Question

Consider the following equation for a cell reaction, then:
$
  A + B \rightleftharpoons C + D,{\text{ }}{{\text{E}}^ \circ } = x{\text{ volt, }}{{\text{K}}_{eq}} = {K_1} \\
  2A + 2B \rightleftharpoons 2C + 2D,{\text{ }}{{\text{E}}^ \circ } = y{\text{ volt, }}{{\text{K}}_{eq}} = {K_2} \\
 $
A.$x = y,{\text{ }}{{\text{K}}_1} = {K_2}$
B.$x = 2y,{\text{ }}{{\text{K}}_1} = 2{K_2}$
C.\[x = y,{\text{ }}{{\text{K}}_1}^2 = {K_2}\]
D.\[{x^2} = y,{\text{ }}{{\text{K}}_1}^2 = {K_2}\]

Answer 1

Hint: We know that the value of ${K_{eq}}$ is determined by the ratio of the product of molecules or compounds present on the product side raise to the power of their coefficient to the product of molecules or compounds present on the reactant side raise to the power of their coefficient. By using it we can compare the values of ${K_1}$ and ${K_2}$. And the value of ${E^ \circ }$ does not depend on the amount of reactants and products. So it will remain the same.

Complete step by step answer:
First of all we will talk about the equilibrium constant and how to find it.
Equilibrium constant: It is defined as ratio of amount of products to the amount of reactants each amount raised to the power of its coefficient in the balanced equation.
In this question the equilibrium constants will be as follows:
${K_1} = \dfrac{{[C][D]}}{{[A][B]}}$ for $A + B \rightleftharpoons C + D$and
${K_2} = \dfrac{{{{[C]}^2}{{[D]}^2}}}{{{{[A]}^2}{{[B]}^2}}}$ for $2A + 2B \rightleftharpoons 2C + 2D$
By comparing we will get ${K_1}^2 = {K_2}$.
Now for the cell voltage is defined as:
Cell voltage: The electrical potential difference between the two electrodes of an electrochemical cell. It does not depend on the amount of reactant and product. So its value will not change. Hence $x = y$
So the answer will be ${K_1}^2 = {K_2},x = y$.
Hence option C is correct.


Note:
It seems by the equation that they both are the same as we only multiply the second equation by factor $2$. But by multiplying an equation by any factor there is a change in the value of equilibrium constant and cell voltage of the cell reaction. So do not think that they are the same. Solve them according to the theory and then mark the answer.