Mathematics-based Chemistry

for

Science, engineering

&

preprofessional majors

WHAT IS CHEMISTRY ????WHAT IS CHEMISTRY ????WHAT IS CHEMISTRY ????WHAT IS CHEMISTRY ????

Chemistry is the Study Of _________

& the ______________________

• Matter is defined as anything that

has both _________________________

Matter Classification

Matter can be subdivided into mixtures and pure

substances.

Homogeneous & Heterogeneous

• Homogeneous matter has the SAME

________, ___________ and _________

throughout.

• Heterogeneous matter has VISIBLY

DIFFERENT ______ that can be seen, or

_________ that vary through the substance.

SAMPLE EXERCISESAMPLE EXERCISESAMPLE EXERCISE

White gold, used in jewelry, contains two elements, gold and palladium.

• The material is uniform throughout, it is

_______________

• Composition varies therefore, it

__________________

• It must be a

_____________________

Mixtures vs Pure Substances

• A mixture is two or more pure substances

that can be separated by ______________.

• Pure substances

– cannot be separated into separate parts by a

________ change

– have a distinct set of physical and chemical

_________.

Which of the following is a pure

substance?

(a) air

(b) concrete

(c) blue-cheese salad dressing

(d) Nitrogen

(e) None of these

Matter is formed from one

or more of the Elements

• Elements Are Fundamental Substances

That Can Not Be Broken Down _________

• Elements Are Symbolized By One Or

Two Letter ___________

See Table 1.2

H

F

Cl

I

N

O

Elemental Hydrogen

Elemental Fluorine

Elemental Chlorine

Elemental Iodine

Elemental Nitrogen

Elemental Oxygen

• A COMPOUND Is A PURE Substance

Formed When TWO or More _______

Combine

• EVERTHING Is Made Of Chemicals.

There Is NO Meaningful Distinction

Between a “NATURAL” Substance

And A “____________” One

Passing an electric current through a

certain substance produces oxygen and

sulfur. This substance cannot be a(n)

(a) Pure substance

(b) mixture

(c) compound

(d) element.

Name

Nitrogen

Oxygen

Argon

Carbon Dioxide

Neon

Helium

Krypton

Xenon

Formula

N2

O2

Ar

CO2

Ne

He

Kr

Xe

Table 1.1 Important Compounds

1. Sulfuric Acid

2. Nitrogen

3. Oxygen

4. Calcium Oxide

5. Ammonia

6. Phosphoric Acid

7. Chlorine

8. Sodium Hydroxide

H2SO4 (aq) NOTE

N2

O2

CaO

NH3

H3PO4 (aq) NOTE

Cl2

NaOH

Properties

•Can be determined without _________the

chemical make–up of the sample.

•Some typical physical changes are:

Melting, Freezing, Boiling, Condensation,

Evaporation, Dissolving, Stretching,

Bending, Breaking

Intensive & Extensive Properties

Intensive Properties have values that

___ _____ depend on the amount of

substance. {e.g. temperature

Extensive Properties have values that

____ depend on the amount of

substance {e.g. weight

CHEMICALCHEMICALCHEMICAL Properties

• are those that ______ the chemical make–up

of the sample.

• Burning, Cooking, Rusting, Color change,

Souring of milk, Ripening of fruit, Browning

of Apples, Taking a photograph, Digesting

food

• Note: Chemical properties are actually chemical

changes.

Pick the chemical change that occurs when a

match is held over a piece of metal

(a) water condensing on the metal

(b) burning a match

(c) metal getting hot

(d) smoke deflecting light

Chemistry is the study of Matter

& the Changes it undergoes

Changes can be EITHER

Physical Changes � Ice ______

or

Chemical Changes ���� Gasoline ________

How Do We Study Chemistry ?

by using the Scientific Method

The scientific method is a systematic approach to

solving problems that involves

1. Making observations (_______________)

2. Devise a hypothesis to (_____________)

3. ____ing these hypotheses with experiments

4. Formulating a _________

HYPOTHESIS , LAW & THEORYHYPOTHESIS , LAW & THEORYHYPOTHESIS , LAW & THEORY

HYPOTHESIS � __________Explanation

LAW � Concise ___________of Fact

THEORY � ____________ of Facts

scientific method

• A hypothesis is a suggested explanation of a

phenomenon, based on whatever resources are

available.

