Question

At 500 degrees celsius, K for the formation of ammonia from nitrogen and hydrogen gases is 1.5x10-5.
N2(g)+3H2(g)->/<-2NH3(g)
Calculate the equilibrium partial pressure of hydrogen if the equilibrium partial pressures of ammonia and nitrogen are 0.015 atm and 1.2 atm, respectively.
I have algebraically determined that
(pH2)^3=(pNH3)^2/(pN2)(K), therefore, (0.015)^2/(1.2)(1.5x10-5), then divided by 1/3 to cube root it. However, I continue to get the answer 4.166666667, where my answer key says it should be 2.3 atm. I have done this multiple times, and I am very good at making sure my parentheses are in the proper place and closed. Is my answer book wrong? What is the correct answer?

Answer 1

.........N2 + 3H2 ==> 2NH3
E........1.2....x......0.015

Kp = p^2NH3/pN2*p^3H2

Your set up is right; you're not doing the algebra right. To take the cube root you don't divide by 1/3; you hit the y^x button and use 0.3333 for the x. That gives you 2.3 atm.
Try these to see that you're doing it right.
2^3 = 8. Enter 2, hit the y^x button, then 3 and equal.

Answer 2

I appreciate the help, but I don't have a y^x button on my calculator, I have a TI-83 Plus. Is there an equivalent button?

Answer 3

Figured it out. I didn't know I had to put parentheses around the 1/3 when I was raising it to the 1/3 power. So I input 12.5^(1/3), and then got the correct answer. Thanks!

Answer 4

Your button just isn't called the y^x button but you see you raised 12.5 to the 1/3 power. I don't do that. I plug in 12.5 and raise it to the 0.3333 power and that way I don't worry about the parentheses.

Answer 5

To raise to the 1/4 power I use 0.25 etc. That parenthesis thing gets confusing to me.