Consider a mixture consisting of $25\%$ mol n$-$pentane $(1),45\%$ mol $n-$hexane $(2),$ and $30\%$ mol n$-$heptane $(3).$

Saturation pressures of components:

$Ln(P_1)=10\mathrm{.}422-\frac{26799}{RT},Ln(P_2)=10\mathrm{.}456-\frac{29676}{RT},Ln(P_3)=11\mathrm{.}431-\frac{35200}{RT}$

$P_{i}in$ bar; $TinK$;$R=8\mathrm{.}314\frac{J}{\text{m}\text{o}\text{l}-K}$

a$)$ Estimate the dew point and bubble point temperatures at $1\mathrm{.}013$ bar $(1$atm$).$