Chapter 8: Gases – Properties, Laws, and Behavior

Gas Pressure

Definition and Measurement

Gas pressure is a fundamental property describing the force exerted by gas molecules on the surfaces they contact. It arises from the constant, random motion of gas particles colliding with container walls.

• Pressure is defined as the force exerted on a given area.

• Common units: pounds per square inch (psi), millimeters of mercury (mm Hg), atmosphere (atm), Pascal (Pa), bar.

• Mercury barometer is used to measure atmospheric pressure.

Example: Atmospheric pressure at sea level is about 14.7 psi, equivalent to the weight of a bowling ball pressing on a human thumbnail.

Units of Pressure

• mm Hg (millimeters of mercury): Used due to the way gas pressure is measured.

• Atmosphere (atm): 1 atm = 760 mm Hg.

• Pascal (Pa): SI unit; 1 Pa = pressure exerted by a 0.1 mm high film of water.

• Kilopascal (kPa): 1 atm = 101.3 kPa.

• Bar: 1 bar = 105 Pa.

Unit	Equivalent
1 atm	760 mm Hg = 760 torr = 14.7 psi = 101.3 kPa

Measuring Atmospheric and Confined Gas Pressure

• Barometer: Measures atmospheric pressure by the height of a mercury column.

• Manometer: Measures pressure of a confined gas relative to atmospheric pressure.

• Pressure depends on number of gas particles, volume, and average speed of particles.

Properties of Gases

Volume, Amount, Temperature, and Pressure

Gases expand uniformly to fill their containers. The four key properties—volume, amount (moles), temperature, and pressure—are interrelated.

• Elements: Ar, He, H2, N2, O2

• Compounds: CO2, CO, H2O, NH3

• Changing one property affects the others.

Gas Laws

Pressure and Temperature: Amonton’s Law (Gay-Lussac’s Law)

At constant volume and amount, the pressure of a gas is directly proportional to its temperature in Kelvin.

• Equation: $P = kT$

• As temperature increases, pressure increases.

Temperature (°C)	Temperature (K)	Pressure (kPa)
-100	173	36.0
0	273	46.4
50	323	56.7
100	373	77.5
150	423	88.0

Volume and Temperature: Charles’s Law

At constant pressure and amount, the volume of a gas is directly proportional to its temperature in Kelvin.

• Equation: $V = kT$

• When comparing two systems: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• As temperature increases, gas particles move faster, causing more frequent and forceful collisions, requiring a larger volume to maintain constant pressure.

Temperature (°C)	Temperature (K)	Volume (L)
-23	250	22
0	273	24
27	300	26
100	373	32

Volume and Pressure: Boyle’s Law

At constant temperature and amount, the volume of a gas is inversely proportional to its pressure.

• Equation: $P \times V = k$

• Comparing two states: $P_1 V_1 = P_2 V_2$

• As pressure increases, volume decreases by the same factor.

Volume and Amount (Moles): Avogadro’s Law

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

• Equation: $V = k n$

• Equal volumes of gases at the same conditions contain equal numbers of molecules.

The Ideal Gas Law

The ideal gas law combines the relationships between pressure, volume, temperature, and amount into a single equation.

• Equation: $PV = nRT$

• $R = 0.08206 \; \frac{L \cdot atm}{mol \cdot K}$

• Assumes no intermolecular attractions and negligible molecular volume (valid at low pressure and high temperature).

Combined Gas Law

When the number of moles is constant but other properties change, the combined gas law is used.

• Equation: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

Standard Temperature and Pressure (STP)

Definition and Molar Volume

STP is a reference condition for gases: 0°C (273 K) and 1 atm. At STP, one mole of any gas occupies 22.4 L and contains $6.022 \times 10^{23}$ molecules.

Density and Molar Mass of Gases

Calculating Density

• Density (d) is the ratio of mass to volume, usually in g/L for gases.

