Question

Calculate the equilibrium concentration ratio of $C$ to $A$ if equimolar ratio of $A$ and $B$ were allowed to come to equilibrium at $300K$.
$A\left(g\right)+B\left(g\right)\leftrightharpoons C\left(g\right)+D\left(g\right);{\Delta G}^o=-830cal$.

Answer 1

As we know,
$\Delta G^0=-RTlnK;$

$-830=-2\times 300\times lnK$

$\Rightarrow K=4$.

For reaction:
$A+B⟶C+D$
initial mole: 1 1 0 0
final mole: 1 - $\alpha$ 1 - $\alpha$ $\alpha$ $\alpha$

For this reaction:

$K_{eq}=\frac{\left[C\right]\times \left[D\right]}{\left[A\right]\times \left[B\right]}=\frac{\left(\alpha \right)\left(\alpha \right)}{(1-\alpha )(1-\alpha )}=4$ so

Ratio of C to A is $=\frac{\left(\alpha \right)}{(1-\alpha )}=2$