A rectangular steel plate is to be electroplated with copper on one side only

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

Problem

A rectangular steel plate

10.0\,\text{cm} \times 15.0\,\text{cm}

is to be electroplated with copper on one side only. Owing to edge effects near the electrical contacts, the thickness of the copper layer is not uniform but varies linearly along the 15-cm dimension, ranging from

1.0\,\mu\text{m}

at the bottom edge to

7.0\,\mu\text{m}

at the top edge. The cell operates at a constant current of

3.20\,\text{A}

for

40.0\,\text{min}

. Copper deposits from

\text{Cu}^{2+}

ions. Relevant data: density of copper =

8.96\,\text{g}\,\text{cm}^{-3}

; atomic mass of Cu =

63.5\,\text{g}\,\text{mol}^{-1}

. (a) Derive an expression for the local thickness

d(y)

as a function of position

y

(in centimetres) measured upward from the bottom edge, assuming a linear variation. (b) Use your expression from part (a) to calculate the average thickness

\bar{d}

across the plated surface. (c) Determine the total mass of copper that should be deposited according to the average thickness found in part (b). (d) Compare the theoretical mass from part (c) with the mass predicted from the electrical operating conditions. Discuss whether the linear-variation model is consistent with the electrochemical data, and propose one experimental method to verify the actual thickness profile on the plate.

Related theory

Browse the problem library