Question

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K) at which the reduction of cassiterite by coke would take place.

At $298K$:${\Delta }_f{H}^{\circ }\left(Sn{O}_2\right(s\left)\right)=-581.0kJmo{l}^{-1},{\Delta }_f{H}^{\circ }\left(C{O}_2\right(g\left)\right)=-394.0kJmo{l}^{-1}$
$S^{\circ }\left(Sn{O}_2\right(s\left)\right)=56.0J{K}^{-1}mo{l}^{-1},S^{\circ }\left(Sn\right(s\left)\right)=52.0J{K}^{-1}mo{l}^{-1},S^{\circ }\left(C\right(s\left)\right)=6.0J{K}^{-1}mo{l}^{-1},S^{\circ }\left(C{O}_2\right(g\left)\right)=210.0J{K}^{-1}mo{l}^{-1}$
Assume that the enthalpies and the entropies are temperature independent.

Answer 1

$Sn{O}_2\left(s\right)+C\left(s\right)\to C{O}_2+Sn$
$\Delta H=({\Delta }_{f}H{)}_P-({\Delta }_{f}H{)}_R$
$=(–394+581)kJ/mol$
$=+187kJ/mol$

$\Delta S=(S{)}_P-(S{)}_R$
$=(210+52)–(56+6)J/Kmol$

$=200J/kmol$

For any reaction to take place, $\Delta G<0$
The minimum temperature is where $\Delta G=0$
$\Delta G=0=\Delta H-T\Delta S$
$187\times 1000–200T=0$

$T=935K$