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.

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.

Answer 5

To find the percent decomposition after the system has reached equilibrium, you need to calculate the concentration of phosphorous pentachloride (PCl5) at equilibrium and then determine the percent it has decomposed.

In your ICE chart, you correctly set up the initial concentration of PCl5 as 0.0192 mol/L. You also correctly set up the change in concentrations as -x for PCl5, and +x for PCl3 and Cl2, since they are both products of the reaction. The equilibrium concentrations of PCl3 and Cl2 are both x.

Using the expression for Kc, which is [PCl3][Cl2]/[PCl5], and plugging in the equilibrium concentrations:

Kc = x * x / (0.0192 - x)

You correctly solved for x as 0.010 mol/L. However, when calculating the concentration of PCl5 at equilibrium, you made a calculation error:

PCl5 concentration at equilibrium = 0.0192 - 0.010 = 0.0092 mol/L

Now, to find the percent decomposition of PCl5:

Percent decomposition = (initial concentration - equilibrium concentration) / initial concentration * 100

Percent decomposition = (0.0192 - 0.0092) / 0.0192 * 100

Percent decomposition = 0.010 / 0.0192 * 100

Percent decomposition = 52.08%

Therefore, the correct percent decomposition of PCl5 at equilibrium is approximately 52.08%.