I noticed that this question has been posted on this forum previously, however, I couldn't see that an actual numerical answer was given. I was just wondering if the following process seemed right, and, as such, if the solution is correct (I have no way of checking). I haven't covered this concept yet in my Chemistry class, but I thought that I'd give it a go anyway:

"Consider the reaction A(g) + D(g) ::equil:: C(g) for which K = 130. Assume that 0.406 mol C(g) is placed in a container fitted with a piston. The temperature is 300.0 K, and the barometric pressure on the piston (which is assumed to be massless and frictionless) is constant at 1.00 atm. The original volume (before the 0.406 mol C(g) begins to decompose) is 10.00 L. What is the volume in the cylinder at equilibrium?

My working was as such:

Vi = 10.00 L
P = 101.325 kPa
T = 300.0 K
ni = 0.406 mol C(g)

CC(g) = 0.406/10 = 0.0406 mol/L

K = [C]/[A][D]
130 = 0.0406/x2
x = 0.0177 mol/L

x = y/Vf
0.0177 = x/Vf

nf = 0.406 - y + y + y = 0.406 + y

PVf = nfRT
101.325Vf = (0.406 + y) × 8.31 × 300.0
Vf = 24.604y + 9.989

0.0177 = y/(24.604y + 9.989)
0.177 = 0.565y
.. y = 0.312 mol

0.0177 = y/Vf
Vf = y/0.0177 = 0.312/0.0177 = 17.674 L

If anyone could let me know if this process is right, that would be greatly appreciated. I'm not certain if the volume is allowed to change in the equilibrium expression (as I have assumed).

Thanks, Small Bio