Chapter 2 The Chemist’s Toolbox Copyright ©2019 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Curious About Oranges Why should nonscience majors study science? Consider an orange tree that produces oranges with different levels of sweetness Why are oranges sweet? Page 27

Measurement Allows 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 Figure 2.2; page 30

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 Offers a solution for writing very large and very small numbers Numbers written in scientific notation have two parts Decimal part Exponential part A scientific calculator accepts numbers in scientific notation; page 32

Concept Check 2.2 Express the following numbers in scientific notation: 0.000232 4531

Concept Check 2.2 Solution The following numbers are expressed in scientific notation: 2.32 × 10−4 4.531 × 103

Units in Measurement Unit: Fixed, agreed-upon quantity by which other quantities are measured A number in association with a unit is a representation of a measurement

International System of Units (SI units) Used by scientists around the world to minimize confusion Based on the metric system Each is a combination of a basic unit and prefix multiplier

Important SI Standard Units Length: Meter (m) Mass: Kilogram (kg) Time: Second (s) Temperature: Kelvin (K)

Basic SI Units Length: Meter (m) Redefined in 1983 as the distance that light travels in 1/2999,792,458 seconds When length is expressed in meters, a human has a height of about 2 m, while the diameter of a dust particle is about 0.0001 m

Basic SI Units (continued 1) Mass: Kilogram (kg) Measure of the quantity of matter Standard SI unit is a block of platinum and iridium kept at the International Bureau of Weights and Measures at Sevres, France Figure 2.3; page 34

Basic SI Units (continued 2) Weight and mass are different Mass - Quantity of matter Weight - Measure of force exerted by the gravitational pull on an object

Basic SI Units (continued 3) Time - Second (s) Originally defined as 1/60 of a minute Second is defined by an atomic standard using a cesium clock Figure 2.4; page 34

Table 2.2: SI Prefix Multipliers Table 2.2; page 34

Derived SI Units Volume Composed of other units multiplied together Expressed in units such as cubic meters (m3) or cubic centimeters (cm3 ) Figure 2.5, page 34

Unit Conversions Some unit conversions are intuitive 60 minutes = 1 hour 12 inches = 1 foot Algebraic expression of unit conversions requires one or more conversion factors Conversion factors can be constructed from any two quantities known to be equal Formula (Quantity given) × (Conversion factor(s)) = (Quantity sought)

Table 2.3: Some Common Units and Their Equivalents Table 2.3; page 35

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. 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:

Reading Graphs Graphs allow for the visualization of trends in numerical data Figure 2.7; page 38

Concept Check 2.5 Using data from the previous graph, calculate the average increase in carbon dioxide concentration per year from 1996 to 2006.

Concept Check 2.5 Solution The data from the previous graph shows that the CO2 concentration in 1996 was 360 ppm and steadily increased to 380 ppm in 2006, 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.

Reading Graphs (continued 1) Representation of graphical data can influence the information extracted from that data Figure 2.6; page 38

Reading Graphs (continued 2) Sulfur dioxide concentration (ppb) (Source: US EPA: https://www.epa.gov/air-trends/sulfur-dioxide-trends); page 40

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 8.6 ppb 2006 3.3 ppb 8.6 ppb − 3.3 ppb = 5.3 ppb decrease in SO2 concentration From 1990 to 2006, the SO2 concentration decreased 5.3 ppb, which translates to a 62% decrease from initial levels.

Steps to Solve Basic Introductory Chemistry Problems Write all quantities given with their associated units under the heading "Given" Write the quantity that is sought, including its units under the heading "Find" Write all known conversion factors

Steps to Solve Basic Introductory Chemistry Problems (continued) Multiply the given quantity by the appropriate conversion factors and canceling units such that the desired units are the algebraic result Round off the answer so that the number of digits in the answer is approximately the same as the number of digits in the given quantities

Density A measure of how much mass is in a given amount of space Which weighs more, a ton of bricks or a ton of feathers? Both weigh the same, 1 ton The ratio of its mass to its volume is m/V Figure 2.8; page 42

Table 2.4: Density of Common Substances Table 2-4; page 43

Density as a Conversion Factor Density (d): Measure of how much mass is in a given amount of space Volume (V): Measure of the amount of space that is occupied Mass (m): 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 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

Chapter Summary Molecular concept Societal impact Measurement tools Neither science nor technology could advance very far without measurements The standard SI units Decisions about which units of measurement need to be used are societal Understanding graphs Be cautious when reading data (scientific or informal) Conversions and conversion factors Carefully evaluate units in data tables and on graphs