Copper of thickness d is plated on the cathode of a copper voltameter. If the total surface area of the cathode is 60 cm\(^2\) and a steady current of 5.0 A...
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Copper of thickness d is plated on the cathode of a copper voltameter. If the total surface area of the cathode is 60 cm\(^2\) and a steady current of 5.0 A is maintained in the voltameter for 1 hour. calculate the value of d. [density of copper = 8.9 x 10\(^3\)kg m\(^{-3}\) electro chemical equivalent of copper = 3.3 x 10\(^{-7}\) kg C\(^{-1}\)
Answer Details
Mass of copper deposited (Faraday's first law): \(m=zIt\).
\[ m=(3.3\times10^{-7})(5.0)(3600)=5.94\times10^{-3}\,\text{kg} \]Volume of this copper: \(V=\dfrac{m}{\rho}\).
\[ V=\frac{5.94\times10^{-3}}{8.9\times10^{3}}=6.67\times10^{-7}\,\text{m}^3 \]The copper is spread over the cathode area \(A=60\,\text{cm}^2=60\times10^{-4}\,\text{m}^2=6.0\times10^{-3}\,\text{m}^2\), and \(V=A\times d\), so
\[ d=\frac{V}{A}=\frac{6.67\times10^{-7}}{6.0\times10^{-3}}=1.11\times10^{-4}\,\text{m} \]So the plating thickness \(d\approx1.1\times10^{-4}\,\text{m}\) (about \(0.11\,\text{mm}\)).
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