Chapter 3 – Scientific Measurement 2H Notes.pdf · Prefix Symbol Scientific Notation Meaning...

Chapter 2

A logical approach to solving problems

by observing and collecting data,

formulating hypotheses, testing

hypotheses, and formulating theories

that are supported by data

There are 4 steps.

OHEC! (A way to remember this.)

Observation (use your senses)

Hypothesis (the educated guess)

Experiments (test the hypothesis)

Conclusion (a broad explanation)

A conclusion leads to:

Model: an explanation of how phenomena occur or how sata or events are related

Can be visual, verbal or mathematical

Theory – a broad generalization that explains a body of facts of phenomena

A scientific law is a concise statement to summarize results

Hypothesis - testable statement

Based on the observations that were made

TESTING HYPOTHESIS

Requires experimentation!

Controls – experimental conditions that remain constant

Variables – conditions that change

To learn more about matter, chemists study systems

System – a specific portion of matter in a given region of space that has been selected for study during an experiment or observation ◦ Ex: reaction in a test tube

◦ Ex: reaction in a beaker

Comparing one object to a standard

There are two types of measurements:

◦ Qualitative & Quantitative

In science we use the SI units

A measurement that is descriptive

and non-numerical in form

A measurement with definite form,

numbers and units

SI Measurement

AKA –

the Metric System!

Americans only use feet, inches, yards…

◦ Based on the king!

New king… new units!

◦ Yard: length of his arm

◦ Foot: size of his foot

◦ Pound: how many marbles he could pick up

with one fist

Metric System – based on powers of 10

Le Systeme International d’Unites The SI Units are a revised version of the metric system

There are 7 base units

All the rest are derived units

Length: meter (m)

Mass: kilogram (kg)

Temperature: kelvin (K)

Time: second (s)

Quantity: mole (mol)

Luminosity: candela (cd)

Current: ampere (A)

Prefix Symbol Scientific

Notation

Meaning

Mega- M 106 Million times

kilo- k 103 thousand times

hecto- h 102 Hundred times

deca- da 101 Ten times

BASE ~ ~ Base Unit

deci- d 10-1 1 / tenth

centi- c 10-2 1 / hundredth

milli- m 10-3 1 / thousandth

Prefix Symbol Scientific

Notation

Pnemonic Device

Mega- M 106 Most

kilo- k 103 Kittens

hecto- h 102 Hate

deca- da 101 Dogs

BASE ~ ~ Because

deci- d 10-1 Dogs

centi- c 10-2 Can’t

milli- m 10-3 Meow !

Tera (T) = 1x1012

Giga (G) = 1x109

Hecto (h) = 1x102

Micro (µ) = 1 x 10-6 Nano (n) = 1 x 10-9

Pico (p) = 1 x 10-12

Femto (f) = 1x10-15

Derived Units – combinations of

SI base units

◦area, volume, density, molar mass,

molar volume, & energy

Volume – amount of space occupied by an object V = L x W x H

V measured in m3, cm3, mL, L

1 cm3 = 1 mL

1000 mL = 1 L

Density – ratio of an objects

mass to its volume

)3

volume(cm

(g) mass D

Substance Density (g/cm3) Substance Density (g/cm3)

Cork 0.24 Gasoline 0.67

Ice 0.92 Ethanol 0.79

Bone 1.85 Water 1.00

Lead 11.35 Mercury 13.6

A sample of aluminum metal has a

mass of 8.4 g. The volume of the

sample is 3.1 cm3. Calculate the

density of aluminum.

Given: mass (m) = 8.4 g

volume (v) = 3.1 cm3

Unknown: density (D) = ?

Equation:

Solve: D = 8.4 g = 2.7 g/cm3

3.1 cm3

v

m D

Dimensional analysis is a way

to analyze and solve problems

using the units, or dimensions

of the measurements.

Conversion factors: ratios of

equivalent measurements used

in dimensional analysis

What does $1 = ?

4 quarters = 10 dimes = 20 nickels = 100 pennies…

Conversion Factor – a ratio of equivalent

measurements (can be written as a dimension)

1 ft = 12 in or 12 in = 1 ft

1 ft 12 in

12 in 1 ft

Three steps to problem

solving:

1. Analyze

2. Calculate

3. Evaluate

Read problem carefully

Read the problem several times if

necessary

Find out what the problem is asking

Write down important information

such as units!

Make all your calculations:

May involve conversions,

substitutions etc…

Check your answer- ◦Does your answer make sense? Is it reasonable?

◦Is it in the correct units? ◦Is it in the correct number of significant figures

How many days are there in 6 weeks?

You are looking

for this!

This is your “given”.

Figure out what relationships you

will have to know in order to

convert from 1 unit to another.

1 week = 7 days

Start with given and work toward what you are looking for.

6weeks = ? days

Conversion Factor : top and bottom must be

equal in value

days week 1

days 7x weeks 6

6 weeks x = 42 days 1 week

7 days

Cancel units : cancel

units to leave correct

units for the answer

Calculate : multiply

across top and bottom

and divide to get final

answer

Uncertainty in Measurement

A digit that must be estimated is called

uncertain.

A measurement always has some

degree of uncertainty.

Why Is there Uncertainty?

• Measurements are performed with instruments

• No instrument can read to an infinite number

of decimal places

Precision and Accuracy

Accuracy refers to the agreement of a particular value with the true value.

Precision refers to the degree of agreement among several measurements made in the same manner.

Neither

accurate nor

precise

Precise but

not accurate

Precise

AND

accurate

Precision and Accuracy

Accepted/actual value – the correct value based on reliable references

Experimental value – the value measured in the lab

Error – difference between actual and experimental values

100

value Accepted

valueal Experiment-value Accepted Error %

numbers that include all the

digits that can be known

accurately plus a last digit

that must be estimated

◦digits that have meaning

Definition:

Rules for Sig Figs

Nonzero integers always count as

significant figures.

3456 has 4 sig figs.

Rules for Sig Figs

Zeros

Leading zeros do not count as

significant figures.

0.0486 has

3 sig figs.

Rules for Sig Figs

Zeros

Captive zeros always count as

significant figures.

16.07 has

4 sig figs.

Rules for Sig Figs

Zeros

Trailing zeros are significant only

if the number contains a decimal

point.

9.300 has 4 sig figs.

Rules for Sig Figs

Exact numbers have an

infinite number of significant

figures.

1 inch = 2.54 cm, exactly

Sig Fig Practice #1

How many significant figures in each of the following?

1.0070 m 5 sig figs

17.10 kg 4 sig figs

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 2 sig figs

Mathematical Operations

Multiplication and Division: # sig figs in the result equals the number

in the least precise measurement used in

the calculation.

6.38 x 2.0 =

12.76 13 (2 sig figs)

Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g 2.87 mL 2.9561 g/mL 2.96 g/mL

Mathematical Operations

Addition and Subtraction: The number of

decimal places in the result equals the

number of decimal places in the least

precise measurement.

6.8 + 11.934 =

18.734 18.7 (3 sig figs)

Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

What is the difference between a directly proportional

relationship and an inversely proportional

relationship?

Directly proportional = when two quantities are divided by one another and gives a constant value

y x or “y is proportional to x”

k

x

y

When x increases,

y increases and vice

versa!

D.D. = direct (relationship?), then

divide!

Inversely proportional – when two quantities products give a constant

“y is proportional to 1 divided by x”

or

x

1 y kxy

When x increases,

y decreases and

vise versa!