$(3)($a$)$ Derive the Gibbs$-$Duhem equation for a two$-$component system, and show how to compute

the activity coefficient of one component from the activity coefficients measured for the other one.

$($b$)$ Consider a $S\frac{n}{H}g$ amalgam $($a non$-$ideal solution$)$ where $Sn$ is a non$-$volatile solute and $Hg$ is a

'solvent' with very low vapour pressure. In this case, instead of determining ${}_{Sn}$ from the $Sn$ vapour

pressure, it is more convenient use the electromotive forces in a battery with $S\frac{n}{H}g$ amalgam

electrodes $($a topic that we'll discuss later in the course$).$ Use $($a$),$ and the ${}_{Sn}$ activity coefficients

below, to estimate ${}_{Hg}$ for the solvent $(Hg)$ in an amalgam with molar fraction $x_{Sn}=0\mathrm{.}060$ :