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 0.1550 M and a Cl2 concentration of 0.172 M at 1000 K.

What is the equilibrium concentration of CO at 1000 K?

What is the equilibrium concentration of Cl2 at 1000 K?

What is the equilibrium concentration of COCl2 at 1000 K?

Answer 1

Answer: The equilibrium concentration of CO at 1000 K is 0.016 M , the equilibrium concentration of $Cl_2$ at 1000 K is= 0.033 M  and the equilibrium concentration of $COCl_2$ at 1000 K is 0.139 M  

Explanation:

Initial concentration of $CO=0.1550M$  

Initial concentration of $Cl_2=0.172M$  

The given balanced equilibrium reaction is,

                            $CO(g)+Cl_2\rightleftharpoons COCl_2(g)$

Initial conc.           0.1550 M           0.172 M          0 M

At eqm. conc.    (0.1550-x) M      (0.172-x) M     (x) M

The expression for equilibrium constant for this reaction will be,

$K_c=\frac{[COCl_2]}{[CO][Cl_2]}$

$K_c=\frac{x}{(0.1550-x)(0.172-x)}$

we are given : $K_c=255$

$255=\frac{x}{(0.1550-x)(0.172-x)}$

Now put all the given values in this expression, we get :

$x=0.139$

Thus the equilibrium concentration of CO at 1000 K is= (0.1550-x) M =(0.1550-0.139) M = 0.016 M  

Thus the equilibrium concentration of $Cl_2$ at 1000 K is= (0.172-x) M =(0.172-0.139) M = 0.033 M  

Thus the equilibrium concentration of $COCl_2$ at 1000 K is= x M = 0.139 M  

Answer 2

The equilibrium concentration will be:

(a) 0.016 M

(b) 0.033 M

(c) 0.139 M

Given reaction is:

• $CO+Cl_2 \Leftrightarrow COCl_2$

  0.1550  0.172         O $\rightarrow$ initial

0.1550-x   0.172-x      x $\rightarrow$ Equilibrium

Now,

→ $K_c = \frac{[COCl_2]}{[CO][Cl_2]}$

By substituting the values, we get

  $255= \frac{x}{(0.1550-x)(0.172-x)}$

        $= \frac{x}{0.0267-0.155x-0.172x+x^ 2}$

 $255x^2- 83.385x+6.808 = x$

 $255x^2-84.385 x+6.808=0$

                                     $x = 0.192$

or,

                                     $x = 0.139$ (correct value)

(a)

Equilibrium constant of [CO],

= $0.1550-x$

= $0.016 \ M$

(b)

Equilibrium constant of [Cl₂],

= $0.172-x$

= $0.033 \ M$

(c)

Equilibrium constant of [COCl₂],

= $x$

= $0.139 \ M$

Thus the above responses are correct.

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