Question

The equilibrium constant, K, for the following reaction is 2.52x10-2 at 620 K. COC12(g) * CO(g) + Cl2(g) An equilibrium mixture of the three gases in a 10.5 L container at 620 K contains 0.264 M COCl2, 8.15x10-2 M CO and 8.15x10-2 M Cl. What will be the concentrations of the three gases once equilibrium has been reestablished, if the equilibrium mixture is compressed at constant temperature to a volume of 4.32 L? M [COCl2] = [CO] = [Cl2] = M

Answer 1

Ans :-

No. of moles of COCl2 = Molarity x Volume in L = 0.264 M x 10.5 L = 2.772 mol

No. of moles of each CO and Cl2 = Molarity x Volume in L = 8.15 x 10-2 M x 10.5 L = 0.85575 mol

Addition of 4.32 L, volume will change the concentration of each species and therefore new initial concentration of each species is :

Initial concentration of COCl2 = Moles/Volume in L = 2.772 mol / 4.32 L = 0.642 M

and

Initial concentration of each CO and Cl2 = Moles/Volume in L = 0.85575 mol / 4.32 L = 0.198 M

Now, ICE table is :

......................................COCl2 (g) <-------------------------> CO (g).....................+.........................Cl2 (g)

Initial.............................0.642 M..........................................0.198 M............................................0.198 M

Change..........................+y.......................................................-y......................................................-y

Equilibrium.................(0.642+y) M........................................(0.198-y) M.................................(0.198-y) M

Where, y = Amount dissociated per mole.

Expression of Equilibrium constant i.e. Kc (which is equal to the product of the molar concentration of products divided by product of the molar concentration of reactants raise to power their stoichiometric coefficient when reaction is at equilibrium stage).

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

2.52 x 10-2 = (0.198-y)2/(0.642+y)

y2 - 0.396 y + 0.039204 = 0.0161784 + 0.0252 y

y2 - 0.4212 y + 0.0230256 = 0

On solving

y = 0.06456

Therefore,

Equilibrium concentrations of each CO and Cl2 = 0.198-y = 0.198 - 0.06456 = 0.133 M

and

Equilibrium concentrations of COCl2 = 0.642+y= 0.642+ 0.06456 = 0.707 M

So,

[COCl2] = 0.707 M

[CO] = 0.133 M

and

[Cl2] = 0.133 M