CHEM 100 Exam I: Essential Concepts and Calculations

Accuracy and Precision

Definitions and Differences

Understanding the distinction between accuracy and precision is fundamental in scientific measurement.

• Accuracy: How close a measured value is to the true or accepted value.

• Precision: How close repeated measurements are to each other, regardless of their closeness to the true value.

• Example: If you weigh a sample three times and get 2.01 g, 2.00 g, and 2.02 g, your measurements are precise. If the true mass is 2.00 g, they are also accurate.

Significant Figures

Identifying and Using Significant Figures

Significant figures (sig figs) indicate the precision of a measured or calculated quantity.

• Rules for Identifying Significant Figures:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros after a decimal point are significant.

• Example: 0.00450 has three significant figures (4, 5, and the trailing 0).

Rounding to Significant Figures

• Round up if the digit after the last significant figure is 5 or greater; round down if it is less than 5.

• Example: 3.476 rounded to three significant figures is 3.48.

Scientific Notation

• Express numbers as a product of a number between 1 and 10 and a power of 10.

• Example: 0.00032 = $3.2 \times 10^{-4}$

Significant Figures in Calculations

• Addition/Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

• Multiplication/Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

• Example: $2.34 \times 1.2 = 2.8$ (rounded to two significant figures)

The Metric System and Unit Conversions

Metric Units

• Length: meter (m)

• Mass: gram (g)

• Volume: liter (L)

• Temperature: Celsius (°C), Kelvin (K)

Metric Prefixes

• Kilo- (k): $10^3$

• Centi- (c): $10^{-2}$

• Milli- (m): $10^{-3}$

• Micro- (\mu): $10^{-6}$

Unit Conversions

• Use conversion factors to change from one unit to another.

• Example: To convert 250 mL to L: $250 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.250 \text{ L}$

Matter and Its Changes

Physical and Chemical Changes

• Physical Change: Alters the form or appearance but not the composition (e.g., melting ice).

• Chemical Change: Produces new substances with different properties (e.g., burning wood).

Mixtures and Pure Substances

• Pure Substance: Matter with a fixed composition (elements and compounds).

• Mixture: Combination of two or more substances not chemically combined.

Homogeneous and Heterogeneous Mixtures

• Homogeneous Mixture: Uniform composition throughout (e.g., saltwater).

• Heterogeneous Mixture: Non-uniform composition (e.g., salad).

States of Matter

Properties of Solids, Liquids, and Gases

• Solids: Definite shape and volume; particles are closely packed.

• Liquids: Definite volume, indefinite shape; particles can move past each other.

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

Behavior of Gases

Gas Laws and Calculations

• Boyle's Law: $P_1V_1 = P_2V_2$ (at constant T and n)

• Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (at constant P and n)

• Ideal Gas Law: $PV = nRT$

• Example: Calculate the volume of 1.00 mol of gas at STP (Standard Temperature and Pressure): $V = \frac{nRT}{P}$

Intermolecular Forces

Types and Effects

• Intermolecular Forces (IMFs): Forces between molecules that affect physical properties.

• Types:

  • London Dispersion Forces (all molecules)

  • Dipole-Dipole Interactions (polar molecules)

  • Hydrogen Bonding (molecules with H bonded to N, O, or F)

• Effect: Stronger IMFs lead to higher boiling and melting points.

Temperature Conversions

Celsius and Kelvin

• To convert Celsius to Kelvin: $K = ^\circ C + 273.15$

• Example: 25°C = $25 + 273.15 = 298.15$ K

Exothermic and Endothermic Processes

Definitions and Examples

• Exothermic: Releases heat to surroundings (e.g., combustion).

• Endothermic: Absorbs heat from surroundings (e.g., melting ice).

Density Calculations

Formula and Applications

• Density (d): $d = \frac{m}{V}$, where m = mass, V = volume.

• Example: If a block has a mass of 10.0 g and a volume of 2.0 mL, $d = \frac{10.0 \text{ g}}{2.0 \text{ mL}} = 5.0 \text{ g/mL}$

Summary Table: States of Matter

State	Shape	Volume	Particle Arrangement
Solid	Definite	Definite	Closely packed, fixed positions
Liquid	Indefinite	Definite	Close, but can move past each other
Gas	Indefinite	Indefinite	Far apart, move freely