Question

$\text{The gas phase reaction},$
$2A\left(g\right)\to A_2\left(g\right)$ $\text{at}400K\text{has}\Delta G^{\circ }=+25.2kJmo{l}^{–1}$
The equilibrium constant, $K_C$ for this reaction is ______ × ${10}^{-2}$ (Round off to the Nearest Integer).

[Use : $R=8.3Jmo{l}^{–1}{K}^{–1}$, ln 10 = 2.3
$lo{g}_{10}2=0.30,1atm=1bar$]
[antilog (– 0.3) = 0.501]

Answer 1

Answer: 2
$\text{The gas phase reaction},$
$2A\left(g\right)\to A_2\left(g\right)$ $\text{at}400K\text{has}\Delta G^{\circ }=+25.2kJmo{l}^{–1}$

Using formula,

$\Delta G^{\circ }=–RTln{K}_P$

$25200=–2.3\times 8.3\times 400\text{log}\left(K_P\right)$

$K_P={10}^{–3.3}={10}^{–3}\times 0.501$

$K_p=5.01\times {10}^{–4}ba{r}^{–1}$

$=5.01\times {10}^{-5}\times {10}^{–4}P{a}^{–1}$
Relation of $K_p$ and $K_c$,

$K_p=K_C(RT{)}^{\Delta n_g}$
$\Delta n_g=-1$
$K_p=\frac{K_c}{RT}$

$K_p=\frac{K_c}{8.3\times 400}$

$K_C=1.66\times {10}^{–5}{m}^3/\text{mole}$

$=1.66\times {10}^{–2}\text{L/mol}$

$\approx 2$