Question 13.7: Suppose that you have a part that requires a tin coating. Yo......
Suppose that you have a part that requires a tin coating. You’ve calculated that you need to deposit 3.60 g of tin to achieve an adequate coating. If your electrolysis cell (using Sn ^{2+}) runs at 2.00 A, how long must you operate the cell to obtain the desired coating?
Strategy This problem is different from the last one because it requires that we use the balanced half-reaction to relate moles of electrons and moles of a desired substance, in this case tin. Because we are given a mass of tin required, we can obtain the moles of tin, and that will tell us the moles of electrons required. We then determine the charge of those electrons with the Faraday constant, and we can use our understanding of electricity to get the time needed at the given current.
Sn ^{2+}( aq )+2\ e ^{-} \rightarrow Sn ( s ) \\3.60\text{ g Sn} \times\left(\frac{1\text{ mol Sn} }{118.7\text{ g Sn} }\right) \times\left(\frac{2\text{ mol e}^{-}}{1\text{ mol Sn} }\right) \times\left(\frac{96,485\ C }{1\text{ mol e}^{-}}\right)=5.85 \times 10^3\ C
Now recall that Q = I × t, so t = Q / I.
t=\frac{5.85 \times 10^3\ C }{2.00\text{ C s} ^{-1}}=2930\ s =48.8\text{ min}
Analyze Your Answer This may seem like a long time to run an experiment. So does this answer make sense? Often, plating a few grams of material at low currents requires on the order of thousands of seconds (as in the last problem for gold). The fact that tin requires two electrons in this process largely accounts for more than double the time compared to the last problem, so the answer is not unreasonable.
Discussion Perhaps this problem seems more complicated than some other stoichiometry problems because we divided it into two steps. Still, the fundamental components of the problem are the same as always. We used a balanced chemical equation to relate moles of a substance (tin) to moles of electrons. Then we used the relationship, Q = I × t, to find the time.
Check Your Understanding Suppose that you need a coating of rhodium (a precious metal) on a part that is to be used as a mirror in a laser. Because rhodium is so expensive, you wish to deposit only 4.5 mg on the surface of the part. If you run an electrolytic apparatus for 5.0 min, what current do you need to deposit the desired amount from a solution containing Rh ^{3+} ions?