Question

For the following reactions
$A \rightleftharpoons B{\text{ }}{{\text{K}}_C} = 2$
$B \rightleftharpoons C{\text{ }}{{\text{K}}_C} = 3$
$C \rightleftharpoons D + E{\text{ }}{{\text{K}}_C} = 5$
Find \[{K_C}\] for the following reaction $A \rightleftharpoons D + E$
A.$2 + 3 + 5$
B.$\dfrac{{2 + 3}}{5}$
C.${{5 \times 3}}{2}$
D.$2 \times {\text{3}} \times {\text{5}}$

Answer 1

Hint: The equilibrium constant ${K_c}$ is the ratio of concentration of products and the concentration of reactions each raised to its stoichiometric coefficient. Hence, whenever we add two reactions, the ${K_c}$ for the overall reaction is the product of the individual ${K_c}$ of the two reactions. Similarly, when reactions are subtracted, , the ${K_c}$ for the overall reaction is the ratio of the individual ${K_c}$ of the two reactions.

Complete answer:
1) Firstly we have to find the combination of how we can add/subtract the given above 3 reactions that would generate the given reaction whose ${K_c}$ is to be calculated.
2) we can see that in the given question reactions:
$A \rightleftharpoons B{\text{ }}{{\text{K}}_C} = 2 - - - - \to a$
$B \rightleftharpoons C{\text{ }}{{\text{K}}_C} = 3 - - - - - \to b$
$C \rightleftharpoons D + E{\text{ }}{{\text{K}}_C} = 5 - - - - \to c$
if we add up reaction a,b and c, the resultant reaction would be the one whose ${K_c}$ is required in the question.
3) Hence, adding reaction a,b and c, we get $A \rightleftharpoons D + E$.
4) Now, when the reactions are added, their ${K_c}$ get multiplied. Hence, in this given operation, it can be clearly inferred that the ${K_c}$ for the overall reaction will be the product of the ${K_c}$ of the individual reaction.
5) thus, multiplying the ${K_c}$ of the individual reactions, we get:
${K_c}$= $2 \times 3 \times 5$
Thus, the correct option is option (D).

Note:
The following method is to be employed only when all the constituent reactions are in equilibrium, and only the ${K_c}$ can be multiplied upon the addition of reaction. We cannot ${K_c}$ with ${K_p}$. Also, keep the stoichiometry of the reactions in mind. There may be few reactions where the stoichiometry of the final reaction is different from the one obtained after performing addition/subtraction of the other given reactions.