Nivaldo J. Tro

http://www.cengage.com/chemistry/tro

Mark Erickson • Hartwick College

Chapter 2The Chemist’s Toolbox

Curious?• Why should non-science

majors study science?

• If you cannot think of a question you want answered, try to think of one for which a group of people might pay for an answer.

Measurement• Measurements allow us to distinguish between small

differences existing within larger classifications, differences which might otherwise go unnoticed.

Uncertainty• Scientists report measured quantities in a way

that reflects the uncertainty associated with the measuring device used.

Concept Check 2.1• A fisherman describes his latest catch as a 61.5 cm

rainbow trout with a mass of 2.35 kg. What is the uncertainty of each measurement?

Concept Check 2.1 Solution• The uncertainty in the length is ±0.1 cm because the

last digit measured is in the first decimal place.

• The uncertainty of the mass measurement is ±0.01 kg because the last digit measured is in the second decimal place.

Scientific Notation• Scientific notation offers a

solution for writing very large and very small numbers.

• Numbers written in scientific notation have two parts:

– The decimal part

– The exponential part

• Make sure you know how to use your own calculator to enter and manipulate numbers in scientific notation.

Concept Check 2.2• Express the following numbers in scientific notation:

a) 0.000232

b) 4531

Concept Check 2.2 Solution• The following numbers are expressed in scientific

notation:

a) 2.32 × 10-4

b) 4.531 × 103

0.000232

1 2 3 4

The decimal point is moved four places tothe immediate right of the first non-zero number.

4531.

3 2 1

The decimal point is moved three places tothe left, immediately before the last non-zero number.

Units• Units are fixed, agreed-upon quantities to which

other quantities are compared.

• A number in association with a unit is a representation of a measurement.

International System of Units (SI units)

• To minimize confusion, scientists around the world agree to use this SI units.

• Based on the metric system

• Each is a combination of:

– A base unit

– A prefix multiplier

Basic SI Units

• Length – meter (m)

• Mass – kilogram (kg)

• Time – second (s)

Basic SI Units• Length: meter (m)

– Defined (1983) as the distance that light travels in 1/2999,792,445 seconds

– Human height: 2 m

– Dust particle: 0.0001 m

– 1 meter = 39.4 inches

Basic SI Units

• Mass: kilogram (kg)

– The quantity of matter

– Standard is a block of platinum and iridium kept at the International Bureau of Weights and Measures at Sevres, France.

– Weight and Mass are different

• Mass: quantity of matter

• Weight: a measure of force exerted by the gravitational pull on an object.

Basic SI Units MKS

• Time – second (s)– Originally defined as

1/60 of a minute– Atomic Standard uses a

cesium clock

Prefix Multipliers

Derived SI Units

• A simple example is volume.

• It is the result of a mathematical operation

• Length × Width × Height

Unit Conversions• Some unit conversions are

intuitive:

– 60 minutes in 1 hour

– 12 eggs in a dozen

• The algebraic expression of unit conversions requires one or more conversion factors.

• Conversion factors can be constructed from any two quantities known to be equal.

•(quantity given) × (conversion factor(s)) = (quantity sought)

Concept Check 2.3• Convert 85.0 kg to pounds.

Concept Check 2.3 Solution• Converting 85.0 kg to pounds (lbs) requires unit

conversion factors for mass.

• Using Table 2-3, we find the unit conversion factors that are necessary to solve the problem. The unit converted from is in the denominator and the unit converted to is in the numerator.

85.0 kg 2.20 lbs

1 kg = 187 lbs

Concept Check 2.4• Convert the length 5.00 m to yards.

Concept Check 2.4 Solution• Converting 5.00 m to yards involves two steps. Starting with

conversion factors provided on Table 2-3, we begin with converting meters to inches, then from inches to yards.

5.00 m 39.37 in

1 m If we stop here, the answer will be in inches.

By adding the conversion factor from inches to yards at the end of

the first step, we get:

5.00 m 39.37 in

1 m

1 yds

12 in = 16.4 yds

Reading Graphs• Graphs allow for the visualization of trends in numerical data.

Concept Check 2.5• Using data from the previous graph, calculate the

average increase in carbon dioxide concentration per year from 1995 to 2005.

Concept Check 2.5 Solution• The data from the previous graph shows that the

CO2 concentration in 1995 was 360 ppm and steadily increased to 380 ppm in 2005, an increase of 20 ppm over 10 years. Dividing the increase of CO2 concentration by the 10 year time period gives the average increase of CO2 concentration per year.

380 ppm - 360 ppm

10 years = 2.0 ppm/year

Reading Graphs• The representation of graphical data can influence

the information extracted from that data.

Reading Graphs

Concept Check 2.6• Using data from the previous graph, what is the total

decrease in sulfur dioxide from 1990 to 2006 and the total percentage decrease from initial levels?

Concept Check 2.6 Solution• Change in SO2 Concentrations:

1990 8.0 ppb

2006 3.6 ppb

8.0 ppb – 3.6 ppb = 4.4 ppb decrease in SO2 concentration

• Decrease in SO2 Concentration From 1990 to 2006

• From 1990 to 2006, the SO2 concentration decreased 4.4 ppb which translates to a 55% decrease from initial levels.

Solving Basic Introductory Chemistry Problems

• Write out all quantities given with their associated units.

• Write the quantity that is sought, including its units.

• Write the relevant conversion factor(s).

• Multiply the given quantity by the appropriate conversion factor(s) such that desired units are the algebraic result.

• Round numerical value to the appropriate number of significant figures.

Density• Which has greater mass, a ton of

bricks or a ton of feathers?

• A measure of how much mass is in a given amount of volume

• A measure of how closely packed the molecules are in a specific amount of space.

• More molecules provide greater mass

• The ratio of mass to volume, m/V

The Density of Common Substances

Density as a Conversion Factor• Density (d): A measure of

how much mass is in a given amount of volume.

• Volume (V): A measure of space that is occupied.

• Mass (m): A measure of the quantity of matter present.

d =

m

V

Concept Check 2.7• What is the mass of a 125 mL-sample of a liquid with

a density of 0.655 g/mL?

Concept Check 2.7 Solution• Density is expressed using the equation: d = m/v.

Rearranging the equation to solve for mass gives us:

m = d × v.

0.655

g

mL 125 mL = 81.9 g

Chapter SummaryMolecular Concept

• Measurement tools

• The standard SI units

• Understanding graphs

• Conversions and conversion factors

Societal Impact

• Neither science nor technology could advance very far without measurements.

• Decisions about units of measurement are societal.

• Be cautious when reading data (scientific or informal). Carefully evaluate units in data tables and on graphs.