Question

Consider the following equations for a cell reaction.
$A + B \rightleftharpoons C + D , \, E ^{\circ}=x$ volt, $K _{ eq }= K _{1}$
$2 A +2 B \rightleftharpoons 2 C +2 D ,\, E ^{\circ}=y$ volt, $K _{ eq }= K _{2}$
Then,

• A. $x=y,\, K _{1}= K _{2}$
• B. $x=y,\, K_{1}^{2}=K_{2}$
• C. $x=2 y,\, K _{1}=2 K _{2}$
• D. $x^{2}=y,\, K _{1}^{2}= K _{2}$

Answer 1

Answer: (B)

When a chemical reaction is multiplied/divided EMF of the changed equation remains constant but equilirbium constant is raised to power of that change.

Thus, $x=y$

$A + B \rightarrow C + D,$

$K_{1}= \frac{[C][D]}{[A][B]}$

$2 A +2 B \rightarrow 2 C +2 D,$

$K_{2}=\frac{[C]^{2}[D]^{2}}{[A]^{2}[B]^{2}}=K_{1}^{2}$