Question

The value of $K_c$ for the following reaction is $1.8\times {10}^{-2}$.

$2NO\left(g\right)\to N_2\left(g\right)+O_2\left(g\right)$

Calculate the value of $K_c$ for the reaction:

$\frac{1}{2}{N}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\to NO\left(g\right)$

• A. $7.6$
• B. $8.5$
• C. $6.5$
• D. $2$

Answer 1

The correct option is A $7.6$

$2NO\left(g\right)\to N_2\left(g\right)+O_2\left(g\right)$ $........i$
Where, $Kc=1.8\times {10}^2$
$\frac{1}{2}{N}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\to NO\left(g\right)$ $...............ii$
For equation $\left(i\right)$,
$\frac{\left[N_2\right]\left[O_2\right]}{[NO{]}^2}=K_c$ $.........iii$
For equation $\left(ii\right)$,
$K_c^{{}^{\prime }}=\frac{\left[NO\right(g\left)\right]}{\left[N_2{]}^{\frac{1}{2}}\right[O_2{]}^{\frac{1}{2}}}$
On squaring,

$(K_c^{{}^{\prime }}{)}^2=\frac{\left[NO\right(g){]}^2}{\left[N_2\right]\left[O_2\right]}$ $................iv$

From equation $\left(iii\right)$ and $\left(iv\right),$

$K_c\times (K_c^{{}^{\prime }}{)}^2=1$

$K_c^{{}^{\prime }}=\frac{1}{\sqrt{K_c}}=\frac{1}{\sqrt{1.8\times {10}^2}}=7.6$