What are the values of K _ p K _ c for the following reactions at...

What are the values of

\dfrac{{K}_{p}}{{K}_{c}}

for the following reactions at

300K

respectively?

(At

300K, RT = 24 .62 {dm}^{2}atm{mol}^{- 1}

)

{N}_{2}\left(g\right) + {O}_{2}\left(g\right) ⇌ 2NO\left(g\right)

{N}_{2}{O}_{4}\left(g\right) ⇌ 2NO\left(g\right)

{N}_{2}\left(g\right) + 3{H}_{2}\left(g\right) ⇌ 2{NH}_{3}\left(g\right)

Options

A $\begin{array}{ll}24 .63 {dm}^{3}atm{mol}^{- 1}, \\ 606 .0 {dm}^{6}{atm}^{2}{mol}^{- 2}, \\ 1 .65 \times {10}^{- 3}{dm}^{- 6}{atm}^{- 2}{mol}^{2}\end{array}$
B $\begin{array}{ll}1 ,24.62 {dm}^{6}{atm}^{3}{mol}^{- 1} \\ 606 .0 {dm}^{6}{atm}^{2}{mol}^{- 2}\end{array}$
C $\begin{array}{ll}1 ,24.62 {dm}^{3}atm{mol}^{- 1} \\ 1 .65 \times {10}^{- 3}{dm}^{- 6}{atm}^{- 2}{mol}^{2}\end{array}$
D $\begin{array}{ll}1 , 4.1 \times {10}^{- 2}{dm}^{- 3}{atm}^{- 1}mol, \\ 606{dm}^{6}{atm}^{2}{mol}^{- 2}\end{array}$

C. $\begin{array}{ll}1 ,24.62 {dm}^{3}atm{mol}^{- 1} \\ 1 .65 \times {10}^{- 3}{dm}^{- 6}{atm}^{- 2}{mol}^{2}\end{array}$

∵ {K}_{P} = {K}_{C}{\left(RT\right)}^{\Delta ng}

\dfrac{{K}_{P}}{{K}_{C}} = {\left(RT\right)}^{\Delta ng}

(i)

{N}_{2} + {O}_{2} ⇌ 2NO\Delta ng = 0 ∴ \dfrac{{K}_{P}}{{K}_{C}} = 1

(ii)

{N}_{2}{O}_{4} ⇌ 2{Na}_{2}\Delta ng = 1 ∴ \dfrac{{K}_{P}}{{K}_{C}} = {\left(RT\right)}^{1} = {\left(24 .62\right)}^{1}

(iii)

{N}_{2} + 3{H}_{2} ⇌ 2{NH}_{3}\Delta ng = - 2

∴ \dfrac{{K}_{P}}{{K}_{C}} = {\left(RT\right)}^{- 2} = {\left(24 .62\right)}^{- 2} = 1 .659 \times {10}^{- 3}

≃ 1.65 \times {10}^{- 3}