Question

For a number of years, it was not clear whether mercury (I) ion existed in solution as $H{g}^{\oplus }$ or as $H{g}_2^{2+}$. To distinguish between these two possibilities, the following set up was made:
Hg(l) | Solution A || Solution B | Hg(l)
where solution A contained 0.263 g mercury (I) nitrate per liter and solution B contained 2.63 g mercury (I) nitrate per litre. If the measured EMF of such a cell is 0.0289 V at ${18}^{\circ }C$, then mercury (I) ions exist in the form of $H{g}_2^{2+}$.
If true enter 1, else enter 0.

Answer 1

$HgCl|\begin{array}{c}H{g}_n^{n+}\\ \left(A\right)\\ \left(0.263M\right)\end{array}||\begin{array}{c}H{g}_n^{n+}\\ \left(B\right)\\ \left(2.63M\right)\end{array}|Hg$
when n = 1 or 2
Anode : $nHg\left(l\right)\to H{g}_n^{n+}+n{e}^{-}$
Cathode : $H{g}_n^{n+}+n{e}^{-}\to nHg\left(l\right)$
$E_{cell}=E_{cell}^{\ominus }-\frac{0.059}{n}log\frac{0.263}{2.63}$
$\Rightarrow 0.0289=-\frac{0.059}{n}log\frac{1}{10}$
$\Rightarrow n=2$
Hence, mercury (I) exists as $H{g}_2^{2+}$.