Question

The equilibrium constant for the reactions $N_{2\left(g\right)}+O_{2_{(}g)}\leftrightharpoons 2N{O}_{\left(g\right)}$ and $N{O}_{\left(g\right)}\leftrightharpoons \frac{1}{2}{N}_{2\left(g\right)}+\frac{1}{2}{O}_{2_{(}g)}$ are k and $k^1$, the relation between k and $k^1$ are

• A. $k=(k^1{)}^2$
• B. $k={\left(\frac{1}{k^1}\right)}^2$
• C. $k^2=l^1$
• D. $k^1={\left(\frac{1}{k}\right)}^2$

Answer 1

The correct option is B $k={\left(\frac{1}{k^1}\right)}^2$

Let concentration of $N_2$ $=x$ ; concentration of $O_2$ $=y$ & the concentration of $NO=z$.
For the reaction; $N_2+O_2\rightleftharpoons 2NO$
$k=$ $\frac{[z{]}^2}{\left[x\right]\left[y\right]}$
For the reaction; $NO\rightleftharpoons \frac{1}{2}{N}_2+\frac{1}{2}{O}_2$
$k^1=\frac{\left[x{]}^{\frac{1}{2}}\right[y{]}^{\frac{1}{2}}}{\left[z\right]}$
Therefore, comparing $k$ & $k^1$ , the relation comes to be:

$k=(\frac{1}{k^1}{)}^2$