Question

A gas mixture contains 0.650 mol of N₂, 0.250 mol of H₂, and 0.300 mol of CH₄. Calculate the pressure of the gas mixture and the partial pressure of each constituent gas if the mixture is in a 13.0 L vessel at 27.00°C.

Answer 1

To calculate the pressure of the gas mixture, use the ideal gas law equation. Plug in the values for the number of moles, gas constant, temperature, and volume to find the pressure. To calculate the partial pressure of each gas, use the mole fraction of each gas and the total pressure.

Step-by-step explanation:

To calculate the pressure of the gas mixture, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. First, we need to calculate the total number of moles in the gas mixture:

Number of moles of N₂ = 0.650 mol

Number of moles of H₂ = 0.250 mol

Number of moles of CH₄ = 0.300 mol

Total number of moles = 0.650 mol + 0.250 mol + 0.300 mol = 1.200 mol

Next, we can plug in the values into the ideal gas law equation to find the pressure:

P = (nRT) / V

P = (1.200 mol)(0.0821 atm L/mol K)(27.00°C + 273.15 K) / 13.0 L

P ≈ 2.86 atm

To calculate the partial pressure of each gas, we can use the mole fraction of each gas:

Partial pressure of N₂ = (moles of N₂ / total moles) * total pressure

Partial pressure of H₂ = (moles of H₂ / total moles) * total pressure

Partial pressure of CH₄ = (moles of CH₄ / total moles) * total pressure

Partial pressure of N₂ = (0.650 mol / 1.200 mol) * 2.86 atm ≈ 1.55 atm

Partial pressure of H₂ = (0.250 mol / 1.200 mol) * 2.86 atm ≈ 0.60 atm

Partial pressure of CH₄ = (0.300 mol / 1.200 mol) * 2.86 atm ≈ 0.72 atm