General Chemistry: Exam 3 Study Guide – Gases and Thermochemistry

Gases and Gas Laws

Pressure Units and Measurement

Pressure is a fundamental property of gases, defined as force per unit area. It is measured in several units, and understanding these is essential for solving gas law problems.

• Pressure (P): The force exerted by gas particles colliding with the walls of their container.

• Common units:

  • Atmosphere (atm)

  • Millimeters of mercury (mmHg) or torr

  • Pascals (Pa)

  • Bar

• Conversions: 1 atm = 760 mmHg = 101,325 Pa = 1.01325 bar

Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and amount of gas.

• Boyle’s Law (Pressure-Volume Relationship): At constant temperature, the volume of a gas is inversely proportional to its pressure.

$P_1V_1 = P_2V_2$

• Charles’s Law (Temperature-Volume Relationship): At constant pressure, the volume of a gas is directly proportional to its absolute temperature.

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Avogadro’s Law (Amount-Volume Relationship): At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles.

$\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Combined Gas Law: Combines Boyle’s, Charles’s, and Gay-Lussac’s laws.

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

• Ideal Gas Law: Relates all four variables (P, V, n, T) for an ideal gas.

$PV = nRT$

• R (Ideal Gas Constant): $0.0821\ \mathrm{L\cdot atm\cdot mol^{-1}\cdot K^{-1}}$

Dalton’s Law of Partial Pressures and Mole Fractions

Dalton’s Law states that the total pressure of a mixture of gases equals the sum of the partial pressures of each component gas.

• Partial Pressure: The pressure exerted by a single gas in a mixture.

$P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Mole Fraction (X): The ratio of moles of a component to the total moles in the mixture.

$X_i = \frac{n_i}{n_{\text{total}}}$

$P_i = X_i \times P_{\text{total}}$

Kinetic Molecular Theory and Gas Behavior

The kinetic molecular theory explains the behavior of gases based on the motion of their particles.

• Gases consist of tiny particles in constant, random motion.

• Collisions between particles and with container walls are elastic (no energy lost).

• The average kinetic energy of gas particles is proportional to the absolute temperature.

Density and Molar Mass of Gases

The density and molar mass of a gas can be determined using the ideal gas law.

• Density (d): $d = \frac{PM}{RT}$, where M is molar mass.

• Molar Mass (M): $M = \frac{dRT}{P}$

Molecular Speed and Molar Mass

The speed of gas molecules is inversely related to their molar mass.

• Root Mean Square Speed ($u_{rms}$):

$u_{rms} = \sqrt{\frac{3RT}{M}}$

• Lighter molecules move faster at a given temperature.

Redox Reactions

Oxidation and Reduction

Redox (reduction-oxidation) reactions involve the transfer of electrons between species.

• Oxidation: Loss of electrons (increase in oxidation state).

• Reduction: Gain of electrons (decrease in oxidation state).

• Oxidizing Agent (Oxidant): Species that is reduced (causes oxidation).

• Reducing Agent (Reductant): Species that is oxidized (causes reduction).

Example: In the reaction $Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu$, Zn is oxidized and Cu2+ is reduced.

Oxidation Numbers

Oxidation numbers (states) are assigned to atoms to track electron transfer in reactions.

• Rules for assigning oxidation numbers include:

  • Elemental form: 0

  • Monatomic ion: charge of the ion

  • Oxygen: usually -2

  • Hydrogen: +1 (with nonmetals), -1 (with metals)

  • Fluorine: always -1

  • Sum of oxidation numbers equals the charge of the molecule or ion

Activity Series and Predicting Redox Reactions

The activity series ranks elements by their tendency to be oxidized. A more active metal will reduce the ion of a less active metal.

• Use the activity series to predict if a redox reaction will occur.

Thermochemistry

Energy, Heat, and Work

Thermochemistry studies energy changes in chemical reactions, focusing on heat and work.

• Energy (E): The capacity to do work or produce heat.

• Kinetic Energy: Energy of motion.

• Potential Energy: Stored energy due to position or composition.

• Heat (q): Energy transferred due to temperature difference.

• Work (w): Energy transferred when an object is moved by a force.

$\Delta E = q + w$

Units of Energy

• Joule (J): $1\ \mathrm{J} = 1\ \mathrm{kg\cdot m^2/s^2}$

• Calorie (cal): $1\ \mathrm{cal} = 4.184\ \mathrm{J}$

Sign Conventions for Heat and Work

• q > 0: Heat absorbed by the system (endothermic)

• q < 0: Heat released by the system (exothermic)

• w > 0: Work done on the system

• w < 0: Work done by the system

Thermochemical Equations and Energy Transfer

Thermochemical equations show the enthalpy change ($\Delta H$) for a reaction.

• Use stoichiometry to relate energy change to the amount of reactant or product.

Exothermic and Endothermic Processes

• Exothermic: Releases heat ($\Delta H < 0$)

• Endothermic: Absorbs heat ($\Delta H > 0$)

Signs for $q$, $\Delta H$, or $\Delta T$ indicate the direction of energy transfer.

Calorimetry

Calorimetry measures heat changes in chemical reactions. In constant pressure calorimetry ("coffee-cup" calorimetry):

• $q_{\text{rxn}} = -q_{\text{solution}}$

• $q_{\text{solution}} = mc\Delta T$

• m = mass of solution, c = specific heat, $\Delta T$ = temperature change

Hess’s Law

Hess’s Law states that the enthalpy change for a reaction is the same, regardless of the pathway taken, and can be calculated by adding the enthalpy changes of individual steps.

• Apply Hess’s Law to determine $\Delta H^\circ$ for a reaction using related thermochemical equations.

Lab Techniques and Mathematical Operations

Significant Figures

All answers must be reported with the correct number of significant figures, reflecting the precision of the measurements.

Unit Conversions

Be familiar with temperature conversions (e.g., Celsius to Kelvin), metric prefixes (e.g., kg to g), and other basic conversions.

• Temperature: $T_{\text{K}} = T_{\text{C}} + 273.15$

• Metric Prefixes: 1 kg = 1000 g, 1 mg = 0.001 g, etc.

Glossary of Key Terms

Term	Definition
Limiting Reactant	The reactant that is completely consumed first, limiting the amount of product formed.
Percent Yield	The ratio of actual yield to theoretical yield, expressed as a percentage.
Solution	A homogeneous mixture of two or more substances.
Solvent	The substance present in the greatest amount in a solution.
Solute	The substance dissolved in the solvent.
Electrolyte	A substance that conducts electricity when dissolved in water.

Additional info: This guide expands on the study guide outline by providing definitions, equations, and examples for each topic, ensuring a comprehensive review for Exam 3 in General Chemistry.