The phase diagram for the system Ga– GaP is shown in Figure 13.13. Calculate the partial pressure of phosphorus vapor, $p_{P_2}$ , exerted by the GaP liquidus melt at 1273 K. The standard Gibbs free energy change for the reaction
$Ga_{(l)}+\frac{1}{2}p_{2(g)}=GaP_{(s)}$
is
$\Delta G^\circ =-178,800+96.2T+3.1T\ln T-3.61\times10 ^{-3}T^2-\frac{1.035\times 10^{5}}{T}$

Question

The phase diagram for the system Ga– GaP is shown in Figure 13.13. Calculate the partial pressure of phosphorus vapor, $p_{P_2}$ , exerted by the GaP liquidus melt at 1273 K. The standard Gibbs free energy change for the reaction

Ga_{(l)}+\frac{1}{2}p_{2(g)}=GaP_{(s)}

is

\Delta G^\circ =-178,800+96.2T+3.1T\ln T-3.61\times10 ^{-3}T^2-\frac{1.035\times 10^{5}}{T}

[latex]Ga_{(l)}+\frac{1}{2}p_{2(g)}=GaP_{(s)} [/latex]

is

[latex]\Delta G^\circ =-178,800+96.2T+3.1T\ln T-3.61 imes10 ^{-3}T^2-\frac{1.035 imes 10^{5}}{T} [/latex]

Accepted Answer

At 1273 K,

[latex]\Delta G^\circ _{1273 K}=-3.968 imes 10^{4}J=-8.3144 imes 1273\ln K_{1273 K} [/latex]

which gives

[latex] K_{1273 K}=24.97=\frac{a_{GaP}}{a_{Ga}p^{1/2}_{P_2}} [/latex]

In the preceding expression, [latex] a_{Ga} [/latex] is the activity of Ga in the liquidus melt with respect to liquid Ga as the standard state, and, since the liquidus melt is in equilibrium with pure solid GaP, the activity of GaP, [latex] a_{GaP} [/latex], is unity. The variation of the liquidus composition with temperature in the range 1173– 1373 K can be expressed as

[latex] \ln X_P=-\frac{16,550}{T}+9.902 [/latex]

which gives the liquidus composition at 1273 K as [latex]X_P=0.0045 [/latex]. In view of the low solubility of the solute P, it can be assumed that the solvent Ga obeys Raoult’ s law, in which case the activity of Ga in the liquidus melt is 0.955, and hence the partial pressure of [latex]P_2 [/latex] exerted by the liquidus melt is [latex]p_{P_2}=\left\lgroup\frac{1}{24.97 imes 0.955} ight group^2 [/latex]

[latex]=1.76 imes 10^{-3} [/latex] atm

Question 13.6.1: The phase diagram for the system Ga– GaP is shown in Figure ...

Related Answered Questions