Study Notes: Properties and Laws of Gases (General Chemistry)

Gases: Properties and Behavior

Composition and Types of Gases

Gases are one of the fundamental states of matter, characterized by their ability to fill any container and mix uniformly. The Earth's atmosphere is primarily composed of nitrogen and oxygen, with trace amounts of other gases.

• Major atmospheric gases: 78% N2, 21% O2, and 1% other gases.

• Common diatomic molecules: N2, O2, Cl2, F2, H2.

• Group 8 elements: Monoatomic noble gases (e.g., He, Ne, Ar).

Physical characteristics of gases:

• Gases assume the volume and shape of their containers.

• They are the most compressible state of matter.

• Gases mix evenly and completely when confined together.

• They have much lower densities than liquids and solids.

• Gas molecules are constantly in motion and exert pressure on surfaces they contact.

Pressure and Measurement

Pressure is a key property of gases, defined as the force exerted per unit area. Atmospheric pressure is the pressure exerted by Earth's atmosphere.

• Pressure units: 1 Pa = 1 N/m2; 1 atm = 760 mmHg = 760 torr = 101,325 Pa

• Barometer: Instrument for measuring atmospheric pressure.

• Standard atmospheric pressure: Pressure exerted by a column of mercury 760 mm high at 0°C.

Pressure Conversion Table

Unit	Equivalent Value
1 atm	760 mmHg
1 atm	760 torr
1 atm	101,325 Pa
1 Pa	1 N/m2

Measuring Gas Pressure: Manometers

Manometers are devices used to measure the pressure of gases other than atmospheric pressure.

• Closed-tube manometer: Measures pressures below atmospheric pressure.

• Open-tube manometer: Measures both above and below atmospheric pressure by adding or subtracting the height of mercury column.

Key equations:

• $P_{gas} = P_{atm} - h_{Hg}$ (if gas pressure is less than atmospheric)

• $P_{gas} = P_{atm} + h_{Hg}$ (if gas pressure is greater than atmospheric)

Gas Laws

Boyle’s Law: Pressure-Volume Relationship

Boyle’s Law describes how the volume of a gas changes with pressure at constant temperature.

• Statement: At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume.

• Equation: $P \propto \frac{1}{V}$ or $PV = k$

• For two conditions: $P_1V_1 = P_2V_2$

• Example: If a sample of chlorine gas has a volume of 946 mL at 726 mmHg, and the volume is reduced to 154 mL at constant temperature, the new pressure is calculated as:

  • $P_2 = \frac{P_1V_1}{V_2} = \frac{726 \times 946}{154} = 4460$ mmHg

Charles’s Law: Volume-Temperature Relationship

Charles’s Law explains how the volume of a gas changes with temperature at constant pressure.

• Statement: At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature (in Kelvin).

• Equation: $V \propto T$ or $\frac{V}{T} = k$

• For two conditions: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Example: A sample of CO gas occupies 3.2 L at 125°C (398 K). To find the temperature at which it occupies 1.54 L:

  • $\frac{3.2}{398} = \frac{1.54}{T_2} \Rightarrow T_2 = 191.5$ K

Avogadro’s Law: Volume-Mole Relationship

Avogadro’s Law relates the volume of a gas to the number of moles present, at constant temperature and pressure.

• Statement: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles.

• Equation: $V \propto n$ or $\frac{V}{n} = k$

Combined Gas Law

The combined gas law incorporates Boyle’s, Charles’s, and Avogadro’s laws to relate pressure, volume, temperature, and moles.

• Equation: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ (for constant n)

• General form: $PV = nRT$ (Ideal Gas Law)

Ideal Gas Constant (R):

• $R = 0.08206$ L·atm/(mol·K)

• $R = 8.314$ J/(mol·K)

• $R = 1.987$ cal/(mol·K)

Standard Temperature and Pressure (STP)

STP is defined as 0°C (273.15 K) and 1 atm pressure. At STP, one mole of an ideal gas occupies 22.4 L.

Applications of the Ideal Gas Law

• Calculating volume: $V = \frac{nRT}{P}$

• Calculating density: $d = \frac{PM}{RT}$, where M is molar mass

• Example: The density of uranium hexafluoride (UF6) at 779 mmHg and 62°C:

  • Molar mass = 352 g/mol

  • Pressure in atm = $779/760 = 1.025$ atm

  • Temperature in K = $62 + 273 = 335$ K

  • $d = \frac{1.025 \times 352}{0.082 \times 335} = 13$ g/L

Stoichiometry of Gaseous Reactions

Volumes of gases in chemical reactions combine in simple ratios as indicated by the coefficients in balanced equations, provided temperature and pressure are constant.

• Example: For the reaction $2C_4H_{10} + 13O_2 \rightarrow 8CO_2 + 10H_2O$, 14.9 L of C4H10 requires:

  • $14.9 \text{ L C}_4H_{10} \times \frac{13 \text{ L } O_2}{2 \text{ L } C_4H_{10}} = 96.85 \text{ L } O_2$

Mixtures of Gases and Partial Pressures

Dalton’s Law of Partial Pressures

In a mixture of non-reacting gases, the total pressure is the sum of the partial pressures of each component.

• Equation: $P_{total} = P_1 + P_2 + ... + P_n$

• Partial pressure: $P_i = X_i P_{total}$, where $X_i$ is the mole fraction of component i

• Mole fraction: $X_i = \frac{n_i}{n_{total}}$

• Example: If a sample contains 8.24 mol CH4, 0.421 mol C2H6, and 0.116 mol C3H8, and total pressure is 1.37 atm, the partial pressure of each gas is calculated using its mole fraction.

Kinetic Molecular Theory of Gases

The kinetic molecular theory explains the behavior of gases at the molecular level.

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

• Collisions between particles and container walls are elastic (no loss of kinetic energy).

• Gas particles are very small compared to the distances between them.

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

Kinetic Energy and Molecular Speed

• Average kinetic energy: $KE = \frac{1}{2}mu^2$

• Root-mean-square (rms) speed: $u_{rms} = \sqrt{\frac{3RT}{M}}$

• Example: Calculate $u_{rms}$ for N2 at 250 K:

  • Molar mass of N2 = 28 g/mol = 0.028 kg/mol

  • $u_{rms} = \sqrt{\frac{3 \times 8.314 \times 250}{0.028}}$

Summary Table: Major Gas Laws

Law	Relationship	Equation
Boyle's Law	P vs. V (T, n constant)	$P_1V_1 = P_2V_2$
Charles's Law	V vs. T (P, n constant)	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Avogadro's Law	V vs. n (P, T constant)	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$
Combined Gas Law	P, V, T (n constant)	$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
Ideal Gas Law	P, V, n, T	$PV = nRT$

Additional info: Some equations and examples have been expanded for clarity and completeness. The notes cover all major concepts from the provided handout, suitable for General Chemistry exam preparation.