MCAT General Chemistry · Lesson 8

The Gas Phase

3 min read4 sectionsUpdated January 3, 2026

Jump to a section4

4 sections

8.1 Gas Phase

Introduces basic properties of gases, their variables, measurement, and units, as well as STP conditions.

Properties of Gases
- Fluids: flow, take shape of container.
- Rapid motion, far apart, weak intermolecular forces.
- Compressible (unlike liquids).
Variables
- Pressure (P), Volume (V), Temperature (T), Moles (n)
- 1 atm = 760 mmHg = 760 torr = 101.325 kPa
- Blood pressure devices use barometer principle.
Volume & Temperature
- Measured in L or mL, temperature in K.
STP (Standard Temperature and Pressure)
- 273 K, 1 atm (used for gas law calculations).
- Different from standard state (25ºC or 298 K, 1 atm).

Discusses ideal gas assumptions, laws governing gas behavior, density, molar mass, and special gas laws.

Ideal Gas
- No intermolecular forces, individual particle volume negligible.
- Real gases deviate at high P, low T.
Ideal Gas Law
- $PV = nRT$
- R (universal gas constant) = 8.21 × 10⁻² L·atm/mol·K or 8.314 J/mol·K
Density
- $d = m/V = PM/RT$
- $\rho$ and $d$ both represent density
Combined Gas Law
- $P_1V_1/T_1 = P_2V_2/T_2$
Molar Mass
- $M = (\text{density at STP})(22.4 L/mol)$
Special Cases
- Avogadro: $n/V = k$ → proportional.
- Boyle: $PV = k$ → inverse relationship.
- Charles: $V/T = k$ → proportional.
- Gay-Lussac: $P/T = k$ → proportional.
- Dalton: $P_{total} = P_a + P_b + P_c$ , $P_a = X_a P_t$ , $X_a = n_a/n_{total}$
- Henry: $[A] = k_H P_A$ , solubility proportional to partial pressure.

Explains microscopic behavior of gases, assumptions of molecular motion, and key kinetic relationships.

Assumptions
- Negligible particle volume.
- No intermolecular forces.
- Continuous, random motion.
- Elastic collisions (momentum conserved).
Applications
- Average KE: $KE = \frac{1}{2}mv^2 = \frac{3}{2}k_B T$ $K E = \frac{1}{2} m v^{2} = \frac{3}{2} k_{B} T$
  - $k_B = 1.38 × 10^{-23}$ J/K
- Root mean square speed: $u_{rms} = \sqrt{3RT/M}$ , M in kg/mol
- Graham’s Law
  - Diffusion: $R_1/R_2 = \sqrt{M_2/M_1}$
  - Effusion: proportional to average speed.

Discusses deviations from ideal behavior due to pressure and temperature, and introduces the Van der Waals equation.

Deviations Due to Pressure
- High P: molecules closer → attractive forces → condense.
- Extremely high P: molecular volume significant → ideal gas law fails.
- Smaller molecules behave more ideally at high P.
Deviations Due to Temperature
- Low T: intermolecular forces cause smaller volume than predicted.
- Near boiling point or extremely low T: gases deviate more from ideal.
Van der Waals Equation
- $(P + \frac{n^2 a}{V^2})(V - nb) = nRT$
- a = attractive forces (smaller for less polarizable gases)
- b = volume of molecules (proportional to size)
- Larger molecule → larger b → real pressure smaller → must increase P to compensate.

Spotted something wrong or unclear? Tell us — these notes are revised continuously.

8.1 Gas Phase

Introduces basic properties of gases, their variables, measurement, and units, as well as STP conditions.

Properties of Gases
- Fluids: flow, take shape of container.
- Rapid motion, far apart, weak intermolecular forces.
- Compressible (unlike liquids).
Variables
- Pressure (P), Volume (V), Temperature (T), Moles (n)
- 1 atm = 760 mmHg = 760 torr = 101.325 kPa
- Blood pressure devices use barometer principle.
Volume & Temperature
- Measured in L or mL, temperature in K.
STP (Standard Temperature and Pressure)
- 273 K, 1 atm (used for gas law calculations).
- Different from standard state (25ºC or 298 K, 1 atm).

8.2 Ideal Gases

Discusses ideal gas assumptions, laws governing gas behavior, density, molar mass, and special gas laws.

Ideal Gas
- No intermolecular forces, individual particle volume negligible.
- Real gases deviate at high P, low T.
Ideal Gas Law
- $PV = nRT$
- R (universal gas constant) = 8.21 × 10⁻² L·atm/mol·K or 8.314 J/mol·K
Density
- $d = m/V = PM/RT$
- $\rho$ and $d$ both represent density
Combined Gas Law
- $P_1V_1/T_1 = P_2V_2/T_2$
Molar Mass
- $M = (\text{density at STP})(22.4 L/mol)$
Special Cases
- Avogadro: $n/V = k$ → proportional.
- Boyle: $PV = k$ → inverse relationship.
- Charles: $V/T = k$ → proportional.
- Gay-Lussac: $P/T = k$ → proportional.
- Dalton: $P_{total} = P_a + P_b + P_c$ , $P_a = X_a P_t$ , $X_a = n_a/n_{total}$
- Henry: $[A] = k_H P_A$ , solubility proportional to partial pressure.

8.3 Kinetic Molecular Theory

Explains microscopic behavior of gases, assumptions of molecular motion, and key kinetic relationships.

Assumptions
- Negligible particle volume.
- No intermolecular forces.
- Continuous, random motion.
- Elastic collisions (momentum conserved).
Applications
- Average KE: $KE = \frac{1}{2}mv^2 = \frac{3}{2}k_B T$ $K E = \frac{1}{2} m v^{2} = \frac{3}{2} k_{B} T$
  - $k_B = 1.38 × 10^{-23}$ J/K
- Root mean square speed: $u_{rms} = \sqrt{3RT/M}$ , M in kg/mol
- Graham’s Law
  - Diffusion: $R_1/R_2 = \sqrt{M_2/M_1}$
  - Effusion: proportional to average speed.

8.4 Real Gases

Discusses deviations from ideal behavior due to pressure and temperature, and introduces the Van der Waals equation.

Deviations Due to Pressure
- High P: molecules closer → attractive forces → condense.
- Extremely high P: molecular volume significant → ideal gas law fails.
- Smaller molecules behave more ideally at high P.
Deviations Due to Temperature
- Low T: intermolecular forces cause smaller volume than predicted.
- Near boiling point or extremely low T: gases deviate more from ideal.
Van der Waals Equation
- $(P + \frac{n^2 a}{V^2})(V - nb) = nRT$
- a = attractive forces (smaller for less polarizable gases)
- b = volume of molecules (proportional to size)
- Larger molecule → larger b → real pressure smaller → must increase P to compensate.