Question

Galvanized steel consists of steel with a thin coating of zinc to reduce corrosion. The zinc can be deposited electrolytically, by making the steel object the cathode and a block of zinc the anode in an electrochemical cell containing a dissolved zinc salt. Suppose a steel garbage can is to be galvanized and requires that a total mass of 7.32gof zinc be coated to the required thickness. How long should a current of 8,50Abe passed through the cell to achieve this?

Short answer

The current should be passed through the cell for 42.4min to galvanize the steel garbage can.

Step-by-step solution

The chemical reaction

The chemical reaction used in the process is $\mathit{Z}\mathit{n}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{\to }\mathit{Z}{\mathit{n}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathit{e}}^{\mathbf{-}}$.

 Calculating the number of moles of zinc to be coated

Formula used, Number of Moles$=\frac{\mathrm{Massofsubstance}}{\mathrm{Massofonemole}}$

$$\begin{gathered} {\mathrm{m}}_{\mathrm{total}}=7.32\mathrm{g} \\ \mathrm{Mr}\left(\mathrm{Zn}\right)=65.38\mathrm{m}/\mathrm{mol} \\ \begin{array}{c}\mathrm{n}\left(\mathrm{Zn}\right)=\frac{7.32\mathrm{g}}{65.38\mathrm{g}/\mathrm{mol}}\\ \mathrm{n}\left(\mathrm{Zn}\right)=0.112\mathrm{molZn}\end{array} \end{gathered}$$

Calculating the total charge required for the process.

Formula used,

of moles of $e^{-}=\frac{\mathrm{Totalcharge}\left(Q\right)}{96,485{\mathrm{Cmol}}^{-1}}$

$\begin{array}{c}0.112\mathrm{molZn}\times \frac{2{\mathrm{mole}}^{-}}{1\mathrm{molZn}}=0.224\mathrm{mole}\\ Q=0.224\mathrm{mol}\times 96,485{\mathrm{Cmol}}^{-1}\\ Q=2.16\times {10}^4\mathrm{C}\end{array}$

Calculating the time required for the process

$\begin{array}{l}t=\frac{2.16\times {10}^4\mathrm{C}}{8.50\mathrm{A}}\\ t=2.54\times {10}^3{\mathrm{CA}}^{-1}\\ \mathrm{t}=2.54\times {10}^3\mathrm{s}\times \frac{1\min }{60\mathrm{s}}\\ t=42.4\min \end{array}$

Thus, the current should be passed through the cell for 42.4min to galvanize the steel garbage can.