Question

For the decomposition of phosphorous pentachloride to phosphorous trichloride and chlorine at 400K the KC is 1.1x10-2. Given that 1.0g of phosphorous pentachloride is added to a 250mL reaction flask, find the percent decomposition after the system has reached equilibrium.

𝑃𝐶𝑙5(𝑔)⟷𝑃𝐶𝑙3(𝑔)+𝐶𝑙2(𝑔)

I did it by an ICE Chart
I......0.0192.......0.......0
C....-x...............+x....+x
E....0.0192-x.....x.......x
Kc = [PCl3][Cl2]/[PCl5]
I then did the math to get x = 0.010 then I found the concentration of PCl5 as 0.0191-0.010 = 0.0092
For % decomposition i got 47.9% but it was wrong.

Answer 1

A quick question. I see the Kc is a relatively large number like 0.011
Your ICE chart looks OK. I suspect you did NOT solve the quadratic equation and made the assumption that 0.0192-x = 0.0192. If that's what you did you should go back, don't make that assuption, solve the quadratic, etc. If you still get the wrong answer show all your work and I'll find the error.

Answer 2

I did this:
1.1x10^-2 = x^2/(0.0192-x)
1.1x10^-2*(0.0192-x) = x^2
x^2 + 1.1x10^-2 - 2.112x10^-4 = 0
x = -b+/- sqrt(b^2 - 4ac) / 2a
I got two solutions: x1 = 0.010 and x2 = -0.02105
then I tried to find the concentration for PCl5 as 0.0192-0.010 = 0.0092.
% = 0.0092 / 0.0192 * 100 = 47.9

Answer 3

All of your math looks OK but I would do percent on the 1 g this way.

You have calculated the %PCl5 still there. So 47.9% is what's left. What decomposed is 100-47.9 = 52.1%

Answer 4

The other way you could have done this is
(PCl3/PCl5 )*100 = (0.01/0.0192)*100 = 52.08%
or (Cl2) works the same since it is 0.01 also.