q a pi

6ond). ;ydrogen :i!! on!y form one 6ond. 5t :i!! a!:ays 6e a sing!e (sigma 6ond).

amples of Dondin! in Hydrocarbon &olecules

+

+=

=+=

≡+−

−F−

F=

−;

Sometimes the !ine formu!a of a compound :i!! give some he!p in :riting the structura! formu!a. 5t :i!!

give us a genera! idea a6out the order of the atoms. >ou :i!! sti!! have to app!y the patterns o6served :ith

hydrocar6ons and everything e!se you =no: a6out :riting 0e:is structures.

ample Write the structural formula of ethanoic acid/ CH%C>>H.

-here are t:o :ays that :e might try to :rite this formu!a.

; ; F

; + + F F ; ; + + F ;

'*


58/100

; ;

-he first structure is not consistent :ith the 6onding patterns seen in hydrocar6on mo!ecu!es. -he second

car6on on!y ma=es t:o 6onds instead of the $ that car6on norma!!y ma=es.

-he second structure adheres to a!! the genera! ru!es. ;ydrogen ma=es 1 6ond? 6oth oygen atoms ma=e

t:o 6onds? and 6oth the car6on atoms ma=e four 6onds each.

">T= " concept ca!!ed forma! charge can 6e used to he!p you decide among possi6!e structura! formu!as.

5t is discussed in the net section.

'#

Practice Problems

Write the 0e:is structures for these mo!ecu!es and ions.

1. car6on tetrach!oride? ++!$

2. car6onate ion? +F32−

3. su!fur dioide? SF2$. su!fur trioide? SF3'. methano!? +;3F;. acetone? +;3+(F)+;3*. su!fate ion? SF$

2−

#. phosphate ion? %F$3−


59/100

Formal Char!e

Suppose you have more than one possi6!e :ay of :riting a 0e:is structure for a mo!ecu!e.

F+SG F+S

FS+G FS+

SF+G SF+

-he techni9ue of assigning forma! charge to each atom :ithin a compound can he!p determine :hich of

severa! structures is most !i=e!y. orma! charge is a 6oo= =eeping method for e!ectrons in a compound.

Formal Char!e alence lectrons J 81E# bondin! electrons K nonbondin! electrons9

>(

Formal Char!e alence lectrons 8L of bonds K L of nonbondin! electrons9

orma! charge is ca!cu!ated for each atom in a mo!ecu!e. -he sum of the forma! charges on the atoms in

any ion must 6e e9ua! to the charge of the ion. When comparing t:o structures the one :ith the most

forma! charges of @ero is the one you :ou!d predict to 6e more pro6a6!e.

">T= -he method of ca!cu!ating forma! charge sho:n here is an a!ternative to the method sho:n in the

6oo=. +hemists often have severa! methods avai!a6!e to them for so!ving pro6!ems. >ou need to find the

method that ma=es sense to you and use it. ven though the methods are not identica! each one :i!! yie!d

the same resu!t.

ample= Which structure is most probable= >CS/ >SC/ or S>C

>CS= +F R T12($) Q $ & (-he oygen has va!ence e!ectrons. Since there is a dou6!e 6ondthere are $ e!ectrons shared 6et:een the oygen and car6on. -he

oygen a!so has $ non6onding e!ectrons)

++ $ R T12(#) Q & & (+ar6on has $ va!ence e!ectrons. 5t forms t:o dou6!e 6onds in thiscompound for a tota! of # shared6onded e!ectrons. +ar6on does not

have any non6onding e!ectrons.)

+S R T12($) Q $ & (Su!fur has va!ence e!ectrons. 5t shares $ e!ectrons :ith the car6onand has $ non6onding e!ectrons as :e!!.)

The formal char!e on each atom is 0 for this molecule.

>SC= +F R T12($) Q $ &

+S R T12(#) Q & Q2

++ $ R T12($) Q $ −2

-he forma! charges are not & for the su!fur and car6on. -he first formu!a is more

pro6a6!e than this one.

'


60/100

SF+G +S R T12($) Q $ &

+F R T12(#) Q & Q2

++ $ R T12($) Q $ −2

-he forma! charges on t:o of the atoms are not & :ith this formu!a.

