Determine the mole fraction of CO in a gas mixture composed of 782.4 grams of CO₂ and 2.10 moles of CO.The mixture is at 703.3 K in a 25.8-liter container.

Question

Quizplus · Accepted Answer

To find the mole fraction of CO, we need to first find the total moles of gas in the mixture. We can do this by using the ideal gas law:

PV = nRT

where P is the pressure (assumed to be constant), V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Solving for n, we get:

n = PV/RT

Plugging in the values given:

n = (1 atm)(25.8 L)/(0.0821 L atm/mol K)(703.3 K) = 1.176 mol

Next, we need to find the moles of CO in the mixture. We are given that there are 2.10 moles of CO, so we just need to convert the mass of COS to moles:

782.4 g COS / 60.07 g/mol = 13.03 mol COS

So the total number of moles in the mixture is:

n_total = n_CO + n_COS = 2.10 mol + 13.03 mol = 15.13 mol

Finally, we can find the mole fraction of CO:

X_CO = n_CO / n_total = 2.10 mol / 15.13 mol = 0.139

So the answer is closest to choice B, 0.89.

Determine the Mole Fraction of CO in a Gas Mixture