An antique automobile bumper is to be chrome plated. The bumper, which is dipped into an acidic Cr₂O₇^2- solution, serves as a cathode of an electrolytic cell. The atomic mass of Cr is 51.996; 1 faraday = 96,485 coulombs.
-If the current is 18.8 amperes, how long will it take to deposit 1.66 × 10² g of Cr(s) onto the bumper?

Question

Quizplus · Accepted Answer

To calculate the time required to deposit 1.66 × 10^12 g of Cr onto the bumper, we use Faraday's laws of electrolysis. First, we need to find the number of moles of Cr to be deposited:$$ \text{Moles of Cr} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{1.66 \times 10^{12} \text{ g}}{51.996 \text{ g/mol}} $$Next, we calculate the total charge needed to deposit this amount of Cr, knowing that 1 mole of Cr requires 1 Faraday (96,485 C) to be deposited:$$ \text{Total Charge} = \text{Moles of Cr} \times 96,485 \text{ C/mol} $$Finally, we find the time required using the current (I) and the total charge (Q) with the formula $ t = \frac{Q}{I} $, where $ t $ is in seconds. To convert seconds to hours, we divide by 3600.Given the current is 18.8 amperes, and using the steps above, the calculation will show that the time required is approximately 27.3 hours.

An Antique Automobile Bumper Is to Be Chrome Plated