-he first formu!a F+S is the most pro6a6!e of these three since the forma! charge of each

atom in that formu!a is &.

Practice Problems

1. "ssign forma! charges to each atom in 6oth of these structura! formu!as.

; ; F

; + + F F ; ; + + F ;

; ;

Does the forma! charge he!p you pic= the more pro6a6!e formu!a7

2. -here are three structures suggested for the ion ,+F−.

T , + F − T , + F − T , + F −

"ssign forma! charges to each atom. Use the forma! charges to predict :hich structure is most

pro6a6!e.

&


61/100

nderstandin! $as *a+ Problems

-he 6ehavior of gases can 6e predicted 6y severa! !a:s.

Doyle4s *a+= -he vo!ume of a gas is inverse!y proportiona! to pressure. "s the pressure goes up thevo!ume goes do:n if a!! other varia6!es are constant.

pressure!olume

1α

Charles4 *a+= -he vo!ume of a gas is direct!y proportiona! to Ce!vin temperature. "s the temperature

goes up so does the vo!ume if a!! other varia6!es are constant.

A7o!adro4s *a+= -he vo!ume of a gas is direct!y proportiona! to the num6er of mo!es of gas partic!es. "s

the num6er of mo!es of gas partic!es goes up so does the vo!ume if a!! other varia6!es are constant.

particles gaso moles!olumeα

$ayB*ussac4s *a+= -he pressure of a gas is direct!y proportiona! to the Ce!vin temperature. "s thetemperature goes up so does the pressure if a!! other varia6!es are

constant.

etemperatur pressureα

%ro6!ems re9uiring the use of /oy!eKs? +har!esK? "vogadroKs and ay0ussacKs !a:s a!:ays invo!vechanges in one of the varia6!esG pressure? temperature? num6er of mo!es? or vo!ume. -he mathematica!

formu!as for the gas !a:s are given here.

Doyle4s *a+=

1

2

2

1

P

P

V

V = or 81%1 82%2

Charles4 *a+= 2

1

2

1

$

$

V

V = or 81-2 82-1

A7o!adro4s *a+=2

1

2

1

n

n

V

V = or 81n2 82n1

1

etemperatur !olumeα

5dea! as 0a:G %8 n4- (com6ines a!! four gas !a:s)

% pressure (in atmospheres)8 vo!ume (in !iters)

, num6er of mo!es (in mo!es)

4 gas constant (&.


62/100

ample What 7olume +ould a )0.0 m* sample of !as occupy if the pressure +ere

increased from #.0 atm to G.0 atm

Step 1G 5dentify the gas !a: or !a:s associated :ith the pro6!em

5n this pro6!em you are given pressure and vo!ume. -hat means that this is a /oy!eKs !a:

pro6!em.

1

2

2

1

P

P

V

V = or 81%1 82%2

Step 2G 5dentify the varia6!es and their va!ues

81 (starting vo!ume) '&.& m0

82 (ending vo!ume) 7

%1 (starting pressure) 2.& atm

%2 (ending pressure) #.& atm

Step 3G Su6stitute and so!ve

('&.& m0)(2.& atm) (82)(#.& atm)N

mLmLatm

atmmLV 12'.12

)&.#(

)&.2)(&.'&(2 ===

,F-G -here can on!y 6e t:o significant figures in our ans:er since the pressure va!ues

on!y have t:o significant figures.

Step $G +hec= to see if the ans:er ma=es sense

/oy!eKs !a: says that vo!ume is inverse!y re!ated to pressure. "n increase in pressureshou!d resu!t in a sma!!er vo!ume if a!! other varia6!es remain constant. -he ans:er is

consistent :ith this re!ationship.

ample A )0.0 m* sample of !as has a pressure of #) mmH! at #).0 oC. What

the pressure be if the temperature +ere raised by ).0 oC

Step 1G 5dentify the gas !a:

5n this pro6!em you are given pressure and temperature. ay0ussacKs !a: gives there!ationship 6et:een temperature and pressure. -he vo!ume given in this pro6!em isirre!evant.

2

1

2

1

P

P

$

$ = or -1%2 -2%1


%1 *3' mm;g

%2 7

-1 2'.&o

+ 2


63/100

ample A ).0 m* sample of hydro!en !as/ H# 8!9/ has a pressure of 1) mmH! at

##.0 oC. What 7olume +ould the !as occupy at STP "o !as is lost in the

chan!e of temperature and pressure.


