General Chemistry: Gases and Thermochemistry Practice Exam Study Notes

Gases: Properties, Laws, and Calculations

Gas Laws Overview

The behavior of gases can be described using several fundamental laws that relate pressure, volume, temperature, and amount of gas. These laws are essential for solving problems involving gases under various conditions.

• Boyle's Law: At constant temperature, the pressure and volume of a gas are inversely proportional.

• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its absolute temperature.

• Gay-Lussac's Law: At constant volume, the pressure of a gas is directly proportional to its absolute temperature.

• Combined Gas Law: Combines Boyle's, Charles's, and Gay-Lussac's laws to relate pressure, volume, and temperature.

• Ideal Gas Law: Relates pressure, volume, temperature, and number of moles: $PV = nRT$

Example: If a 5.03 L sample of a gas exerts a pressure of 750 torr, what pressure will result in a volume of 4.20 L? (Assume temperature is constant; use Boyle's Law.)

Kinetic Molecular Theory

The kinetic molecular theory explains the behavior of gases at the molecular level. It assumes that gas particles are in constant, random motion and that collisions between particles are perfectly elastic.

• Key Assumptions:

  • Gas particles have negligible volume compared to the container.

  • No attractive or repulsive forces between particles.

  • Average kinetic energy is proportional to temperature in Kelvin.

Example: Explain Boyle's Law and Gay-Lussac's Law using kinetic molecular theory.

Gas Density and Molar Mass

The density of a gas at standard temperature and pressure (STP) can be calculated using the ideal gas law. The molar mass of a gas can be determined if its density, temperature, and pressure are known.

• Density Formula: $d = \frac{PM}{RT}$ where $d$ is density, $P$ is pressure, $M$ is molar mass, $R$ is the gas constant, and $T$ is temperature in Kelvin.

• Molar Mass from Density: $M = \frac{dRT}{P}$

Example: What is the density of dinitrogen monoxide at STP?

Gas Stoichiometry

Gas stoichiometry involves using balanced chemical equations to relate volumes of gases (at the same temperature and pressure) or to calculate the amount of product formed from a given volume of reactant gas.

• Example Reaction: $N_2 + 3H_2 \rightarrow 2NH_3$

• Use molar volume at STP (22.4 L/mol) for conversions.

Example: For the reaction above, if 10.0 L of nitrogen react, what volume of ammonia gas is produced?

Graham's Law of Effusion

Graham's Law compares the rates of effusion or diffusion of two gases. The rate is inversely proportional to the square root of the molar mass.

• Formula: $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$

Example: What is the relative rate of diffusion of nitrogen gas and argon?

Gas Law Applications

• Calculating new pressure, volume, or temperature when conditions change (using combined gas law).

• Determining moles of gas from volume, pressure, and temperature.

• Finding the molecular mass of a gas from density and STP conditions.

Example: How many moles of gas will occupy 20.0 L at 0.990 atm and 15.7°C?

Thermochemistry: Enthalpy and Calorimetry

Enthalpy Changes ($\Delta H$) and Calorimetry

Thermochemistry studies the heat changes that accompany chemical reactions. The enthalpy change ($\Delta H$) is the heat absorbed or released at constant pressure.

• Standard Enthalpy of Formation ($\Delta H_f^\circ$): The enthalpy change when one mole of a compound is formed from its elements in their standard states.

• Hess's Law: The total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.

• Bond Enthalpy: The energy required to break one mole of a bond in a gaseous molecule.

Example: Calculate $\Delta H$ for the reaction $2NOCl_2 \rightarrow 2NO + Cl_2$ using given enthalpy values.

Using Calorimetry to Measure $\Delta H$

Calorimetry involves measuring temperature changes to determine the heat exchanged in a reaction.

• Formula: $q = mc\Delta T$ where $q$ is heat, $m$ is mass, $c$ is specific heat, and $\Delta T$ is temperature change.

• For reactions in solution, use the heat capacity of water and the measured temperature change.

Example: If 50.0 mL of 0.100 M AgNO3 and 50.0 mL of 0.100 M HCl are mixed and the temperature rises, calculate $\Delta H$ per mole of AgCl formed.

Standard Enthalpies of Formation Table

The table below lists standard enthalpies of formation ($\Delta H_f^\circ$) for selected inorganic substances at 25°C. These values are used to calculate reaction enthalpies.

Substance	$\Delta H_f^\circ$ (kJ/mol)	Substance	$\Delta H_f^\circ$ (kJ/mol)
AgCl (s)	-127.0	MgO (s)	-601.6
CO2 (g)	-393.5	H2O (l)	-285.8
NO (g)	90.3	NO2 (g)	33.2
NH3 (g)	-45.9	NaCl (s)	-411.2
H2 (g)	0	O2 (g)	0
Cl2 (g)	0	MgCl2 (s)	-641.8

Bond Enthalpy Calculations

Bond enthalpy values can be used to estimate the enthalpy change of a reaction by comparing the total energy required to break bonds in reactants and the energy released when new bonds form in products.

Bond	Bond Energy (kJ/mol)
C-H	414
C=C	614
O-H	464
O=O	498
C=O	799

Formula: $\Delta H_{rxn} = \sum \text{Bond Energies Broken} - \sum \text{Bond Energies Formed}$

Sample Calculations and Applications

• Calculating $\Delta H$ for reactions using enthalpy of formation values.

• Estimating enthalpy changes using bond energies.

• Applying calorimetry data to determine heat of reaction.

Example: Estimate the enthalpy of combustion of propylene using bond energies.

Constants and Useful Values

• Gas constant, $R = 0.08206$ L·atm·mol-1·K-1

• Heat capacity of water, $c = 4.18$ J·g-1·°C-1