Question

Data given for the following reaction is as follows:

$Fe{O}_{\left(s\right)}+C_{\left(graphite\right)}⟶F{e}_{\left(s\right)}+C{O}_{\left(g\right)}$

Substance	${\Delta }_f{H}^o$ $\left(kJ{\text{mol}}^{-1}\right)$	$\Delta S^o$ $\left(J{\text{mol}}^{-1}{K}^{-1}\right)$
$Fe{O}_{\left(s\right)}$	-266.3	57.49
$C_{\left(graphite\right)}$	0	5.74
$F{e}_{\left(s\right)}$	0	27.28
$C{O}_{\left(g\right)}$	-110.5	197.6

The minimum temperature in K at which the reaction becomes spontaneous is

Answer 1

$Fe{O}_{\left(s\right)}+C_{\left(graphiite\right)}⟶F{e}_{\left(s\right)}+C{O}_{\left(g\right)}$

${\Delta }_f{H}^o\left(reaction\right)=(0+(-110.5\left)\right)-(-266.3)=155.8kJ/mol$

$\Delta S^o\left(reaction\right)=27.28+197.6-(57.49+5.74)=224.88=63.23\Delta S^o\left(reaction\right)=161.65J{\text{mol}}^{-1}{K}^{-1}$

For spontaneity
$\Delta G=\Delta H-T\Delta S(\Delta G=0)$

$\Delta H=T\Delta S$

$T=\frac{\Delta H}{\Delta S}=\frac{155.8\times 1000}{161.65}=963.8K$

$\simeq$ 964 (nearest integer)