Chapter 1: Matter, Energy, and Measurement – Study Guide

Chapter 1: Matter, Energy, and Measurement

Significant Figures Rules

Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated. They are important for expressing the precision of measured values.

• Nonzero digits are always significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros in a number with a decimal point are significant.

Example: 0.00450 has three significant figures.

Multiplication and Division with Measured Numbers

When multiplying or dividing, the result should have the same number of significant figures as the measurement with the fewest significant figures.

• Example: $2.5 \times 3.42 = 8.6$ (rounded to two significant figures)

Addition and Subtraction with Measured Numbers

For addition and subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places.

• Example: $12.11 + 18.0 = 30.1$ (rounded to one decimal place)

Units of Measurement

Measurements in chemistry use the International System of Units (SI). Common units include:

• Length: meter (m)

• Mass: kilogram (kg)

• Time: second (s)

• Temperature: kelvin (K)

• Amount of substance: mole (mol)

Metric and SI Prefixes

Prefixes indicate multiples or fractions of units.

• Kilo- (k): $10^3$

• Centi- (c): $10^{-2}$

• Milli- (m): $10^{-3}$

• Micro- (\mu): $10^{-6}$

Measuring Length, Volume, Mass, and Temperature (Different Scales)

Measurements can be made using various instruments and scales:

• Length: rulers, calipers (meters, centimeters, millimeters)

• Volume: graduated cylinders, pipettes (liters, milliliters)

• Mass: balances (grams, kilograms)

• Temperature: thermometers (Celsius, Kelvin, Fahrenheit)

Problem Solving Using Conversion Factors

Conversion factors are ratios used to express the same quantity in different units. Dimensional analysis is a method for converting between units.

• Example: To convert 5.0 cm to meters: $5.0\ \text{cm} \times \frac{1\ \text{m}}{100\ \text{cm}} = 0.050\ \text{m}$

Dimensional Analysis (Unit Conversions)

Dimensional analysis ensures that units cancel appropriately, leaving the desired unit.

• Example: Converting 25.0 g to kg: $25.0\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 0.0250\ \text{kg}$

Intensive vs. Extensive Properties

Properties of matter can be classified as:

• Intensive properties: Do not depend on the amount of substance (e.g., density, boiling point).

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

Density

Density is the mass per unit volume of a substance.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units: g/cm3 or kg/m3

• Example: A block with mass 10 g and volume 2 cm3 has density $5\ \text{g/cm}^3$.

Energy, Work, and Calculating Energy Changes

Energy is the capacity to do work or transfer heat. Work is done when a force moves an object.

• Work formula: $w = F \times d$ (force times distance)

• Energy units: Joule (J), calorie (cal)

• 1 cal = 4.184 J

Classification of Matter

Matter can be classified as:

• Pure substances: Elements and compounds

• Mixtures: Homogeneous (solutions) and heterogeneous

Properties of Matter: Chemical vs. Physical

Physical properties can be observed without changing the substance’s identity (e.g., melting point, color). Chemical properties describe a substance’s ability to undergo chemical changes (e.g., flammability, reactivity).

Formulas for Laws

Some important laws and their formulas:

• Law of Conservation of Mass: Mass is neither created nor destroyed in a chemical reaction.

• Law of Definite Proportions: A compound always contains the same elements in the same proportion by mass.