Physical Chemistry: Gas Laws

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Gas laws describe how pressure (P), volume (V), temperature (T) and amount (n) of a gas are interrelated under ideal conditions. The four cornerstone laws are Boyle’s law (P₁V₁ = P₂V₂ at constant T), Charles’s law (V₁/T₁ = V₂/T₂ at constant P), Gay-Lussac’s law (P₁/T₁ = P₂/T₂ at constant V), and Avogadro’s law (equal volumes of gases at the same T and P contain equal numbers of molecules). All four combine into the ideal gas equation PV = nRT, where R = 0.0821 atm·dm³/(mol·K). Always convert temperature to Kelvin (K = °C + 273) before substitution. At STP (0 °C, 1 atm) the molar volume is 22.4 dm³/mol; at RTP (25 °C, 1 atm) it is 24 dm³/mol. NECO SSCE Chemistry tests these laws in Objectives (Paper I) as well as in calculation questions in Paper II Essay.

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The Core Gas Laws

Boyle’s law states that at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure: P₁V₁ = P₂V₂. A P–V graph is a rectangular hyperbola.

Charles’s law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature: V₁/T₁ = V₂/T₂. A V–T plot is a straight line that extrapolates to zero volume at 0 K (absolute zero, −273.15 °C).

Gay-Lussac’s law states that at constant volume, pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂.

Avogadro’s law states that equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules (hence equal moles). Two consequences: (i) 1 mole of any gas occupies 22.4 dm³ at STP, and (ii) gas volumes at equal T and P can be compared directly as moles.

The Ideal Gas Equation

Combining all four laws and inserting a proportionality constant R gives PV = nRT. Using R = 0.0821 atm·dm³/(mol·K) when P is in atm and V in dm³, or R = 8.314 J/(mol·K) when P is in Pa and V in m³. The combined gas equation P₁V₁/T₁ = P₂V₂/T₂ is used when none of P, V or T is held constant.

Dalton’s Law of Partial Pressures

In a mixture of non-reacting gases, the total pressure equals the sum of the individual partial pressures: P(total) = P₁ + P₂ + P₃ + …. A gas collected over water has its dry partial pressure calculated by subtracting the saturated vapour pressure of water at that temperature from the total pressure.

Graham’s Law of Diffusion

The rate of diffusion of a gas is inversely proportional to the square root of its molar mass: r₁/r₂ = √(M₂/M₁). Hydrogen diffuses fastest; heavy gases such as CO₂ diffuse slowly.

Quick Reference Table

Condition held constant	Law	Equation
Temperature	Boyle’s	P₁V₁ = P₂V₂
Pressure	Charles’s	V₁/T₁ = V₂/T₂
Volume	Gay-Lussac’s	P₁/T₁ = P₂/T₂
T and P	Avogadro’s	V ∝ n

NECO SSCE Question Patterns

Paper I typically offers a calculation on molar volume or a graph-interpretation item (identify which straight line represents an ideal gas at constant P). Paper II essay questions often combine Dalton’s law with collection over water, or ask for the molar mass of a gas using gas density (M = dRT/P).

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Behaviour of Real Gases

An ideal gas assumes negligible molecular volume and zero intermolecular forces. Real gases deviate from PV = nRT at high pressure (molecular volume becomes significant) and low temperature (intermolecular attractions matter). The van der Waals equation introduces two correction constants a (attraction) and b (volume): (P + a(n/V)²)(V − nb) = nRT. NECO rarely requires a and b numerically, but candidates should explain qualitatively why a real gas curve dips below the ideal straight line on a P–V isotherm.

Connecting to Adjacent Topics

Stoichiometry of gaseous reactions: From balanced equations, gas volumes at equal T and P are in the same ratio as moles (Avogadro’s law), so 2 H₂ + O₂ → 2 H₂O tells us 2 volumes H₂ react with 1 volume O₂ to give 2 volumes steam.
Molar mass determination: Two practical methods — (i) Regnault’s method uses M = dRT/P with measured mass, T, P and V; (ii) Victor Meyer’s method measures the volume of vapour displaced by a known mass of volatile liquid, then applies M = mRT/PV.
Relative molecular mass from gas density: d = PM/RT, so M = dRT/P — a standard Paper II calculation.

Common Mistakes

Temperature unit slip: Substituting °C instead of K is the single most common error. A gas at 27 °C must be entered as 300 K, not 27.
Wrong R for the units: Using 0.0821 with pressure in Pa produces answers off by a factor of ~101 325. Match the constant to the units of P and V first.
STP vs RTP confusion: NECO questions may use either; 22.4 dm³ at 0 °C/1 atm versus 24 dm³ at 25 °C/1 atm.
Collection over water: Ignoring the vapour pressure of water at the recorded temperature inflates the calculated amount of dry gas.
Mixing Boyle’s and Charles’s conditions: If both T and P change, use the combined gas equation, not Boyle’s alone.
Adding volumes directly: In a mixture of gases, you cannot add partial volumes to get total pressure; convert each to moles first, or use partial pressures directly with Dalton’s law.

Worked Micro-Example

A 0.44 g sample of a gaseous hydrocarbon occupies 240 cm³ at 27 °C and 1.05 atm. Find its molar mass.

PV = nRT → n = PV/RT = (1.05 × 0.240)/(0.0821 × 300) = 0.252/24.63 ≈ 0.01023 mol. M = mass/n = 0.44 / 0.01023 ≈ 43 g/mol (molecular formula likely C₃H₇).

Practice Prompts

A gas occupies 500 cm³ at 760 mmHg. What pressure reduces its volume to 250 cm³ at the same temperature? (Answer: 1520 mmHg, by Boyle’s law.)
200 cm³ of oxygen diffused through a porous plug in 30 s. How long will the same volume of carbon dioxide take? (M(O₂) = 32, M(CO₂) = 44.) (Answer: t₂ = t₁ × √(44/32) = 30 × 1.172 ≈ 35.2 s.)

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Physical Chemistry: Gas Laws