Question

For the following reaction, Kc = 255 at 1000 K.
CO (g) + Cl2 (g) ⇌ COCl2 (g)
A reaction mixture initially contains a CO concentration of 0.1470 M and a Cl2 concentration of 0.172 M at 1000 K.

Part A

What is the equilibrium concentration of CO at 1000 K?

Express your answer in molarity to three significant figures.

Part B

What is the equilibrium concentration of Cl2 at 1000 K?

Express your answer in molarity to three significant figures.

Part C

What is the equilibrium concentration of COCl2 at 1000 K?

Answer 1

Given,

K_c = 255 at 1000 K

Initial concentrations, [CO]_i = 0.1470 M, [Cl₂]_i = 0.172 M

At equilibrium, K_c = [COCl₂] / [CO] [Cl₂]

Condition	[CO]	[CO]	[COCl2]
Initial	0.1470	0.172	0
Change	-x	-x	+x
Equilibrium	0.1470-x	0.172-x	x

K_c = x / (0.1470-x)(0.172-x)

or 255 = x / (x² - 0.319x + 0.0253 )

   255x² - 82.345 x + 6.452 = 0

solving for x,

x = [−b ± √(b²−4ac)] / 2a

   = [- (-82.345) ± √ {(-82.345)2 - 4(255)(6.452)}] / 2(255)

   = [82.345 ± 14.13] / 510

now, x = 0.189 or 0.133

Because there are two possible solutions, we have to determine which is the real solution.

[CO]_i - 0.189 = 0.1470 - 0.189 = - 0.042

[Cl₂]_i - 0.189 = 0.172 - 0.189 = - 0.017

So, possible value of x is 0.133

Thus at equilibrium (at 1000 k),  

Part A : [CO] = 0.01470 - x = 0.1470 - 0.133 = 0.014 M

Part B : [Cl₂] = 0.172 - 0.133 = 0.039 M

Part C : [COCl₂] = 0.133 M