A gas mixture of 0.13 mol NH3, 1.27 mol N2, and 0.025 mol H2O vapor is contained at a total pressure of 830 mm Hg and 323 K. Calculate the following:
(a) Mole fraction of each component.
(b) Partial pressure of each component in mm Hg.
(c) Total volume of mixture in m3 and ft3.
Xi = ni/ntotal
Ptotal = P1 + P2 + P3 ... + Pn
Pi = XiPtotal
PV = nRT
The Attempt at a Solution
OK, so I have been working on this for a while now and can't seem to find the answer. Since water vapor only behaves like an ideal gas at pressures below 75 mm Hg, it cannot be treated as so in this problem.
I calculated the mole fractions no problem:
(0.13 mol NH3)/1.425 mol total = 0.0912
(1.27 mol N2)/1.425 mol total = 0.891
(0.025 mol H2O)/1.425 mol total = 0.0175
The problem comes when I try to calculate partial pressures of each gas and the water vapor. Since vapor pressure is a function of temperature alone, I was able to reference a table of values which says at 323 K (50 C), water vapor has a saturation pressure of 92.5 mm Hg. Subtracting this from 830 mm Hg gives 737.5 mm Hg, which should be the remaining combined pressures of ammonia and nitrogen gas. Next, I multiplied each gas's mole fraction by 737.5 mm Hg to obtain their partial pressures. However, according to the ideal gas law, these partial pressures should add up to the total pressure in the container, but they don't.
Can someone please help me understand how to approach and complete this problem? Thank you so much!