Calculating maximum amount of water vapor per unit volume

[guitarstorm]

Homework Statement

Compute the maximum amount of water vapor per unit volume that air can hold at the surface, where Ts = 288 K, and at a height of 10 km where T = 220 K. Express your answers in kg m-3.

Homework Equations

e_{s}=Ae^{\beta T}

e=\rho _{v}R_{v}T

The Attempt at a Solution

Since saturation occurs when e=e_{s}, I figured I would set the two equations equal to each other. However, solving for \rho _{v} doesn't work... The units don't work out, and I get a really large number... I feel like I have to somehow relate this to the total pressure of the air, but I'm unsure how to go about this.

 

[guitarstorm]

I was incorrect in my previous post saying that the units didn't work out... Solving for {\rho _{v}} when e=e_{s} does produce an answer in \frac{kg}{m^{3}}... However I'm getting 1,103,248.397 \frac{kg}{m^{3}}, for the first case where T=288 K, which is way off from what I should be getting (0.0126 \frac{kg}{m^{3}}).

I believe I then have to use the ideal gas equation, pV=nRT, plugging in p for e... But this is where the confusion comes in. Hopefully someone can help me with this tonight, since this HW is due tomorrow morning...