Question

In the reaction $C(s) + C{O_2} \rightleftharpoons 2CO(g)$, the equilibrium pressure is 12 atm. If 50% of $C{O_2}$ reacts then ${K_p}$ will be:
A.12 atm
B.16 atm
C.20 atm
D.24 atm

Answer 1

Hint:Equilibrium constant is calculated from the partial pressure of reaction. ${K_p}$ is the equilibrium constant used to express the partial pressure of the reactant gases and the product gases. Equilibrium constant is a unitless number.

Complete step by step answer:
Pressure is the force applied to a surface of an object or a particle or a wall per unit area over which the force was applied.
SI unit of pressure is Pascal (Pa).
Partial pressure: In a mixture of gases, each gas has a partial pressure which is the individual pressure of that gas constituent. The total pressure of a given mixture is the sum of the partial pressures of all the gasses present in that mixture.
Let P be the total pressure.
P (total) = 12 atm
Let x be the initial partial pressure of carbon dioxide.
If half of carbon dioxide reacted, then carbon dioxide is $\dfrac{x}{2}$ and carbon monoxide is x
Then,
$\dfrac{x}{2}$ + x = 12
$1.5$ x = 12
Therefore, the value of x will be,
x = 8
Hence, we can say, partial pressure of carbon dioxide that is $p(C{O_2})$ is four atm and partial pressure of carbon monoxide that is $p(CO)$ is eight atm.
Initial partial pressure of carbon dioxide was 8 atm and now 4 atm is left after it reacted.
And the pressure of carbon monoxide is two times the pressure of carbon dioxide, which is 8atm.
If, $aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)$
Then, ${K_p} = \dfrac{{{P_C}^cP_D^d}}{{P_A^aP_B^b}}$
Hence, from the given reaction,
${K_p} = \dfrac{{p{{(CO)}^2}}}{{p(C{O_2})}}$
${K_p} = \dfrac{{{8^2}}}{4} = 16$
So, equilibrium constant that is ${K_p}$ = 16 atm.

Therefore, the correct option is B.

Note:
The state in which the rate of the forward reaction is the same as the rate of the backward reaction, is called chemical equilibrium. In chemical equilibrium, there is no net change of reactant and product concentration. The other name of chemical equilibrium is dynamic equilibrium.