Introduction:
Electrolysis is a process that involves the decomposition of a compound by passing an electric current through it. In this case, we are considering the electrolysis of a solution containing HSO4^- ions, which results in the production of S2O8^2- ions. The current efficiency is given as 75%.

Given:
- Current efficiency = 75%
- Desired production rate = 1 mole of S2O8^2- per hour

Calculating the current:
To calculate the current required for the desired production rate, we can use Faraday's laws of electrolysis. According to Faraday's laws:

1. The amount of substance produced at an electrode is directly proportional to the quantity of electricity passed through it.
2. The quantity of electricity required to produce one mole of a substance is equal to the charge carried by one mole of electrons (Faraday's constant).

The formula to calculate the quantity of electricity (Q) is given by:
Q = n * F
Where Q is the quantity of electricity in coulombs, n is the number of moles of substance produced, and F is Faraday's constant (96485 C/mol).

In this case, we want to produce 1 mole of S2O8^2- per hour. Therefore, the quantity of electricity required (Q) can be calculated as:
Q = 1 mol * 96485 C/mol = 96485 C

Since the current efficiency is given as 75%, we can calculate the actual current (I) required by dividing the desired quantity of electricity (Q) by the current efficiency (CE):
I = Q / CE = 96485 C / 0.75 = 128647 C

Therefore, the current that should be employed to achieve a production rate of 1 mole of S2O8^2- per hour is 128647 C.

Explanation:
- Electrolysis is the process of decomposing a compound using an electric current.
- In this case, we are considering the electrolysis of a solution containing HSO4^- ions.
- The desired product of this electrolysis is S2O8^2- ions.
- The current efficiency is given as 75%.
- To calculate the current required for the desired production rate, we can use Faraday's laws of electrolysis.
- Faraday's first law states that the amount of substance produced at an electrode is directly proportional to the quantity of electricity passed through it.
- Faraday's second law states that the quantity of electricity required to produce one mole of a substance is equal to the charge carried by one mole of electrons (Faraday's constant).
- Using these laws and the given information, we can calculate the quantity of electricity required to produce 1 mole of S2O8^2- per hour.
- Finally, by dividing this quantity of electricity by the current efficiency, we can determine the actual current that should be employed to achieve the desired production rate.