A 200-mL solution of KCl(aq) was electrolyzed for 10.0 minutes, producing Cl2 gas at the anode and H2 gas at the cathode. If the pH of the final solution was 12.40, what was the average current (in amps) used?

pOH= 14- 12.4 = 1.6

[OH-] = 10^-1.6 = .025 M OH-
mols of OH- = .025 M * .2L =.005 mols
.005 mols OH- * (2 mols e-/ 2mols )OH-) * (96500 C / 1 mole e-) = 484.8 C
amps = 484.8 C / (10 min*60) = .81 A

To find the average current used during electrolysis, we need to use Faraday's laws of electrolysis. Faraday's laws state that the amount of substance produced or consumed during electrolysis is directly proportional to the amount of electric charge passed through the solution.

First, we need to determine the amount of substance produced or consumed during electrolysis. In this case, Cl2 gas is produced at the anode, so we need to calculate the amount of Cl2 gas produced using the ideal gas law.

1. Use the ideal gas law to calculate the number of moles of Cl2 produced:
PV = nRT

Assuming that the pressure (P) and temperature (T) are constant, we can simplify the equation to:
V = nRT/P

Given:
V = 200 mL = 0.2 L (converted from mL to L)
R = 0.0821 L·atm/mol·K (the ideal gas constant)
T = ? (not given in the question)
P = ? (not given in the question)

Since the values for pressure and temperature are not provided in the question, we cannot calculate the number of moles of Cl2 produced directly using the ideal gas law. We have to use the given information about the pH of the solution to find the concentration of OH- ions.

2. Calculate the concentration of OH- ions using the given pH:
pOH = 14 - pH = 14 - 12.40 = 1.60
[OH-] = 10^(-pOH) = 10^(-1.60) = 0.0251 M

3. Since KCl is a strong electrolyte, it fully dissociates into K+ and Cl- ions in solution. Therefore, the concentration of K+ ions is the same as the concentration of Cl- ions, which is 0.0251 M.

4. Calculate the number of moles of Cl- ions present in the solution:
moles of Cl- = concentration x volume = 0.0251 M x 0.2 L = 0.00502 moles

5. Since Cl2 gas is produced by the reaction: 2Cl- -> Cl2 + 2e-, we know that 2 moles of Cl- ions produced 1 mole of Cl2 gas.

6. Calculate the number of moles of Cl2 gas produced:
moles of Cl2 = 0.00502 moles / 2 = 0.00251 moles

Now that we have the number of moles of Cl2 produced, we can determine the amount of electric charge passed through the solution using Faraday's laws.

7. Use Faraday's constant (F) to determine the amount of electric charge passed:
F = 96,485 C/mol (the Faraday constant)
Q = n x F

Given:
n = 0.00251 moles
F = 96,485 C/mol

8. Calculate the amount of electric charge passed during electrolysis:
Q = 0.00251 moles x 96,485 C/mol = 242.63 C (Coulombs)

Finally, we can calculate the average current used by dividing the amount of electric charge passed by the time of electrolysis.

9. Calculate the average current:
Average Current = Q / t

Given:
t = 10.0 minutes = 600 seconds (converted from minutes to seconds)

Average Current = 242.63 C / 600 s = 0.404 Amperes (rounded to three decimal places)

Therefore, the average current used during electrolysis is approximately 0.404 Amperes.