Question

For reduction of ferric oxide by hydrogen, $F{r}_2{O}_3\left(s\right)+3H_2\left(g\right)\to 2Fe\left(s\right)+3H_{2}O\left(l\right)$
$\Delta H_{300}^o=35kJ$.The reaction was found to be too exotheric to be convenient. It is desirable that $\Delta H^o$ should be at the most $-26kJ$. At what temperature is it possible?
$C_p\left[F{e}_2{O}_2\right]=105,C_p\left[Fe\right(s\left)\right]=25,C_p\left[H_{2}O\right(l\left)\right]=75,C_p\left[H_2\right(g\left)\right]=29$ (all are in J/mol)

Answer 1

$F{e}_2{O}_3\left(s\right)+3H_2\left(g\right)⟶2Fe\left(s\right)+3H_{2}O\left(l\right)$

$\Delta H_{300}^o=-35$ $kJ$ (Since, the reaction is exothermic, given)

$C_p^{reaction}=3\times 75+2\times 25-105-87=83$ $J/mol$

$\Delta H_{T_1}^o-\Delta H_{T_2}^o={\int }_{T_2}^{T_1}{C}_p^{reaction}dT$

$\Delta H_{300}^o-\Delta H_T^o={\int }_T^{300}\frac{83\times dT}{1000}$

$⟹-9=\frac{83}{100}(300-T)$

$⟹T=408.43$ $K$