Nivaldo J. Tro Mark Erickson Hartwick College Chapter 2 The 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) b)4531

Concept Check 2.2 Solution The following numbers are expressed in scientific notation: a)2.32 × b)4.531 × 10 3

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: 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.

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.

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 CO 2 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 CO 2 concentration by the 10 year time period gives the average increase of CO 2 concentration per 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 SO 2 Concentrations: ppb ppb 8.0 ppb – 3.6 ppb = 4.4 ppb decrease in SO 2 concentration Decrease in SO 2 Concentration From 1990 to 2006 From 1990 to 2006, the SO 2 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.

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

Chapter Summary Molecular 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.