50 ml of ZnSO4 solution was transferred to a mercury cathode and enough solid potassium nitrate is added to make the solution 0.1 M in KNO3. The electrolysis of Zn2+ is carried to completion of -1.3 V vs. SCE with the passage of 241 C of electricity. calculate the initial concentration of zinc ion ?
To calculate the initial concentration of zinc ion (Zn2+), we need to use Faraday's law of electrolysis. Faraday's law states that the amount of substance produced or consumed during an electrolysis reaction is directly proportional to the amount of electrical charge passed through the system.
Let's break down the given information and use the formula:
1. The electrolysis was carried out until a total charge of 241 C was passed (Q = 241 C).
2. The potential for the completion of the Zn2+ electrolysis is -1.3 V vs. SCE.
3. The transfer of electrons (n) for the Zn2+ electrolysis is 2 (since Zn2+ gains 2 electrons to form Zn metal).
Now, we can use Faraday's law to calculate the initial concentration of Zn2+:
1. Calculate the number of moles of electrons passed (nF):
nF = Q / Faraday constant
Faraday constant (F) = 96,485 C/mol
nF = 241 C / 96485 C/mol = 0.0025 mol
2. Since the transfer of electrons (n) for Zn2+ electrolysis is 2, we can find the number of moles of Zn2+ ions:
Moles of Zn2+ = 0.0025 mol / 2 = 0.00125 mol
3. Finally, we calculate the initial concentration of Zn2+ ions in the 50 ml of solution:
Initial concentration of Zn2+ ions (M) = Moles of Zn2+ / Volume of solution in liters
Volume of solution = 50 ml = 50/1000 = 0.05 L
Concentration of Zn2+ = 0.00125 mol / 0.05 L = 0.025 M
Therefore, the initial concentration of zinc ion (Zn2+) in the solution is 0.025 M.