Question

At $300K$,the equilibrium partial pressure of $\mathop {CO}\nolimits_2 $ , $CO$ and ${O_2}$ are $0.6$ ,$0.4$ and $0.2$ atmospheres respectively . $\mathop K\nolimits_p $ for the reaction ,
$2C{O_2}(g) \rightleftarrows 2CO(g) + {O_2}(g)$ is
A.$0.088$
B.$0.0533$
C.$0.133$
D.$0.177$

Answer 1

Hint: ${K_p}$ is the equilibrium constant in terms of partial pressure of gases present in reactants and products . It is a unit of less quantity . It is also defined as the product of the partial pressure of the gaseous products divided by the gaseous reactants raised to the power of their respective stoichiometric coefficient in the balanced chemical equation .

Complete step by step answer:
The given reaction is : $2C{O_2}(g) \rightleftarrows 2CO(g) + {O_2}(g)$ .
Above reaction has two gaseous products and one gaseous reactant . ${K_p}$ is calculated as the product of the partial pressure of the gaseous products divided by the gaseous reactants raised to the power of their respective stoichiometric coefficient in the balanced chemical equation . Now if $a$ is partial pressure of $\mathop {CO}\nolimits_2 $ , $b$ is the partial pressure of $CO$ and $c$ is the partial pressure of ${O_2}$, then as per definition $\mathop K\nolimits_p $$ = \dfrac{{{{(b)}^2}(c)}}{{{{(a)}^2}}}$ .
According to the question : \[a = 0.6\], $b = 0.4$ and $c = 0.2$\[\]
So ${K_p} = \dfrac{{{{(0.4)}^2} \times (0.2)}}{{{{(0.6)}^2}}}$$ = 0.088$.
Hence option (A) is correct .
 ${K_p}$ is an equilibrium constant and any equilibrium constant does not change by change in pressure of the system or by change in concentration . Equilibrium constants depend upon temperature only . It changes only by change in temperature . If we change pressure or concentration then this will affect the position of equilibrium only . As per Le Chatelier’s principle the position of equilibrium moves in such a way as to tend to undo the change that we have made .

Note:
${K_p}$${K_c}$ is also an equilibrium constant in terms of concentration of reactants and products . If it is given the question or concentration of every reactants and products is given the question then we can easily calculate ${K_p}$ also by using the relation : ${K_p} = {K_c} \times {(RT)^{\vartriangle {n_g}}}$