• Any useful hypothesis will enable predictions.

Once predictions are made, they can be tested

by experiments. If test results contradict

predictions, then the hypotheses are called into

question and explanations may be sought.

WE “DO” EXPERIMENTS

What do we “do” in EXPERIMENTS ?

We _____________ things

“GOOD” ARE THE

MEASUREMENTS?

An object was weighed three times

1. 13.036 grams

2. 13.040 grams

3. 13.031 grams

What do you report as the weight ?

ACCURACY & PRECISION

• ACCURACY refers to how closely a

measured value agrees with the correct

value

• PRECISION refers to how closely

individual measurements agree with one

another.

ACCURACY & PRECISION

Weight

Should record weight in ___________

Length

Should record length in ________

Temperature

Should record temperature in __________

Amount

Should record amount in __________

S I Base Units(See Table 1.4 Text)

Mass Kilogram kg

Length Meter m

Time Second s

Temperature Kelvin K

Amount Mole mol

Some Derived Quantities

• .

Quantity Definition Derived Unit Area Length times Length m

2

Volume Area times Length m

3

Density Mass per unit kg / m

3

Speed Distance per unit m / s

Must Know Prefixes

Used in Science

Metric System

See Table 1.5 Text

Metric to Metric

Convert pm to meters

Let the UNITS solve the problem

meters ??? ?

?? pm ?? =

pm

mχ

English to Metric

Convert inches to cm

Let the UNITS solve the problem

cm ?? inches ??

cm ?? ?? =χinches

English to English

Convert 5.68762 x 10 3 feet to miles

• Inches in a foot ?

• Feet in a mile ?

See Back of Book

For useful conversions

Exponential Notation

In Scientific Notation, Numbers Are

Written in The EXPONENTIAL Format

A x 10n

5687.62 feet = 5.68762 x 10 3 feet

= 5.68762 Kilo feet

= 5.68762 kft

CONVERSION FACTORS

You MUST Know A Conversion Factor For

• Length : Metric ↔ English

• Mass : Metric ↔ English

• Volume : Metric ↔ English

• See Text For Useful Conversion Factors

TYPES OF NUMBERSTYPES OF NUMBERSTYPES OF NUMBERS

Some Conversions are EXACTEXACTEXACTEXACT Numbers

12 inches ≡ 1 foot

4 quarts ≡ 1 gallon

1 pound ≡ 16 oz

Many Conversion Are APPROXIMATEAPPROXIMATEAPPROXIMATEAPPROXIMATE

1 pound ≈ 453.59 grams

TYPES OF NUMBERS

1. EXACT ( COUNTED ) NUMBERS

e.g. 54 STUDENTS, 100 BOOKS, 6 ANTS

2. APPROXIMATE ( MEASURED )

NUMBERS

e.g. 54 LITERS, 100 METERS, 6 GRAMS

SIGNIFICANT FIGURESSIGNIFICANT FIGURESSIGNIFICANT FIGURES

1. Digits of a measured number that have

uncertainty only in the last digit

2. The NUMBER Of Digits That Are

KNOWN With CERTAINTY

3. Digits that indicate the precision of

measurements

DETERMINING THE NUMBER OF

SIGNIFICANT FIGURES

ALL Digits Are SIGNIFICANT

EXECPT TWO TYPES

1. ZEROS That Come BEFORE The First

NONZERO Digit e.g. 047.54

2. ZEROS That Come AFTER The LAST

NONZERO Digit (Most Of The Time)

How many significant figures do each

of the following have ?

1. 13.036 grams

2. 13.230 grams

3. 13.217 grams

4. 12.947 grams

5. 12.949 grams

6. 12.758 grams

7. 12.967 grams

8. 13.122 grams

?

How many significant figures do

each of the following have ?

