A current of 3.04 A is passed through a Cr(NO3)2 solution for 1.80 hours. How much chromium is plated out of the solution?
Coulombs = amperes x seconds
C = 3.04 x 1.80 hr x (60 min/hr) x (60sec/min) = estimated 20,000
96,485 C will deposit 52/3 g Cr or estimated 17 g Cr.
17 g x (20,000/96,485) = g Cr deposited.
How did you get 52/3??
To determine how much chromium is plated out of the solution, we need to use Faraday's Law of Electrolysis, which states that the amount of substance discharged or plated out is directly proportional to the quantity of electricity passed through the solution.
The formula for Faraday's Law is:
Q = nF
Where:
Q is the quantity of electricity passed in Coulombs (C)
n is the number of moles of the substance being plated out
F is the Faraday constant, which is equal to 96,485 C/mol
First, let's calculate the quantity of electricity passed (Q) using the formula:
Q = I * t
Where:
I is the current in Amperes (A)
t is the time in seconds (s)
Given:
I = 3.04 A
t = 1.80 hours = 1.80 * 3600 seconds = 6480 seconds
Substituting the values into the equation:
Q = 3.04 A * 6480 s = 19699.2 C
Next, we'll calculate the number of moles of chromium (n). We need to know the oxidation state of chromium in the Cr(NO3)2 solution and the Faraday constant.
Since the question does not provide the oxidation state, let's assume that it's Cr(III), with a 3+ charge.
In Cr(III), the charge comes from the metal itself, so the number of moles of chromium plated out is equal to the quantity of electricity passed.
n = Q / F = 19699.2 C / 96485 C/mol = 0.204 mol
Therefore, approximately 0.204 moles of chromium are plated out of the solution.
To determine the amount of chromium plated out of the solution, we need to use Faraday's Law of Electrolysis. Faraday's Law relates the amount of substance formed or consumed in an electrolytic cell to the electrical charge passed through the cell.
The formula for Faraday's Law is given by:
moles of substance = (current * time) / (Faraday's constant * charge of the ion)
In this case, we have the current (I) of 3.04 A and the time (t) of 1.80 hours. We also need to know the Faraday's constant (F) and the charge of the chromium ion (Cr^2+).
The Faraday's constant, which represents the amount of charge per mole of electrons, is approximately 96,485 C/mol.
The charge of the chromium ion (Cr^2+) is 2+ since it has a positive charge of 2.
Plugging in these values into the formula, we get:
moles of substance = (3.04 A * 1.80 hours) / (96,485 C/mol * 2)
Simplifying further:
moles of substance = (5.472) / (192,970)
Calculating the final result, we find:
moles of substance ≈ 2.8375596 x 10^(-5) mol
Therefore, approximately 2.83756 x 10^(-5) moles of chromium are plated out of the solution.