Chapter 1

Matter,

Measurement, and Problem Solving

Chemistry is about changes.

Chemistry is the science that seeks to understand the

composition and properties of matter by studying the

behavior of atoms and molecules.

atoms

•are submicroscopic particles •are the fundamental building blocks of all matter

molecules •two or more atoms attached together in a specific geometric arrangement

oattachments are called bonds oattachments come in different strengths

•come in different shapes and patterns

I. Scientific Method

It is a cyclical process in which we gather and assemble

information about nature, formulate explanations for what

we’ve observed and then test the explanation with new

experiments.

1) Making observations

Qualitative observation: does not involve a number.

Quantitative observation: involves a number and a unit.

2) Formulating hypotheses

A hypothesis is a possible explanation for the observation.

3) Performing experiments.

An experiment is carried out to test the validity of the

hypothesis.

4) Theory

A theory or model is a set of tested hypotheses that gives an

overall explanation of some natural phenomenon.

5) A natural law

A law is a verbal or mathematical description of a

phenomenon that allows for general predictions.

II. The Classification of Matter

Matter is anything that has mass and occupies space.

1) Classifying matter according to its state

We can classify matter based on whether it’s solid, liquid,

or gas.

2) Classification of matter according to its composition

A pure substance is composed of only a single type of

atom or molecules.

•Because the composition of a pure substance is always the

same, all samples have the same characteristics.

•An element is a substance that cannot be chemically

broken down into simpler substances (example He).

•A compound is a substance composed of 2 or more

elements in fixed and definite proportions (example water).

A mixture is a substance composed of 2 or more different

type of atoms or molecules that can be combined in

continuously variable proportions.

•Mixtures can be divided into 2 types – heterogeneous or

homogenous – depending on how uniformly the substances

within them mix.

•Because composition varies, different samples have

different characteristics.

III. Physical and Chemical changes and properties

Physical changes are changes that alter only state or

appearance, but not composition.

Chemical changes are changes that alter the composition

of matter are called.

A physical property is one that substances display

without changing its composition (odor, taste, color,

appearance, melting point, boiling point and density).

A chemical property is one that a substance displays only

by changing its composition via chemical changes

(corrosiveness, flammability, acidity, toxicity etc).

IV. Units of Measurement

1) Units

The unit indicates the standard against which the measured

quantity is being compared.

2) SI units

In 1960 a simplification of the metric system was adopted

by the General Conference of Weights and Measures. It is

called the international System of Units (SI).

Physical Quantity Name of Unit Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature kelvin K

Electric current ampere A

Amount of substance mole mol

3) Other SI units are built from the base units

The SI units for any physical quantity can be built from these seven base

units. Example: The area of a rectangular room can be determined by

multiplying its length by its width. Length Length = area

(meter) (meter) = (meter)2

m m = m2

N.B. : Volume is not a fundamental SI unit but it can be derived from length:

any length unit cubed • SI unit = cubic meter (m3) • commonly measure solid volume in cubic centimeters (cm3) • commonly measure liquid or gas volume in milliliters (mL)

1 m = 10 dm

1m3 = (10 dm)3 = 1000 dm3

1 dm3 = 1 L

1m3 = 1000 L

1 cm3 = 1 mL

1 mL = 20 drops!

Sometime the base unit is either to large or too small to be used.

Prefix Symbol Decimal

Equivalent Power of 10

mega- M 1,000,000 Base x 106

kilo- k 1,000 Base x 103

deci- d 0.1 Base x 10−1

centi- c 0.01 Base x 10−2

milli- m 0.001 Base x 10−3

micro- m or mc 0.000 001 Base x 10−6

nano- n 0.000 000 001 Base x 10−9

pico p 0.000 000 000 001 Base x 10−12

4) Temperature

There are 3 systems for

measuring temperature:

1) Fahrenheit

2) Celsius

3) Kelvin

K C C K

C F F C

+ 273.15 273.15

5 C 9 F 32 F + 32 F

9 F 5 C

T T T T

T T T T

5) Density

“What weighs more, a ton of bricks or a ton of cotton?”

Density is the ratio of mass to volume.

massDensity =

volume

Mass and volume are both extensive properties.

An extensive property is dependent on the quantity of matter

observed.

An intensive property is independent on the quantity of matter

observed.

