Question

For reduction of ferric oxide by hydrogen,
${Fe}_2{O}_3\left(s\right)+3H_2\left(g\right)\to 2Fe\left(s\right)+3H_{2}O\left(l\right)$ :
$\Delta H_{300}^o=-26.72kJ$. The reaction was found to be too exothermic. To be convenient. it is desirable that $\Delta H^o$ should be at the most - 26 kJ . At what temperature difference it is possible ?
$C_p\left[{Fe}_2{O}_3\right]=105,C_p\left[Fe\right(s\left)\right]=25,C_p\left[H_{2}O\right(l\left)\right]=75,C_p\left[H_2\right(g\left)\right]=30\left(\text{all are in J/mol}\right)$

Answer 1

$\begin{array}{c}\Delta H=\int CpdTor\int DCpdT\\ \Delta H=-26KJ\\ \Delta Cp=3C{p}_{H_{2}O}+2C{p}_{Fe}-3C{p}_{H_2}-C{p}_{Fe{O}_3}\\ \Rightarrow 3\times 75+2\times 25-3\times 30-105\\ \Rightarrow 75+50-90-105\Rightarrow -70J\\ \Delta H=\int 70dT\\ dT=\frac{DH}{-70}\Rightarrow \frac{-26KJ}{-70J}\Rightarrow \frac{26\times 1000}{70}=371.43\\ dT=371.43\end{array}$