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?
.........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.
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?
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!
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.
To raise to the 1/4 power I use 0.25 etc. That parenthesis thing gets confusing to me.
To solve this problem, we can use the equilibrium expression and the given values to calculate the equilibrium partial pressure of hydrogen (pH2). Let's go step by step:
1. Write down the equilibrium expression:
K = (pNH3)² / ((pN2)(pH2)³)
2. Plug in the given values:
K = 1.5 x 10^-5
(pNH3) = 0.015 atm
(pN2) = 1.2 atm
3. Rearrange the equation to solve for pH2:
(pH2)³ = (pNH3)² / ((pN2)(K))
4. Substitute the given values:
(pH2)³ = (0.015)² / ((1.2)(1.5 x 10^-5))
5. Simplify the right side of the equation:
(pH2)³ = 0.0001875 / (1.8 x 10^-5)
6. Divide the right side of the equation by (1/3) to take the cube root:
pH2 = (0.0001875 / (1.8 x 10^-5))^(1/3)
Now, let's calculate the result using a calculator:
pH2 = (0.0001875 / (1.8 x 10^-5))^(1/3)
= 2.298
Therefore, the equilibrium partial pressure of hydrogen (pH2) is approximately 2.3 atm, which matches the result in your answer key. It seems that the answer book contains the correct value.