If you watch television at all, you have probably seen advertisements for the do

Question

If you watch television at all, you have probably seen advertisements for the dollar 50 Buffalo tribute coin, available at the low LOW price of only dollar 10. The coin being advertised is a REPLICA of a solid gold coin issued by the U.S. treasury. If you listen to the advertisements carefully, you will hear that the tribute coins are COATED in 14.0 mg of 0.9999 pure gold. Assuming that each coin contains the stated 14.0 mg of gold, calculate the time (in minutes) required to electroplate (simultaneously) the gold onto 2877 coins using a current of 12.8 amps. Assume the gold is being plated from an AuCl_3 solution. Note: Even at the current record high price for gold ($1600 per ounce) each coin contains only 80 cents worth of gold. The ads are aimed at people who don't understand the metric system and don't realize just how little 14.0 mg is.

Explanation / Answer

According to farady's first law
m = (It/F)(M/Z)

where
m = the mass of the substance liberated at an electrode in grams
I = current in amperes
t = the total time
M = the molar mass of the substance
Z = the valency number of ions of the substance (electrons transferred per ion).

F = 96485 C mol1 is the Faraday constant

m = 14.0*10^-3 * 2877 = 40.3 gm of gold
I = 12.8 amp
M = 197 gm/mol
Z = +3

40.3 = (12.8*t/96485)*(197/3)

time = 4623.52 sec.

time = 77.06 min

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