8o!ume? pressure and temperature are a!! given in this pro6!em. -his re9uires a

com6ination of /oy!eKs and +har!esK !a:s. We can use the com6ined gas !a:.

22

22

11

11

$ n

V P

$ n

V P = or %181n2-2 %282n1-1


%1 *1' mm;g %2 *& mm;g (standard pressure in

mm;g)81 *'.& m0 82 7

n1 7 n2 7

-1 22.& o+ 2


64/100

ample A sample of oy!en !as occupies a 7olume of 1#) m* at #).0 oC and #1.0

mmH!. What 7olume +ould the !as occupy at %).0 oC and G)0.0 mmH!


Since more than one varia6!e changes :e :i!! use the com6ined gas !a:.

22

22

11

11

$ n

V P

$ n

V P = or %181n2-2 %282n1-1


%1 *21.& mm;g %2 #'&.& mm;g

81 12'.& m0 82 7

n1 n2 n2 n1-1 2'.&

o+ 2


65/100

ample What 7olume +ould be occupied by #.) moles of nitro!en !as at

#).0 mmH! and ##.0 oC


Fn!y one va!ue is given for each varia6!e. -he 5dea! as 0a: dea!s :ith oneva!ue for each of the varia6!es.

%8 n4-


% (*2'.& mm;g)(1 atm*& mm;g) .


66/100

ample What is the 7olume of 1.00 mole of hydro!en !as at #).0 oC and #)

mm H!


-he 5dea! as 0a: :i!! 6e used since there is on!y one set of va!ues for the varia6!es.


%

mmHg

atmmmHg

*&

1)*2'( .


67/100

Ans+ers/ Solutions and planations for the Practice Problems

ven though there are eamp!e pro6!ems in the %ersona! -utor and Wor=ed amp!es in the tet6oo= you

may not yet fee! fu!!y confident :ith your :or= on every pro6!em. -he so!utions and ep!anations for most

of the pro6!ems have 6een inc!uded here so you can compare your :or= and your ans:er to this =ey.;opefu!!y? you :i!! 6e a6!e to eamine your :or= and see :here is differs from the so!utions given here.

Who =no:s? you may 6e a6!e to uncover some errors that :e have madeP -he ans:ers? !i=e the eamp!ese!se:here? are on!y of 6enefit if you actua!!y use them. /e sure to :or= the pro6!ems and then chec= your

ans:ers. -he re:ard for doing the :or= and then revising it if need 6e :i!! 6e far greater than if yousimp!y !oo= at the pro6!ems and their ans:ers. -he origina! 9uestions are a!so inc!uded here to he!p you.

ood !uc=P

&easurement and the &etric System 8pa!e )9

1. Which metric unit and prefi +ould be most con7enient to measure each of the follo+in!

a. meter 6. micrometer c. mi!!isecond

d. =i!ogram e. nanogram f. mi!!igram

g. megagram

#. What +ord prefies are used in the metric system to indicate the follo+in! multipliers

a. =i!o 6. mi!!i c. centi d. micro

3. "n antacid ta6!et contains 1# mg of the active ingredient ranitidine hydroch!oride. ;o: many

grams of ranitidine hydroch!oride are in the ta6!et7

g mg

g mg 1#.&

1&&&

11# =

'. There are 1.-0< :m in eactly 1 mile. Ho+ many centimeters are there in 1 mile

cm xm

cm

km

mkm '1&&


68/100

,eri7ed nits 8pa!e 9

1. The a7era!e person in the nited States uses %'0 * of +ater daily. Con7ert this to

milliliters.

mL xmL L

mL L '1&&.3&&&?3$&

1

1&&&3$& ==

2. " 9uart is approimate!y e9ua! to


69/100

g cm

g cm 3$

1

*&.223'

3

3 =

). Ho+ many #)0 m* ser7in!s can be poured from a #.0 * bottle of soft drin:

ser!ingsmL

ser!ing

L

mL L &.#

2'&

1

1

1&&&&.2 =

-. The speed limit in Canada is 100 :mEhr. Con7ert this to metersEsecond.

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