$4$

$($a$)$ Define chemical potential and state the requirements for

when a $($chemical$)$ reaction reaches chemical equilibrium.

$(4$ marks$)$

$($b$)$ Starting from the definition of the Gibbs energy, derive the

fundamental property relation $dG=VdP-SdT$ for a closed

system.

$(5$ marks$)$

$($c$)$ Develop and extend the fundamental property relation for

the Gibbs energy above to give the Gibbs$-$Duhem

equation. Explain the significance of the Gibbs$-$Duhem

equation for binary $($two component$)$ mixtures.

$(3$ marks$)$

$($d$)$ The Haber process for the production of ammonia requires

the following reaction

$N_2+3H_{2}2N{H}_3.$

The standard Gibbs free energy change, $G^0,$ for this

reaction at $298K$ and $1$ bar is $-33\mathrm{.}6k\frac{J}{m}ol$ of $N_2.$

What is the change in Gibbs energy, $G,$ for this reaction

at partial pressures of $0\mathrm{.}20$MPaN,$0\mathrm{.}15MPa{H}_2,$ and

$0\mathrm{.}09$MPa$(N{H}_3)?$ Is the reaction at equilibrium or does it

proceed in the forward or reverse directions? You may

assume that the components form an ideal gas.

$(8$ marks$)$