When a football bladder contains equimolar amounts of two gases (e.g., nitrogen N₂ and carbon dioxide CO₂), each gas has a mole fraction of 0.5. By Dalton's Law of Partial Pressures, the partial pressure of each gas equals 0.5 × total pressure. This is a standard Class 11 Chemistry problem on Dalton's Law.
Equimolar mixture: equal moles of each gas → equal mole fractions (0.5 each for binary mixture).
Dalton's Law: P_total = P_A + P_B (for non-reacting gases).
Partial pressure = Mole fraction × Total pressure.
In equimolar binary mixture: each gas contributes 50% of total pressure.
N₂ and CO₂ in football bladder: P_N₂ = P_CO₂ = P_total / 2.
Dalton's Law does NOT apply to reacting gases.
Problem Statement: 'A football bladder contains equimolar amounts of nitrogen (N₂) and carbon dioxide (CO₂). If the total pressure inside the bladder is P atm, find the partial pressure of each gas.'
Dalton's Law of Partial Pressures: The total pressure of a mixture of non-reacting gases = sum of partial pressures of all gases. P_total = P₁ + P₂ + P₃ + ...
Partial Pressure Formula: Partial pressure of a gas = Mole fraction × Total pressure P_A = x_A × P_total
Where mole fraction x_A = n_A / n_total
Solution: • Given: equimolar mixture → n_N₂ = n_CO₂ • Total moles = n_N₂ + n_CO₂ = 2n (say) • Mole fraction of N₂: x_N₂ = n/(2n) = 0.5 • Mole fraction of CO₂: x_CO₂ = n/(2n) = 0.5 • Partial pressure of N₂: P_N₂ = 0.5 × P_total • Partial pressure of CO₂: P_CO₂ = 0.5 × P_total
Numerical Example: If total pressure = 2 atm: • P_N₂ = 0.5 × 2 = 1.0 atm • P_CO₂ = 0.5 × 2 = 1.0 atm
If partial pressure of N₂ = 1.5 atm (equimolar mixture): • Since equimolar: P_CO₂ = P_N₂ = 1.5 atm • Total pressure = 1.5 + 1.5 = 3.0 atm
Key Concept: • In an equimolar binary mixture, both gases have EQUAL partial pressures, each equal to half the total pressure. • This is because mole fraction directly determines partial pressure in Dalton's Law.
Important Notes: • Dalton's Law applies only to non-reacting gases • N₂ and CO₂ do not react → Dalton's Law applies • Real gases deviate slightly from ideal behaviour at high pressures
Since equimolar: mole fraction of each gas = 0.5. By Dalton's Law: Partial pressure of N₂ = 0.5 × 3 = 1.5 atm. Partial pressure of CO₂ = 0.5 × 3 = 1.5 atm. Both gases exert equal partial pressure because they are present in equal moles.
Dalton's Law states that the total pressure of a mixture of non-reacting gases is equal to the sum of their individual partial pressures: P_total = P₁ + P₂ + P₃ + ... The partial pressure of each gas = its mole fraction × total pressure.
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