A Fe$-$P liquid alloy is in equilibrium with a solid solution and

a gas phase at $1419C.$ The solid solution behaves ideally and

contains two components, CaO and $CaP_{2O8}(3$CaO.P$2$O$5).$

The $P$ content in the solid solution is $1\mathrm{.}9wt.\%.$ The gas phase

includes $9\mathrm{.}110-10$atm oxygen. The activity of $P$ in the alloy,

with respect to the $1wt.\%$ in $Fe$ standard state $($ in

$Fe)$ is $11\mathrm{.}99.$ The given data follows:

$\}\{2O8\}(s),GT=-1083210$

$+237\mathrm{.}5T(\frac{J}{m}ol),$

$\frac{1}{2}P2(g)=P(1wt\%inFe),GT=$

$-122200-19\mathrm{.}2T(\frac{J}{m}ol),$

a$)$ Calculate $GT$ for the reaction $P2(g)+\frac{5}{2}O2(g)=$

$P2O5(g)$ at $14ZBC.$

b$)$ Calculate the activity of $P$ in the alloy with respect to the

Henrian std$.$ state $($hP$)$ at $1419C.$

c$)$ Calculate the activity of $P$ in the alloy with respect to the

Raoultian std$.$ state $($aP$)$ at $1419C($if $P=0\mathrm{.}019).$

d$)$ Calculate the activity of $Fe$ in the alloy $(aFe)$ at

obeys Raoult's Law$).$

$($The atomic weight: $O=16\mathrm{.}0,P=31\mathrm{.}0,Ca=40\mathrm{.}0,Fe=55\mathrm{.}9$

g$)(R=8\mathrm{.}314\frac{J}{m}ol.K)$