(a)0.0360653 meters

(b)7.2100 x 10-3 gms

(c)7210000000 sec

(d)$25.03

________

________

________

_______

Rounding Off Numbers

1. If the digit to be removed is LESS than 5

number is left unchanged.

2. If the digit to be removed is 5 or greater,

number is increased.

Round off the following measurements

(a) 3.774499 L to four significant figures ____

(b) 255.0974 K to three significant figures ____

(c) 55.265 Kg to four significant figures ______

MATHEMATICAL SKILLS

ONLY A FEW Mathematical Skills

Are Required For General Chemistry,

But a THOROUGH

UNDERSTANDING

Of Them Is Necessary

ADDITION And SUBTRACTION

• The Number Of Significant Figures to

the RIGHT of the DECIMAL POINT

in the Final Sum or Difference is

determined by the SMALLEST number

of Significant Figures to the RIGHT of

the DECIMAL POINT in ANY of the

ORIGINAL NUMBERS

Examples

1. 89.332 m Five Significant Figures

+ 1.1 m ONE Sig. Fig. After Decimal

90.432 m = ???? m

2. 2.097 m Four Significant Figures

- 0.12 m TWO Sig. Fig. After Decimal

1.977 m = ???? m

How many significant figures are in the following summation ?

6.220

+ 1.0

+ 125

(a) 2

(b) 3

(c) 4

(d) 5

(e) 6

A “practical” Example

MEASUREMENT DATA

Mass Of Solid + Weighing paper….13.6801 g

Mass Of Weighing paper…………….0.12 g

What do you report weight solid to be?

Multiplication And Division

The WEAKEST Link DETERMINES

The STRENGTH Of The CHAIN

The Number Of SIGNIFICANT FIGURES

in the Final Product or Quotient is

determined by the ORIGINAL Number

that has the SMALLEST number of

SIGNIFICANT FIGURES

How Many Significant Figures in

6 ft x 6 ft = ?

6.0 ft x 6 ft = ?

6.0 ft x 6.0 ft = ?

6.00 ft x 6.0 ft = ?

6.000 ft x 6.0 ft = ?

6.0000 ft x 6.0 ft = ?

Examples

1. 2.8 m x 4.5039 m = 12.61092 m 2 = ???????

2. 6.85 m 2= 0.0611388789 m

112.04 m

= 0.0611 m = 6.11 x 10 –2 m

3. 2.5 m x 4 m = ? (a) 10.0 m2 (b) 1 m 2

(c) none of these

How many significant figures are there in the result of the following multiplication:

(2.54) ×××× (6.2) ×××× (12.000)= ???

(a) 2(b) 3(c) 4(d) 5

A “practical” Example

MEASUREMENT DATA

LENGTH 6.45 cm

WIDTH 2.50 cm

THICKNESS 3.1 cm

(6.45)(2.50)(3.1) = 49.9875 cm3

What do you report volume = ?

SAMPLE EXERCISE 1.11 page 28

Earth’s oceans contain about 1.36 × 109 km3

of water. Calculate the volume in liters.

Dimensional–Analysis method for

SOLVING PROBLEMS makes

use of conversion factors

Use UNITS

To Solve Problems !!!!!!

1. What do you want to know

2. What information are you given?

3. What conversion factors are available to take us

from what we are given to what we want?

In Dimensional Analysis In Dimensional Analysis

Ask 3 QuestionsAsk 3 Questions

An average adult has 5.2 Liters of Blood

How many quarts of Blood?

How many gallons of Blood?

ML

UNITS first, then numbers

mL ??? L

mL

???

??? ??? =×L

Convert pounds to milligrams

What do you want to know

Now put in numbers

mg ??? grams

mg

???

???

lbs

grams

???

??? lbs ??? =××

Convert Liters to pints

What do you want to know

Now put in numbers

pints ??? quarts

pints

???

???

liters

quarts

???

??? liters ??? =××

5.850 gal/hr to L/s

UNITS first, then numbers

??? sec

min

?

?

min

hr

?

?

qt

L

???

???

gal

qt

?

? ??? =××××

hr

gal

If the volume of an object is 5.0 ft3 what

is it in cubic meters?

Volume = 0.14158422 cubic meters

Is that the correct answer?

