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 determine the time required for a current to deposit a certain amount of zinc, we can use Faraday's law of electrolysis, which states that the amount of a substance deposited or liberated at an electrode is directly proportional to the quantity of electricity passed through it.
The equation for Faraday's law is:
m = (Q * M) / (n * F)
Where:
m = mass of the substance deposited (in grams)
Q = total charge passed through (in coulombs)
M = molar mass of the substance (in g/mol)
n = number of moles of electrons involved in the reaction
F = Faraday's constant (approximately 96485 C/mol e-)
In this case, we want to deposit 87.5 g of Zn (m = 87.5 g). The molar mass of Zn is approximately 65.38 g/mol (M = 65.38 g/mol). Zinc has a 2+ charge, so two moles of electrons are involved in the reaction (n = 2). And finally, the value of Faraday's constant is approximately 96485 C/mol e- (F = 96485 C/mol e-).
Now, let's calculate the total charge passed through using the equation:
Q = (m * n * F) / M
Substituting the values, we have:
Q = (87.5 g * 2 * 96485 C/mol e-) / 65.38 g/mol
Q ≈ 2533868 C
Since the current is given as 5.40 A (amperes), we can calculate the time required using the equation:
Q = I * t
Where:
I = current (in amperes)
t = time (in seconds)
We need to convert the current from amperes to coulombs per second by multiplying it by the conversion factor 1 A / 1 C/s.
Using this, we have:
Q = (5.40 A * t) / (1 A / 1 C/s)
2533868 C = 5.40 t
Solving for t, we find:
t = 2533868 C / 5.40 ≈ 469807 s
To convert this to minutes, we divide by 60 (since there are 60 seconds in a minute):
t ≈ 469807 s / 60 ≈ 7830 minutes
Therefore, it will take approximately 7830 minutes for a 5.40 A current to deposit 87.5 g of Zn in an aqueous solution of zinc nitrate.