Respuesta :
Answer:
The mole fraction of H₂ gas in the given mixture: χ₁ = 0.44
The total pressure of the gas mixture: P = 10.825 atm
The partial pressure of H₂ gas in the given mixture: p₁ = 4.76 atm
The partial pressure of N₂ gas in the given mixture: p₂ = 1.19 atm
The partial pressure of CH₄ gas in the given mixture: p₃ = 4.76 atm
Explanation:
Given: mass of H₂: W₁= 2 g, mass of N₂: W₂= 7 g, mass of CH₄: W₃= 16 g
Molar mass of H₂: M₁= 2g/mol, molar mass of N₂: M₂= 28g/mol, molar mass of CH₄: M₃=16g/mol
Number of moles of H₂: n₁ = W₁ ÷ M₁ = 2 ÷ 2 = 1 mol
Number of moles of N₂: n₂ = W₂ ÷ M₂ = 7 ÷ 28 = 0.25 mol
Number of moles of CH₄: n₃ = W₃ ÷ M₃ = 16 ÷ 16 = 1 mol
Therefore, the total number of moles: n = n₁ + n₂ + n₃ = 1 +0.25 +1 = 2.25 mol
The mole fraction of H₂ gas in the given mixture: χ₁ = n₁ ÷ n = 1 ÷ 2.25 = 0.44
The mole fraction of N₂ gas in the given mixture: χ₂ = n₂ ÷ n = 0.25 ÷ 2.25 = 0.11
The mole fraction of CH₄ gas in the given mixture: χ₃ = n₃ ÷ n = 1 ÷ 2.25 = 0.44
The total pressure of the gas mixture can be calculated by the ideal gas equation: P = n.R.T ÷ V
Given: total volume:V = 5L, total number of moles:n = 2.25 mol, gas constant: R= 0.08206 L.atm.mol⁻.K⁻, temperature: T = 20°C= 20 + 273.15 = 293.15 K, total pressure: P=?
Therefore, total pressure of the gas mixture: P = (2.25 mol × 0.08206 L.atm.mol⁻.K⁻ × 293.15 K) ÷ (5L) = 10.825 atm
The partial pressure of H₂ gas in the given mixture: p₁ = χ₁ × P = 0.44 × 10.825 atm= 4.76 atm
The partial pressure of N₂ gas in the given mixture: p₂ = χ₂ × P = 0.11 × 10.825 atm= 1.19 atm
The partial pressure of CH₄ gas in the given mixture: p₃ = χ₃ × P = 0.44 × 10.825 atm= 4.76 atm
