# For the reaction

Question:

For the reaction $2 \mathrm{H}_{2}(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ the observed rate expression is, rate $=\mathrm{k}_{\mathrm{f}}[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right]$. The rate expression for the reverse reaction is:

1. $\mathrm{k}_{\mathrm{b}}\left[\mathrm{N}_{2}\right]\left[\mathrm{H}_{2} \mathrm{O}\right]^{2}$

2. $\mathrm{k}_{\mathrm{b}}\left[\mathrm{N}_{2}\right]\left[\mathrm{H}_{2} \mathrm{O}\right]^{2} /[\mathrm{NO}]$

3. $\mathrm{k}_{\mathrm{b}}\left[\mathrm{N}_{2}\right]\left[\mathrm{H}_{2} \mathrm{O}\right]$$\mathrm{k}_{\mathrm{b}}\left[\mathrm{N}_{2}\right]\left[\mathrm{H}_{2} \mathrm{O}\right]^{2} /\left[\mathrm{H}_{2}\right]$

4. $\mathrm{k}_{\mathrm{b}}\left[\mathrm{N}_{2}\right]\left[\mathrm{H}_{2} \mathrm{O}\right]^{2} /\left[\mathrm{H}_{2}\right]$

Correct Option: , 4

Solution:

Rate of forward reaction $=\mathrm{k}_{\mathrm{f}}[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right]^{2}$

Observed rate $=\mathrm{k}_{\mathrm{f}}[\mathrm{NO}]^{2}\left[\mathrm{H}_{2}\right]$

Observed rate $=\frac{\text { Rate of forward reaction }}{\left[\mathrm{H}_{2}\right]}$

$\therefore$ Rate of backward reaction $=\frac{k_{b}\left[\mathrm{~N}_{2}\right]\left[\mathrm{H}_{2} \mathrm{O}\right]^{2}}{\left[\mathrm{H}_{2}\right]}$