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 0.1450 M and a Cl2 concentration of 0.177 M at 1000 K.

What is the equilibrium concentration of Cl2 at 1000 K?

Answer 1

Given that; Kc = 255 at 1000 K. A reaction mixture initially contains a CO concentration of 0.1450 M and a Cl2 concentration of 0.177 M at 1000 K

CO (g) + Cl2 (g) ⇌ COCl2 (g)

Kc = [COCl2]/ [CO][Cl2]

ICE-Table
........... [CO]......... [Cl₂].......... [COCl₂]
I.......... 0.1450....... 0.177............. 0
C........... -x............ -x...............+x
E....... 0.1450 -x.... 0.177-x.......... x

Kc = [COCl2]/ [CO][Cl2]

255 = x/ (0.1450 –x)(0.177-x)

255 = x / 0.0256 -0.1450 x-0.177 x+ x^2

6.54 -82.11 x +255 x^2=x

255X^2 -83.11 x+6.54= 0

X1= 0.193113037971041

X2=0.132808530656409

First solution is infeasible because it would lead to negative concentrations for CO and Cl₂

Hence,
a) [CO] = 0.1450 M - x = 0.1450 M - 0.133 = 0.012 M

b) [Cl₂] = 0.177 M - x = 0.176 M - 0.133 = 0.043 M

c) [COCl₂] = x = 0.133 M

Cross check

Kc = [COCl2]/ [CO][Cl2]

Kc = 0.133/ 0.012*0.043

= 255