Gas Laws & Kinetic Molecular Theory

Gases have definite mass but no definite shape and volume. The forces between gas molecules are almost negligible, resulting in low density and high compressibility.

Property	Characteristic
Forces	Almost negligible
Density	Low
Motion	Large rotatory, vibratory and translatory motion
Compression	High
Intermixing	Spontaneous

The three fundamental gas laws describe the relationship between pressure, volume, temperature, and amount of gas.

Law	Statement	Mathematical Form
Boyle’s Law	Volume inversely proportional to pressure at constant temperature	PV = constant P₁V₁ = P₂V₂
Charles’s Law	Volume directly proportional to absolute temperature at constant pressure	V/T = constant V₁/T₁ = V₂/T₂
Avogadro’s Law	Volume directly proportional to number of moles at STP	V/n = constant V₁/n₁ = V₂/n₂

Experimental Observations:

• Boyle’s Law: Adding weight on piston decreases volume
• Charles’s Law: Heating gas increases volume
• Avogadro’s Law: Adding moles increases volume

Combining Boyle’s, Charles’s, and Avogadro’s laws gives the ideal gas equation: PV = nRT

Ideal Gas Constant (R): Independent of gas nature, depends on units used.

Units of P	Units of V	Value of R
atm	dm³	0.0821 atm dm³ K⁻¹ mol⁻¹
mmHg (torr)	dm³	62.4 dm³ torr K⁻¹ mol⁻¹
Nm⁻² (SI)	m³ (SI)	8.314 J K⁻¹ mol⁻¹

Density of ideal gas: d = PM/(RT) where d ∝ P, d ∝ M, d ∝ 1/T

KMT explains gas behavior based on molecular motion. Key scientists:

• Bernoulli: Founder of KMT
• Clausius: Derived kinetic equation
• Maxwell: Distribution of velocities
• Boltzmann: Distribution of energies
• Van der Waal: Corrected ideal gas equation

Postulates of KMT:

1. Gases consist of small particles (molecules)
2. Molecules move randomly with elastic collisions
3. Pressure results from collisions with container walls
4. Molecules are widely separated with empty spaces
5. No attractive forces between molecules
6. Volume of molecules is negligible
7. Gravity effect is negligible compared to collisions
8. Average KE ∝ absolute temperature

Root Mean Square Velocity: C_rms = √(3RT/M)

Kinetic Interpretation of Temperature: Temperature is a measure of average translational KE of molecules.

Ideal Gases	Real Gases
Obey gas laws strictly at all T and P	Deviate from gas laws at high P and low T
Molecular volume negligible	Molecular volume significant at high P
No intermolecular forces	Weak attractive forces exist
Elastic collisions	Inelastic collisions
Cannot be liquefied	Can be liquefied at critical T and P

Compressibility Factor (Z):

• Z = 1: Ideal gas behavior
• Z < 1: Attractive forces dominant (volume less than predicted)
• Z > 1: Repulsive forces dominant (volume greater than predicted)

Corrects ideal gas equation for real gas behavior:

For n moles: [P + a(n/V)²] (V – nb) = nRT

For 1 mole: (P + a/V²)(V – b) = RT

Van der Waals Constants:

• a: Coefficient of attraction (greater for easily liquefiable gases)
• b: Excluded volume (related to molecular size)

Units:

• a: atm·dm⁶·mol⁻² or N·m⁴·mol⁻²
• b: dm³·mol⁻¹ or m³·mol⁻¹

Corrections:

1. Volume correction: V_free = V – nb (subtract excluded volume)
2. Pressure correction: P_ideal = P + an²/V² (add correction for attraction)

Absolute Zero: 0K = -273.16°C = -459°F. The temperature at which molecular motion ceases. Currently achievable to ~10⁻⁵K.

Pressure Conversions:

• 1 atm = 760 mmHg = 760 torr = 101325 Pa = 1.01325 bar = 14.7 psi
• 0.1 atm = 76 mmHg = 1.47 psi

Volume Conversions:

• 1 m³ = 1000 dm³ = 10⁶ cm³
• 1 dm³ = 1 L = 1000 cm³

Energy Conversions:

• 1 cal = 4.18 J
• 1 J = 0.239 cal = 10⁷ ergs