Chemistry help!

Question

You would like to produce a gold-plated coin by plating gold onto a penny 1.90 cm in diameter. How many days will it take to produce a layer of gold 0.250 mm thick (on both sides of the coin) from an Au³⁺ bath using a current of 0.0200 A? (density of gold = 19.3 g/cm³) For the purposes of this problem, you can ignore the edges of the coin.

Answer 1

First, find the moles of Au needed to plate 0.250 mm thick layer on both sides of the coin:

volume of a cylinder = π r² h = (3.14)(0.95cm)²(2.5x10^-4cm) = 7.08x10^-4 cm³

mass of Au per side of coin = 7.08x10^-4 cm³ x 19.3 g / cm³ = 0.01367 g Au per side

total mass of Au needed = 0.01367 g Au per side x 2 sides = 0.02735 g Au

Total moles Au needed = 0.02735 g Au x 1 mol Au / 197 g = 1.39x10^-4 moles Au needed

Next, we'll find the number of coulombs (C) needed:

Au³⁺ + 3e- ==> Au(s)

1.39x10^-4 mol Au x 3 mols electrons / mol Au x 96,500 C / mol electrons = 40.2 C

Finally, calculate time needed using 0.0200 amps (A)

1 amp = 1 C/sec

0.0200 amps = 0.0200 C/sec

40.2 C x 1 sec / 0.0200 C = 2010 sec

2010 sec x 1 min / 60 sec x 1 hr / 60 min x 1 day / 24 hr = 0.0233 days

(be sure to check all of the math)