How long (in minutes) must a 5.40 A current be passed through an aqueous solution of zinc nitrate to deposit 87.5 g Zn?
To find out how long it would take to deposit 87.5 g Zn, we need to use Faraday's law of electrolysis. Faraday's law states that the amount of substance produced or consumed during electrolysis is directly proportional to the quantity of electric charge passed through the electrolyte.
To apply Faraday's law, we need to find the quantity of electric charge passed through the solution. The formula to calculate the quantity of electric charge (Q) is given by:
Q = I * t
Where:
Q is the quantity of electric charge in Coulombs (C)
I is the current in Amperes (A)
t is the time in seconds (s)
First, let's convert the current from Amperes to Coulombs per second (C/s) by multiplying it by the number of seconds in a minute (60):
I = 5.40 A * 60 s = 324 C/s
Next, we rearrange Faraday's law to solve for time:
t = Q / I
Substituting the known values, we have:
t = (87.5 g × (1 mol Zn / molar mass of Zn)) × (1 Faraday / 2 mol e-) / I
The molar mass of zinc (Zn) is approximately 65.38 g/mol, and one mole of zinc requires two moles of electrons (2e-) to be deposited. The Faraday constant is approximately 96,485 C/mol.
Substituting the values:
t = (87.5 g × (1 mol Zn / 65.38 g)) × (1 Faraday / (2 mol e-)) / 324 C/s
Now we can calculate the time:
t = (87.5 / 65.38) * (1 / 2) * (1 / 324) * (96485 C/mol)
t ≈ 2827 s or 47.12 minutes
Therefore, it would take approximately 47.12 minutes to deposit 87.5 g of Zn with a current of 5.40 A.