333

3

cm 100

m 1

inch 1

cm 54.2

1

12)0.5(

=

foot

inchesftvolume

Density

• Density relates the mass of an object to its

volume.

volume

weight =Density

If you have equal volumes of the following,

which will have the largest mass?

Au, density = 19.3 g/cm3

Pb, density = 11.3 g/cm3

Ag, density = 10.5 g/cm3

Cu, density = 8.92 g/cm3

Al, density = 2.70 g/cm3

How do

you know

If you have equal masses of the following,

which will occupy the largest volume?

Au, density = 19.3 g/cm3

Pb, density = 11.3 g/cm3

Ag, density = 10.5 g/cm3

Cu, density = 8.92 g/cm3

Al, density = 2.70 g/cm3

How

do

you

know

Densities (g/cc)

Air 0.001185

Balsa wood 0.16

Water 1.00

Table sugar 1.59

Aluminum 2.7

Iron 7.9

Gold 19.32

Two Practical Examples

Involving DENSITY

• Example 1: What is the material

• Example 2: Is the material Gold

MEASUREMENT DATA

Mass Of Solid + paper …….. 13.6801gm

Mass Of Weighing paper ….. 0.12 gm

LENGTH ………. 6.45 cm

WIDTH ………… 2.50 cm

THICKNESS …… 3.1 mm

DENSITY = WEIGHT

VOLUME

Weight = 13.6801 – 0.12 = ????

Volume = L x W x T = ????

V = 6.45 cm x 2.50 cm x 3.1 mm

V = 6.45 cm x 2.50 cm x ? cm

V = 6.45 cm x 2.50 cm x 0.31 cm

DENSITY = WEIGHT

VOLUME

Wt = 13.6801 – 0.12 = 13.5601 gm

V = 4.99875 cc

Density = 13.5601 gm / 4.99875 cc

Density = 2.71267817 g/ml

Density = ????

What is the solid ?

Weights of

Unknown

Material

1. 13.036 grams

2. 13.230 grams

3. 13.217 grams

4. 12.947 grams

5. 12.949 grams

6. 12.758 grams

7. 12.967 grams

8. 13.122 grams

Average Weight ?

13.02825 ?

Size of Unknown Material

LENGTH ………. 4 inches

WIDTH ………… ¾ inches

THICKNESS …… 1 mm

Is the material Gold?

Is the material Gold?

YES YES YES YES If the density is 19.3 grams / cc

NO If the density is not 19.3 grams/cc

DENSITY = WEIGHT

VOLUME

Weight = 13.028gm

Volume = L x W x T = ????

Length = 4 inches x 2.54 cm/in = 10.16cm

Width = ¾ inches x 2.54 cm/in = 1.905cm

Thickness = 1 mm x 1/10 cm/mm = 0.1 cm

DENSITY = WEIGHT

VOLUME

Weight = 13.028gm

Volume = L x W x T = ????

V = 4 inches x ¾ inch x 1 mm

V = 10.16 cm x 1.905 cm x 0.1 cm

V = 1.93548 mL

DENSITY = WEIGHT

VOLUME

Density = 13.028 gm / 1.93548 cc

Density = 6.7311467 g/mL

WELL

IS IT GOLD ???????

Thermometers

If you were given a thermometer in

which all the markings had been

removed, how would you calibrate it ?

Temperature Conversions

1. Kelvin (K) ↔ Celsius (°C)

Kelvin (K) = °C + 273.15

2. Celsius (°C) ↔ Fahrenheit (°F)

325

9 and )32(

9

5+

°=°−°=° CFFC

Carry out the indicated

temperature conversions

98.6°F = ? °C

98.6°F = ? K

37.0°C = ? °F

310 K = ? °C

oC = (°F –32) (5/9) = ?????

K = °C + 273.15 = ?????

°F = oC (9/5) + 32 = ????

°C = K – 273.15 = ????

What are you suppose to get out of What are you suppose to get out of

Chapter 1 ?Chapter 1 ?

In Text

1. Strategies in Chemistry - Page 29

2. Summary & Key Terms -Page 30