Question

Question: Zirconium is used in the fuel rods of most nuclear power plants. The following half-cell reduction potential applies to aqueous acidic solution:

${\mathbf{ZrO}}_{\mathbf{2}}\mathbf{+}\mathbf{4}{\mathbf{H}}_{\mathbf{3}}{\mathbf{O}}^{\mathbf{+}}\mathbf{+}\mathbf{4}{\mathbf{e}}^{\mathbf{-}}\mathbf{\to }\mathbf{Zr}\mathbf{+}\mathbf{6}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}{\mathbf{E}}^{\mathbf{\circ }}\mathbf{=}\mathbf{-}\mathbf{14}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{V}$

(a)Predict whether zirconium can reduce water to hydrogen. Write a balanced equation for the overall reaction.

(b)Calculate$\mathbf{∆}{\mathbf{E}}^{\mathbf{\circ }}$and $\mathbf{K}$for the reaction in part (a).

(c)Can your answer to part (b) explain the release of hydrogen in the Three Mile Island accident and the much greater release of hydrogen (which subsequently exploded) at Chernobyl?

Short answer

1. The balanced equation for the reduction of water by zirconium is given below.$\mathrm{Zr}\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)\to {\mathrm{ZrO}}_2\left(\mathrm{s}\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)$
2. $∆{\mathrm{E}}^{\circ }=14.3\mathrm{V}$and $\mathrm{K}=4\times {10}^{96}$
3. The reaction is very spontaneous and occurs readily as predicted by the high value of the equilibrium constant. The high equilibrium constant of the reaction accounts for the release of large amount of hydrogen gas.

Step-by-step solution

Balanced equation for the redox reaction

A redox reaction is such a reaction in which oxidation and reduction takes place simultaneously.

The half-cell reduction potential in acidic medium is given for Zirconium.

${\mathrm{ZrO}}_2+4{\mathrm{H}}_3{\mathrm{O}}^{+}\left(\mathrm{aq}\right)+4{\mathrm{e}}^{-}\to \mathrm{Zr}\left(\mathrm{s}\right)+6{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right){\mathrm{E}}^{\circ }=-14.3\mathrm{V}$

Let us write down the half-cell reaction for reduction of water.

role="math" localid="1661511405020" $2{\mathrm{H}}_3{\mathrm{O}}^{+}\left(\mathrm{aq}\right)+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right){\mathrm{E}}^{\circ }=0.0$

Balancing and combining the two half-cell reaction we can get the overall reaction.

role="math" localid="1661511724252" $\frac{\begin{array}{c}\mathrm{Zr}\left(\mathrm{s}\right)+6{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\to {\mathrm{ZrO}}_2+4{\mathrm{H}}_3{\mathrm{O}}^{+}\left(\mathrm{aq}\right)+4{\mathrm{e}}^{-}\\ 4{\mathrm{H}}_3{\mathrm{O}}^{+}\left(\mathrm{aq}\right)+4{\mathrm{e}}^{-}\to 2{\mathrm{H}}_2\left(\mathrm{g}\right)+4{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\end{array}}{\mathrm{Zr}\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)\to {\mathrm{ZrO}}_2\left(\mathrm{s}\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)}$

∆E∘ and K

$\begin{array}{rcl}∆{\mathrm{E}}^{\circ }& =& {\mathrm{E}}_{\mathrm{reduction}}^{\circ }-{\mathrm{E}}_{\mathrm{oxidation}}^{\circ }\\ & =& 0-\left(-14.3V\right)\\ & =& 14.3V\end{array}$

For a cell reaction to be spontaneous, $∆G^{°}<0$. As we know, $∆{\mathrm{G}}^{\circ }=-{\mathrm{nFE}}^{\circ }$

We can say that a cell reaction is spontaneous when $∆{\mathrm{E}}^{\circ }>0$.

Therefore, we can say that zirconium can reduce water.

At equilibrium conditions,

$$\begin{gathered} ∆{\mathrm{E}}^{\circ }=\frac{0.0592}{\mathrm{n}}\mathrm{logK} \\ \Rightarrow \mathrm{logK}=\frac{\mathrm{n}}{0.0592}∆{\mathrm{E}}^{\circ } \\ \Rightarrow \mathrm{logK}=\frac{4}{0.0592}\times 14.3 \\ \Rightarrow \mathrm{logK}=96.62 \\ \Rightarrow \mathrm{K}=4\times {10}^{96} \end{gathered}$$

Release of Hydrogen

The balanced equation for the reduction of water is given below.

$\mathrm{Zr}\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)\to {\mathrm{ZrO}}_2\left(\mathrm{s}\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)$

The equilibrium constant is very high for this reaction and hence it is very spontaneous. This accounts for the release of hydrogen gas in the nuclear disaster.