Solving Gas Laws: 3H2 + N2 -> 2NH3 at 110 ATM

[Lancelot59]

It's a gas problem:

3 volumes N₂ and 1 volume of H₂ react at 344 degrees Celsius to form NH₃. The equilibrium total pressure is 110 ATM and is 41.49% NH₃ by volume. Find Kp assuming the gases behave ideally.

So I started by assuming that I had 100L of gas. I worked the ICE table like so:

3H2 + N2 <--> 2NH3
75L_____25L_____0L
-3x_____-x______+2x
12.765L_4.255L___41.49L

Well this gives me volumes. But it's wrong. This is clearly not working. How can I go about it correctly?

 

[Borek]

Why is it not working? I can be missing something, but I think you are on the right track, just not there yet.

 

[Lancelot59]

Well to be honest I have no idea what to do now. I have their volumes, but without knowing how many mols of each I have I can't determine their concentrations. Also, I started with 100L, and ended up with only 58.51L at equlibrium...something seems wrong there.

 

[Borek]

Can you calculate partial pressure of the ammonia at equilibrium? Sum of partial pressures of other gases? Assuming you started with stoichiometric mixture of gases, can you split this sum into pressures of other gases?

 

[Lancelot59]

I can't see a way to get the pressure of ammonia. I don't know how many mols I have, so the ideal gas law is out.

 

[Borek]

Not exactly out.

Number of moles of gas is - for a given p, T - directly proportional to its V. If gas occupies half the volume, it also has half the moles of the mixture. This will not give you number of moles, but it will give you their ratio.

 

[Lancelot59]

I see where you're going, but I'm confused.

Lets say this fake gas at 110atm is: 30% X 60%Y and 10%Z by pressure. The empirical formula for the mixture is 3X 6Y Z?

 

[Borek]

You can put it that way, although it is better to say that mole fraction of X is 0.3, of Y 0.6 and of Z 0.1. Then you can use molar fractions to calculate pressure (Dalton's law).