Question

Calculate the boiling point of bromine from the following data: $△H^{o}and△S^o$ values of $B{r}_2\left(l\right)\to B{r}_2\left(g\right)$ are 30.91 $kJ/mol$ and 93.2 $Jmo{l}^{-1}{K}^{-1}$ respectively. (Assume that $△Hand△S$ do not vary with temperature.)

Answer 1

Consider the process: $B{r}_2\left(l\right)\to B{r}_2\left(g\right).$
The b.p. of a liquid is the temperature at which the liquid and the pure gas coexist at equilibrium at 1 atm.
$\therefore △G=0.$
As it is given that $△Hand△S$ do not change with temperature $△H=△H^o=30.91kJmo{l}^{-1}$
$△S=△S^o=93.2Jmo{l}^{-1}{K}^{-1}=0.0932kJmo{l}^{-1}{K}^{-1}$
We have,
$△G=△H-T△S=0$
$\therefore T=\frac{△H}{△S}=\frac{30.91}{0.0932}=331.6K$
This is the temperature at which the system is in equilibrium, that is, the b.p. of bromine.