General Chemistry Study Notes: Gases, Gas Laws, and Stoichiometry

Gas Laws and Properties of Gases

Introduction to Gas Laws

The behavior of gases is described by several fundamental laws that relate pressure, volume, temperature, and amount of gas. These laws are essential for understanding how gases respond to changes in their environment and are widely used in chemical calculations.

• Boyle's Law: At constant temperature, the pressure of a gas is inversely proportional to its volume. $P_1V_1 = P_2V_2$

• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin). $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Avogadro's Law: 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 Avogadro's laws. $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

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

Key Terms:

• Pressure (P): Force exerted by gas particles per unit area.

• Volume (V): Space occupied by the gas.

• Temperature (T): Measure of the average kinetic energy of gas particles (in Kelvin).

• Moles (n): Amount of substance.

• Gas Constant (R): $0.0821 \text{ L·atm·mol}^{-1}\text{K}^{-1}$ or $8.314 \text{ J·mol}^{-1}\text{K}^{-1}$

Equations and Formulas

These equations are used to solve problems involving gases:

• $PV = nRT$

• $P_1V_1 = P_2V_2$

• $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

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

• $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• $d = \frac{PM}{RT}$ (Density of a gas)

• $M = \frac{dRT}{P}$ (Molar mass from density)

• $P_{\text{total}} = P_A + P_B + P_C + \ldots$ (Dalton's Law of Partial Pressures)

• $u = \sqrt{\frac{3RT}{M}}$ (Root mean square speed of gas molecules)

Standard Temperature and Pressure (STP)

STP conditions are commonly used as reference points in gas calculations:

• Standard Temperature: 0°C (273.15 K)

• Standard Pressure: 1 atm (101.325 kPa)

• Molar Volume at STP: 1 mole of an ideal gas occupies 22.4 L

Kinetic Molecular Theory of Gases

Postulates and Implications

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.

• The volume of the particles is negligible compared to the volume of the container.

• Collisions between particles and with the container walls are perfectly elastic.

• There are no intermolecular forces between gas particles.

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

Implications:

• All gases at the same temperature have the same average kinetic energy.

• Heavier gas molecules move more slowly than lighter ones at the same temperature.

Deviations from Ideal Gas Behavior

Real Gases vs. Ideal Gases

Real gases deviate from ideal behavior under certain conditions:

• At high pressures and low temperatures, intermolecular forces and the finite volume of gas particles become significant.

• Deviations are greater for gases with strong intermolecular attractions or large molecular sizes.

Van der Waals Equation: Adjusts the ideal gas law for real gases:

• $\left(P + a\frac{n^2}{V^2}\right)(V - nb) = nRT$

• Where a and b are constants specific to each gas.

Gas Stoichiometry

Stoichiometric Calculations Involving Gases

Gas stoichiometry involves using balanced chemical equations to relate volumes, masses, and moles of gases in reactions.

• At STP, use molar volume (22.4 L/mol) to convert between volume and moles.

• Use the ideal gas law for non-STP conditions.

• Apply stoichiometric coefficients from balanced equations to relate reactants and products.

Example: Calculate the volume of hydrogen gas produced when magnesium reacts with hydrochloric acid:

• $\text{Mg}(s) + 2\text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g)$

• Use mole ratios and the ideal gas law to find the volume of $\text{H}_2$ produced.

Dalton's Law of Partial Pressures and Gas Collection Over Water

Partial Pressures

Dalton's Law states that the total pressure of a mixture of gases is the sum of the partial pressures of each component:

• $P_{\text{total}} = P_A + P_B + P_C + \ldots$

• Partial pressure is the pressure a gas would exert if it occupied the container alone.

Gas Collection Over Water

When a gas is collected over water, the total pressure includes both the gas and water vapor:

• $P_{\text{gas}} = P_{\text{total}} - P_{\text{H}_2\text{O}}$

• Use tables to find the vapor pressure of water at the given temperature.

Root Mean Square Speed of Gas Molecules

Calculation and Temperature Dependence

The root mean square (rms) speed of gas molecules is a measure of the average speed of particles in a gas sample:

• $u = \sqrt{\frac{3RT}{M}}$

• Where R is the gas constant, T is temperature in Kelvin, and M is molar mass in kg/mol.

• As temperature increases, rms speed increases.

• Lighter molecules have higher rms speeds at the same temperature.

Tables: Vapor Pressure of Water

Main Purpose

The table provides vapor pressure values of water at various temperatures, which are necessary for calculations involving gas collection over water.

Temperature (°C)	Vapor Pressure (mmHg)
15	12.8
16	13.6
17	14.5
18	15.5
19	16.5
20	17.5
21	18.7
22	19.8
23	21.1
24	22.4
25	23.8

Example Problems and Applications

Representative Problems

• Calculate the final pressure, volume, or temperature of a gas after a change in conditions using the gas laws.

• Determine the number of moles of a gas collected over water, accounting for vapor pressure.

• Find the molar mass of a vapor from its density and pressure.

• Calculate the rms speed of a gas molecule at STP.

• Apply stoichiometry to reactions involving gases to find volumes or masses of products.

Example: A 5.00-mL sample of oxygen is collected over water at a total pressure of 699.7 mmHg and 19°C. The vapor pressure of water at 19°C is 16.5 mmHg. Find the partial pressure of oxygen and the number of moles of oxygen at 19°C.

• $P_{\text{O}_2} = 699.7 \text{ mmHg} - 16.5 \text{ mmHg} = 683.2 \text{ mmHg}$

• Convert pressure to atm and use the ideal gas law to find moles.

Summary Table: Gas Law Equations

Law	Equation	Variables Held Constant
Boyle's Law	$P_1V_1 = P_2V_2$	Temperature, moles
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Pressure, moles
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	Pressure, temperature
Combined Gas Law	$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$	Moles
Ideal Gas Law	$PV = nRT$	None

Additional info: These notes expand on the provided equations and questions, offering definitions, explanations, and context for each law and concept. The tables are reconstructed from the exam material and standard chemistry references.