Calculating Kp for Decomposition of NH4Cl at High Temperature

[Masschaos]

A 9g sample of solid NH₄Cl is heated in a 4L container to 924.4^oC and decomposes according to the following equation.
NH₄Cl(s) -> HCl(g) + NH₃(g)

at equalibrium the partial pressure of NH₃ (g) is 1.346 atm. Calculate the equilibrium constant for K_p for this reaction

Homework Equations

K_p = P_productⁿ/P_reactantⁿ

or

K_c equation and Pv = nRT

The Attempt at a Solution

First I used the Ideal gas equation the amount of NH₃ in the system.
So n = PV/RT
n = (136383.45 Pa * (4 *10^-3 L))/(8.3144*1197.4K)
n = 5.48*10^-5

This means the concentration of the NH₄Cl is.
n = 9/54.45 = 0.1653
0.1653 - 2(5.48*10^-5) = 0.1652

I assumed then that Cl would also have this concentration.
So the K_c of the reaction = ([5.48*10^-5*[5.48*10^-5)/0.1652 = 1.817 * 10^-8

Then Kp = Kc(RT)^(delta)n
Kp= 1.817 * 10^-8 * (8.3144*1197.4K)¹
Kp = 0.00018 = 1.8*10^-4

The more I look at this the more I feel there is a much easier solution, is my solution even right?

 

[Borek]

You have to calculate Kp, you are given pressure, why do you calculate concentrations instead of using pressure directly?

Besides, what is the activity of the solid (hint: it is always identical)? Does your calculation of NH₄Cl make any sense in this context?

 

[Masschaos]

Well, the thing that confused me is that NH₄Cl is a solid, so it is not counted in the calculation for Kp. Doesn't that mean it will be [products]/0? Or do you just not divide the product by anything?

What do you mean about the solid? it says its heated, and gas forms so presumably it gets smaller. My calculations would suggest that the reaction doesn't react very far.
I'm not really clear on what Kp is. Pressure are equilibrium?

 

[Borek]

Activity of solids is always 1, period. Whenever you see a solid in reaction equation, just put 1 in the reaction quotient.

How come you are asked to calculate Kp, but you don't know what it is? Please check your book or lecture notes. Seems like you are missing many basic parts of the theory, and that impedes your ability to solve the question.

 

[Masschaos]

Ah! So I am wrong.
I assumed it was pressure at equilibrium. And after some searching I thought I had come up with the right answer.
Thanks! I'll keep looking.

 

[Masschaos]

If, the activity of a solid is always 1.
Then would Kp =[Products]
Kp = [ 5.48*10-5] * [ 5.48*10-5]?