Question

A student wants to electroplate a nickel wire with copper. The student has 1 g of copper sulfate and a 2 M solution of sulfuric acid. The wire has a surface area of 3 cm², and the desired copper thickness on the wire is 0.025 cm. How long should the student electroplate the wire with a current of 1.5 A to achieve the desired thickness of copper? Calculate the current density in the electrochemical cell.

Answer 1

To calculate the time required for electroplating, we first need to determine the amount of copper needed to achieve the desired thickness. We can use the formula:mass = volume  densitywhere mass is the mass of copper needed, volume is the volume of copper needed  surface area  thickness , and density is the density of copper  8.96 g/cm .Volume of copper needed = surface area  thickness = 3 cm  0.025 cm = 0.075 cmMass of copper needed = volume  density = 0.075 cm  8.96 g/cm = 0.672 gNow, we need to determine the number of moles of copper needed. We can use the formula:moles = mass / molar masswhere moles is the number of moles of copper needed, mass is the mass of copper needed  0.672 g , and molar mass is the molar mass of copper  63.55 g/mol .Moles of copper needed = 0.672 g / 63.55 g/mol = 0.0106 molNext, we need to determine the number of coulombs required for the electroplating process. The number of coulombs can be calculated using Faraday's law:coulombs = moles  Faraday's constant  valence electronswhere coulombs is the number of coulombs required, moles is the number of moles of copper needed  0.0106 mol , Faraday's constant is 96485 C/mol, and valence electrons are the number of electrons involved in the redox reaction  2 for copper .Coulombs required = 0.0106 mol  96485 C/mol  2 = 2045.8 CNow, we can calculate the time required for electroplating using the formula:time = coulombs / currentwhere time is the time required for electroplating, coulombs is the number of coulombs required  2045.8 C , and current is the current used for electroplating  1.5 A .Time required = 2045.8 C / 1.5 A = 1363.87 sFinally, we can calculate the current density in the electrochemical cell using the formula:current density = current / surface areawhere current density is the current density in the electrochemical cell, current is the current used for electroplating  1.5 A , and surface area is the surface area of the wire  3 cm .Current density = 1.5 A / 3 cm = 0.5 A/cmSo, the student should electroplate the wire for 1363.87 seconds  approximately 22 minutes and 44 seconds  to achieve the desired thickness of copper, and the current density in the electrochemical cell is 0.5 A/cm.