• Equation: $d = \frac{M P}{R T}$, where M is molar mass.

• Density depends on pressure, temperature, and molar mass.

Calculating Molar Mass

• Molar mass (M) is the mass per mole of a substance.

• Equation: $M = \frac{grams}{mole} = \frac{m}{n}$

• Substitute into the ideal gas law: $PV = \frac{m}{M} RT$

Dalton’s Law of Partial Pressures

Mixtures of Gases

In a mixture of non-reacting gases, each gas exerts its own pressure as if it were alone in the container.

• Equation: $P_T = P_A + P_B + P_C + \ldots$

• Partial pressure is the pressure exerted by each individual gas.

Mole Fraction and Partial Pressure

• Mole fraction (X) is the ratio of moles of a component to total moles in the mixture.

• Equation: $P_A = X_A P_T$

Gas	Mole Fraction (X)	Partial Pressure (P)
A	$X_A$	$P_A = X_A P_T$
B	$X_B$	$P_B = X_B P_T$

Collecting Gases Over Water

Wet Gas Mixtures and Vapor Pressure

When collecting a gas over water, the total pressure includes both the gas and water vapor.

• Equation: $P_T = P_{H_2O} + P_{gas}$

• Vapor pressure of water is temperature dependent and is an intensive property.

Temperature (°C)	Pressure (mm Hg)
0	4.58
25	23.76
50	92.6

Stoichiometry with Gas Volumes

Volume Ratios in Reactions

At constant temperature and pressure, the volume ratio of gases in a reaction matches the stoichiometric ratio in the balanced equation.

• Equation: $V = k n$ (at constant T, P)

Effusion and Diffusion of Gases

Definitions

• Diffusion: The process of molecules spreading from high to low concentration.

• Effusion: The process of gas molecules escaping through a small hole into a vacuum.

• Lighter gases diffuse and effuse faster due to higher average speeds.

Process	Description
Diffusion	Spreading of molecules throughout a space
Effusion	Escape of molecules through a small opening

Graham’s Law

• For two gases at the same temperature, the rate of effusion is inversely proportional to the square root of their molar masses.

• Equation: $\text{Rate}_1 / \text{Rate}_2 = \sqrt{M_2 / M_1}$

Kinetic Molecular Theory (KMT)

Assumptions and Explanation of Gas Laws

KMT models gases as particles in constant, random motion. It explains the relationships described by the gas laws.

• Average kinetic energy is proportional to temperature (in Kelvin).

• Collisions are elastic; energy is conserved.

• There is a large amount of empty space between particles.

• Pressure results from collisions with container walls.

Temperature and Molecular Velocities

• At the same temperature, all gases have the same average kinetic energy.

• Heavier molecules move more slowly than lighter ones.

• Root mean square velocity: $u_{rms} = \sqrt{\frac{3RT}{M}}$

Non-Ideal Gas Behavior

Real Gases vs. Ideal Gases

Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular attractions and finite molecular volume.

• At high pressure, molecular volume becomes significant.

• At low temperature, intermolecular attractions reduce pressure.

• Van der Waals equation modifies the ideal gas law to account for these factors:

Van der Waals Equation:

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

• a: accounts for intermolecular attractions

• b: accounts for molecular volume

Summary Table: Major Gas Laws

Law	Equation	Variables Held Constant	Relationship
Boyle's Law	$P_1 V_1 = P_2 V_2$	n, T	Pressure inversely proportional to volume
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	n, P	Volume directly proportional to temperature
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	P, T	Volume directly proportional to moles
Gay-Lussac's Law	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	n, V	Pressure directly proportional to temperature
Combined Gas Law	$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$	n	Relates P, V, T
Ideal Gas Law	$PV = nRT$	None	Relates P, V, n, T

Additional info: These notes are based on textbook slides and cover all major aspects of the behavior of gases, including measurement, laws, kinetic theory, and deviations from ideality. Tables and equations have been expanded for clarity and completeness.