# Electrolytic Cell Problem involvng the mass of gold plated

A metallurgist wants to goldplate a thing sheet with the following dimensions:  1.5 in. x 8.5 in. x .0012in.  The gold plate must be .0020 in. thick.

a. How many grams of gold (d = 19.3 g/cm^3) are required?
b. How long will it take to plate the sheet from AuCN using a current of 7.00 A? (Assume 100% efficiency.)

Can anyone help me with the above problem.  For a. the answer is 16 grams and I am perplexed on how you arrive at the answer.  Multiplying 1.5 x 8.5 x.0012 and raising it to the .0020 and multiplying by 2.54cm/1 inch and raising this number to the 3rd power gets you 16 but I am guessing this is the incorrect way to do this.

For b, I did 16 g AuCN x I mol AuCN/197 g Au x 1 mol e-/1 mol AuCN x 9.648 x 10^4/1 mol e- = 7.8 x 10^3/7.00 C/s = 1.1 x 10^3 sec x 1min/60sec = 18 minutes - however the book says the answer is 19minutes.

1 mol e- = 9.648 x 10^4
1A = 1 C/s

I am assuming I did these wrong.  Can anyone help me find where I went wrong.  Any input would be greatly appreciated.  Thank you

### Re: Electrolytic Cell Problem?

spock Mon, 04/14/2008 - 08:23

You would need to find the area of the sheet to be plated:
area plated = l x w  = 1.5 in  x 8.5 in x 2 (since it will be plated on both sides)
Now find the volume of gold required:
volume of gold = area plated x .002 in
Now convert from cubic inches to cubic cm
volume of gold in cm3 = volume of gold in in3  x  (2.54 cm/1 in)3
Find the mass of the gold by multiplying by the density
mass of Au = vol in cm3  x density
I came up with 16.1 grams of Au

For b)
charge required = 16.1 g Au  x (1 mol/197 g)   x (1 mol e-/mol Au)  x (9.65 x 104 C/mol e-)

time in seconds=   charge required / (7.00 C/sec)
time in minutes  = time in sec  x  (1 min/60 sec)
Then you would require the density of gold.
If the density is given in g/cm3 you would need to convert from cubic inches to cubic cm  (   2.54 cm/1.0 in )3 )

When I did this I came up with 18.77 seconds which would round to 19 seconds.  Are you rounding each step?  If so that might account for your difference.  Generally you do all the steps on your calculator without rounding and then round once at the end.