If the initial pressure of HD(g) is 8.913 atm, calculate the % decomposition of HD(g) when the reaction comes to equilibrium according to the balanced equation. The value of Kp at 1000 K is 0.26. The initial pressure of the reaction products is 0 atm.
2HD(g) = H2(g)+D2(g)
So I set it up using the ice method. with the i step already given. So for the c step, I put -2x going in the forward direction arrow and +x under H2 and D2. Then I set up the e step with (8.913-2x) under 2HD and x under the products. I then set up the Kp equation with equilibrium products over reactants. But I don't know if that last step is correct or not. If it isn't, how am I supposed to proceed?
You're right on target. Solve the equation you've set up. Then
% decomp = (2x/8.913)*100 = ?
Yes, but what do I put in for x? That's were I got stuck.
oh wait. I set up the equation
0.26=(x^2)/(8.913-2x).
my x=2.032476713
then I used the % decomp equation and got...0.45607017 so 45.6%
Yes, x comes from the solution of your ICE table. I didn't check you math but that's what you do.
Your steps so far are correct. In the equilibrium expression, the products are always written in the numerator and the reactants in the denominator, with each species raised to the power of its coefficient in the balanced equation. So, in this case, the equilibrium expression would be:
Kp = [H2] * [D2] / [2HD]^2
Since the initial pressure of the reaction products is 0 atm, the concentrations of H2 and D2 at equilibrium would be represented as "x". The concentration of 2HD at equilibrium would be (8.913 atm - 2x).
Therefore, the equilibrium expression would be:
Kp = x * x / (8.913 -2x)^2
Now, you can substitute the given equilibrium constant and solve for "x".
0.26 = x^2 / (8.913 - 2x)^2
You can cross-multiply to get rid of the denominator:
0.26 * (8.913 - 2x)^2 = x^2
Now, you can solve this equation for "x" using algebraic methods like factoring or quadratic formula. Once you find the value of "x", you can use it to determine the % decomposition of HD.
% decomposition = (x / initial pressure of HD) * 100
Hope this helps!