6) Dimensional Analysis

For numerical problems, scientists usually use a system called a

dimensional analysis to help them to perform the correct arithmetic. A

numerical problem is treated as one involving conversion of units from one

kind to another. To do this, we use one or more conversion factors.

OldUnit

NewUnitNumber in original unit New number in new unit

Example: A golfer putted a golf ball 6.8 ft across a green. How many

inches does this represent?

To convert from one unit to another, use the equivalence statement that

relates the two units.

1 ft = 12 in

The two unit factors are:

1 ft 12 in and

12 in 1 ft

6.8 ft12 in

1 ft

in

6.8 ft12 in

1 ft

82 in

Example : An iron sample has a mass of 4.50 lb. What is the mass of this

sample in grams? (1 kg = 2.2046 lbs; 1 kg = 1000 g)

4.50 lbs1 kg

2.2046 lbs

1000 g

1 kg

3= 2.04 10 g

Example: the stainless steel in a solid cylindrical rod has a density of

7.75 g/cm3. If we want a 1.00 kg mass of this rod with a diameter of 1.0

in, how long the section must we cut off? (V cylinder = r2h)

33

12975.7

1

1

100000.1 cm

g

cm

Kg

gkg

d

mV

V

md

cmin

cm

r

Vh

incm

5.25)500.0(

1292

154.2

3

2

V. The uncertainty in the scientific

measurements

A measurement always has some degree of uncertainty.

A digit that must be estimated is called uncertain.

Record the certain digits and the first uncertain digit => sig.fig.

• The volume is read at the bottom of the

liquid curve (meniscus).

• Meniscus of the liquid occurs at about

20.15 mL.

Certain digits: 20.15

Uncertain digit: 20.15

All measurements are subject to errors!

Systematic Error (Determinate Error) - Occurs in the same direction

each time (high or low). Ex: Calibration problem.

Random Error (Indeterminate Error) - Measurement has an equal

probability of being high or low. Ex: Limitations in an experimenter’s

skill or ability.

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

Precision refers to the degree of agreement among several elements of the

same quantity.

Precision is often used as an indicator of accuracy: we assume that the

average of a series of precise measurement (average out random errors) is

accurate if the system errors are absent.

VI. Significant Figures

1) Determining the significant figures.

All nonzero digits are significant.

Ex: 2365 has 4 sig.fig.

Zeros:

1. Leading zeros: They precede all the nonzero digits. They do not count as

significant figure. Ex: 0.048 has 2 sig. fig.

2. Captive zeros: They are between non zero digits. They count as

significant figure. Ex: 16.07 has 4 sig.fig.

3. Trailing zeros: They are at the right end of the number. They are

significant only if the number contains a decimal place.

Example: 9.300 has 4 sig.fig. 150 has 2 sig.fig.

Exact numbers:

These numbers were not obtained by a measuring device. They can be

demined by counting (2 apples), or they have an infinite number of

significant figures (), or they are conversion factors (1 in = 2.54 cm), or

they are part of a formula (2r = circumference of a circle). These

numbers do not count as significant figures.

Exponential or scientific notation:

351 can also be written 3.51 102 and has 3 sig. fig.

350 can be written 3.5 102 and has 2 sig. fig.

350. can be written 3.50 102 and has 3 sig. fig.

2) Significant figures in mathematical operations:

1. For multiplication or division, the number of significant

figures in the result is the same as the number in the least

precise measurement used in the calculation.

1.342 × 5.5 = 7.381 7.4

2. For addition or subtraction, the result has the same number

of decimal places as the least precise measurement used in

the calculation.

Corrected

23.445

7.83

31.2831.275

When using scientific notation, first write each quantity with the

same exponent n (the highest n), then carry out the calculations.

(2.06 102) + (1.32 104) – (1.26 103)

= (0.0206 104) + (1.32 104) – (0.126 104) = 1.2146 104 =

1.21 104

Rules for rounding: In a series of calculation, carry the extra digits

through the final result then round it. If digit to be moved is 0, 1, 2,

3, 4*, the preceding digit stays the same. If digit to be moved is 5, 6,

7, 8, 9, the preceding digit is increased by one. *15.44 round to 15.4 and 15.45 round off to 15.5

3. Multistep Calculations

• Keep all the digits on your calculator through out the entire

calculation.

• For each step, determine the proper number of sig.fig. or

decimal places that the result would have had at that given

step.

• Keeping that in mind, determine the sig. fig. of the final

answer.