Dalton's Law of Partial PressuresFoundation

Each gas presses as if alone — interactive Chemistry simulation for IIT-JEE.

Concept

Non-reacting gases in a container ignore each other: each exerts the pressure it would alone (partial pressure), and the total is simply the sum. Equivalently, each gas's share of the pressure equals its share of the molecules: $p_i = x_iP_{total}$ .

Key formula

P_{total} = p_1 + p_2 + \cdots, \qquad p_i = x_iP_{total} = \frac{n_iRT}{V}

Derivation

Ideal molecules don't interact, so each species independently satisfies $p_iV = n_iRT$ . Summing: $P_{total}V = (\Sigma n_i)RT$ .

Dividing the two: $p_i/P_{total} = n_i/n_{total} = x_i$ — pressure fraction IS mole fraction. This is what let us split vapour compositions in Raoult's law.

Scenarios to explore

Dalton's Partial Pressures — Each gas presses as if alone — pᵢ = xᵢP.

Real-world applications

Collecting gas over water: P_gas = P_atm − P_water-vapour.
Breathing: alveolar O₂ partial pressure drives uptake; hypoxia at altitude.
Scuba mixes (nitrox/trimix) engineered by partial-pressure limits.

JEE exam tips

p_i = x_i·P — one multiplication answers most sub-questions.
Connecting vessels: total moles conserved; final P = ΣpᵢVᵢ/V_total (same T).
Average molar mass of mixture: M̄ = Σx_iM_i — pairs constantly with Dalton.

Common mistakes

Applying Dalton to REACTING gases (NH₃ + HCl form solid — law breaks).
Using mass fractions instead of mole fractions.
Forgetting water vapour when gas is collected over water.

Exam traps to avoid

Same mass ≠ same moles: equal grams of H₂ and O₂ give H₂ 16× the partial pressure.
Vapour pressure of water depends only on T — not on how much gas is above it.