Chapter 1: Matter, Measurement, and Problem Solving

Introduction

This chapter introduces foundational concepts in general chemistry, including the nature of matter, the importance of measurement, and the rules for handling significant figures in calculations. Mastery of these topics is essential for accurate scientific work and problem solving in chemistry.

Significant Figures in Calculations

What Are Significant Figures?

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. They reflect the precision of a measured quantity.

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros are significant only if there is a decimal point.

Example: The number 0.00470 has three significant figures (4, 7, and the trailing 0).

Rules for Significant Figures in Calculations

When performing calculations with measured quantities, the result must reflect the precision of the input values. This ensures that we do not imply greater precision than the measurements allow.

Multiplication and Division Rule

• The result should have the same number of significant figures as the factor with the fewest significant figures.

Example:

• (2 significant figures)

• (2 significant figures)

Addition and Subtraction Rule

• The result should have the same number of decimal places as the quantity with the fewest decimal places.

Example:

• (2 decimal places)

• (2 decimal places)

Rounding Rules

• Round down if the leftmost digit to be dropped is 4 or less.

• Round up if the leftmost digit to be dropped is 5 or greater.

• Only round the final answer in multistep calculations; do not round intermediate results.

Example: Round 5.346125 to 3 significant figures: 5.35 (since the digit after the third sig fig is 6, round up).

Summary Table: Rules for Significant Figures in Calculations

Significant Figures in Multistep Calculations

• Carry extra digits through intermediate steps.

• Round only the final answer to the correct number of significant figures.

• Underline the least significant digit in intermediate results to keep track.

Example: (rounded to 2 significant figures).

Units of Measurement

SI Base Units

Scientists use the International System of Units (SI) for consistency in measurements. The main SI base units are:

Mass

• Mass is a measure of the amount of matter in an object.

• The SI unit of mass is the kilogram (kg).

• 1 kg = 2.205 lb (pounds).

• The gram (g) is a commonly used subunit: 1 g = 1/1000 kg.

Prefix Multipliers

SI units use prefix multipliers to represent quantities that are much larger or smaller than the base unit. These prefixes change the value of the unit by powers of ten.

Example: 1 kilometer (km) = 1,000 meters (m); 1 millimeter (mm) = 0.001 meters (m).

Temperature and Temperature Scales

Temperature: Definition and Importance

• Temperature measures the average kinetic energy of the particles in a substance.

• It determines the direction of heat transfer: heat flows from hot to cold objects.

Kelvin Scale (Absolute Scale)

• The Kelvin (K) is the SI unit for temperature.

• Absolute zero (0 K) is the lowest possible temperature, where molecular motion virtually stops.

• Absolute zero:

Temperature Conversions

• To convert between Celsius and Kelvin:

or

• To convert between Celsius and Fahrenheit:

or

Example: A child has a temperature of . What is this in Kelvin and Fahrenheit?

• Kelvin:

• Fahrenheit:

Practice Problems

• Calculate the following to the correct number of significant figures:

• Convert to and K.