Calculate the boiling point temperature and vapor phase concentration of the liquid mixture consisting of $0\mathrm{.}3$ i$-$butane, $0\mathrm{.}32$ nbutane and $0\mathrm{.}38$ pentane as mole fractions at $1$ atm pressure, manually and using a computer program. Take the first default temperature value as $50$oC$.$ Using:

kij$=(1$pi $)$exp$(\backslash$beta j$1+\backslash$beta j$2$ ti$+\backslash$beta j$3$ti $+\backslash$beta j$4$ pi$+\backslash$beta j$5$ pi$2+(\backslash$beta j$6$ pi$)$ti $+(\backslash$beta i$7$ pi$2)$ti

Constants for Calculation of Fugacity Ratios Using Equation $4\mathrm{.}3-3$