Solid tin $($Sn$)$ exists in two forms: white and gray.

For the phase change: $Sn($white$)Sn($gray$)$

$H_r=-2\mathrm{.}1kJmo{l}^{-1}$ and $S_r=-7\mathrm{.}4J{K}^{-1}mo{l}^{-1}$

$($a$)$ Calculate the $G_r$ of the conversion of white tin to gray tin at $-30C.$

$($b$)$ Calculate the $G_r$ accompanying the conversion of $2\mathrm{.}50$mol of white tin to gray tin at $-30C.$

$($c$)$ Does white tin convert spontaneously to gray tin at $30C$ and $1$atm $?$

$($d$)$ Estimate the temperature at which white tin and gray tin are in equilibrium at a pressure of $1$atm.