Matter, Measurement, and Significant Figures: Foundations of General Chemistry

Matter, Measurement, and Problem Solving

Introduction to Matter

Matter is defined as anything that occupies space and has mass. Understanding the properties and classification of matter is fundamental to the study of chemistry.

• Substance: A specific instance of matter, such as air or water.

• Composition of Matter: Refers to the basic components that make up matter, including elements and compounds.

• Element: A pure substance consisting of only one type of atom (e.g., Helium, He).

• Compound: A substance composed of two or more elements chemically combined (e.g., H2O).

• Mixtures: Can be heterogeneous (e.g., wet sand) or homogeneous (e.g., salt water).

States of Matter

Matter exists in three primary states, each with distinct physical properties:

• Solid: Definite shape and volume; particles are closely packed in a fixed arrangement. Can be crystalline (ordered) or amorphous (disordered).

• Liquid: Definite volume but indefinite shape; particles are close but can move past one another.

• Gas: Indefinite shape and volume; particles are far apart and move freely.

Physical and Chemical Properties and Changes

Properties and changes of matter are classified as physical or chemical:

• Physical Property: Observed without changing the substance's composition (e.g., boiling point, density).

• Chemical Property: Observed only by changing the substance's composition (e.g., flammability).

• Physical Change: Alters only the state or appearance (e.g., melting ice).

• Chemical Change: Alters the composition of matter (e.g., rusting of iron).

Accuracy and Precision

Measurement quality is described by accuracy and precision:

• Accuracy: Closeness of a measured value to the true value.

• Precision: Closeness of a set of measurements to each other.

Measurement and Units

SI Base Units

The International System of Units (SI) is used for scientific measurements. The most common SI base units are:

Quantity	Unit	Symbol
Length	Meter	m
Mass	Kilogram	kg
Time	Second	s
Temperature	Kelvin	K
Amount of Substance	Mole	mol

• Meter (m): Standard unit of length.

• Kilogram (kg): Standard unit of mass; 1 kg = 2.205 lb.

• Second (s): Standard unit of time.

• Kelvin (K): Standard unit of temperature; measures average kinetic energy.

• Mole (mol): Standard unit for amount of substance.

Prefix Multipliers

Prefix multipliers are used to express very large or small quantities:

• 1 kilometer (km) = $10^3$ meters (m)

• 1 millimeter (mm) = $10^{-3}$ meters (m)

• 1 micrometer (μm) = $10^{-6}$ meters (m)

Derived Units: Volume and Density

Volume is a derived unit, calculated as length cubed. The SI unit is cubic meter ($m^3$), but liters (L) and milliliters (mL) are commonly used in the laboratory.

• 1 L = $10^{-3}$ $m^3$

• 1 mL = $1$ cm3 (or 1 cc)

Intensive and Extensive Properties

• Intensive Property: Independent of the amount of substance (e.g., density, temperature).

• Extensive Property: Dependent on the amount of substance (e.g., mass, volume).

Unit Conversions

Unit conversions are essential for expressing measurements in different units. Conversion factors are based on defined relationships (e.g., 1 m = 100 cm).

• To convert density from $g/cm^3$ to $kg/m^3$, multiply by $10^3$.

Significant Figures

Definition and Importance

Significant figures (sig figs) are the digits in a measurement that reflect the precision of the value. They include all certain digits plus one uncertain digit. The number of significant figures depends on the measurement method and instrument precision.

• Precision: Indicates how close repeated measurements are to each other.

Rules for Determining Significant Figures

1. All nonzero digits are significant. Example: 225.8 has four significant figures.

2. All zeros between nonzero digits are significant. Example: 2007 has four significant figures.

3. Leading zeros (to the left of the first nonzero digit) are not significant. Example: 0.0085 has two significant figures.

4. Trailing zeros in a whole number with a decimal point are significant. Example: 320. has three significant figures; 320 has two.

5. Trailing zeros to the right of the decimal point are significant. Example: 12.000 has five significant figures.

6. Exact numbers (defined values or counts) have infinite significant figures. Example: 1 meter = 100 cm (both are exact).

7. For numbers in scientific notation, only the coefficient (argument) is considered for significant figures. Example: $4.5 \times 10^3$ has two significant figures; $4.50 \times 10^3$ has three.

Applying Significant Figures in Calculations

• Addition and Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places. Example: $101.70 + 0.252 = 101.952$ (rounded to 101.95, two decimal places).

• Multiplication and Division: The result should have the same number of significant figures as the measurement with the fewest significant figures. Example: $1.4 \times 8.011 = 11.2154$ (rounded to 11, two significant figures).

• Exact Numbers: Do not limit the number of significant figures in a calculation.

• Multi-step Calculations: Retain extra digits in intermediate steps and round only the final answer.

Rounding Rules

• If the digit to be dropped is less than 5, round down.

• If the digit to be dropped is 5 or greater, round up.

Examples of Significant Figures in Calculations

• Addition: $16.2 \text{ cm} + 9.203 \text{ cm} = 25.403 \text{ cm}$ (rounded to 25.4 cm, one decimal place).

• Multiplication: $2.171 \text{ cm} \times 4.20 \text{ cm} = 9.1152 \text{ cm}^2$ (rounded to 9.12 cm2, three significant figures).

• Multi-step: $(80.219 - 79.939) \div 0.289 = 0.280 \div 0.289 = 0.969$ (rounded appropriately based on significant figures).

Exact Numbers

• Defined quantities (e.g., 1 kg = 1000 g), counts (e.g., number of atoms), and integers in formulas are considered exact and have infinite significant figures.

Scientific Notation

Purpose and Format

Scientific notation expresses very large or small numbers in the form $A \times 10^n$, where A is the coefficient and n is the exponent.

• Only the coefficient is used to determine significant figures.

• Example: $4.5 \times 10^3$ (two significant figures); $4.50 \times 10^3$ (three significant figures).

Operations with Scientific Notation

• When adding or subtracting, exponents must be the same before combining coefficients.

• When multiplying or dividing, multiply/divide the coefficients and add/subtract the exponents.

Summary Table: Significant Figures Rules

Rule	Example	Sig Figs
All nonzero digits	225.8	4
Zeros between nonzeros	2007	4
Leading zeros	0.0085	2
Trailing zeros (decimal)	320.	3
Trailing zeros (no decimal)	320	2
Trailing zeros (right of decimal)	12.000	5
Exact numbers	1 m = 100 cm	Infinite
Scientific notation	4.50 × 103	3

Additional info:

• Order of operations in calculations follows PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

• When converting units, always use the correct conversion factor and track significant figures throughout the calculation.