Electrolysis is the process of using an electric current to drive a non-spontaneous chemical reaction. A common application is the deposition of a metal onto an electrode. To determine the amount of substance deposited, we use Faraday’s laws of electrolysis. Here’s a breakdown:
Key Concepts and Formulas
- Charge (Q): The total amount of electric charge passed through the electrolytic cell.
- Formula: Q = I * t
- Where:
- Q = Charge (Coulombs, C)
- I = Current (Amperes, A)
- t = Time (seconds, s)
- Where:
- Formula: Q = I * t
- Electrochemical Equivalent (Z): The mass of a substance deposited per unit of charge.
- Formula: Z = M / (n * F)
- Where:
- Z = Electrochemical equivalent (grams per Coulomb, g/C)
- M = Molar mass of the substance (grams per mole, g/mol)
- n = Number of electrons transferred per ion (dimensionless)
- F = Faraday’s constant (approximately 96,485 Coulombs per mole, C/mol)
- Where:
- Formula: Z = M / (n * F)
- Mass Deposited (m): The actual mass of the substance deposited at the electrode.
- Formula: m = Q * Z
- Where:
- m = Mass deposited (grams, g)
- Where:
- Formula: m = Q * Z
- Combined Formula: By substituting the formulas for Q and Z into the equation for m, we get a combined formula that directly relates the mass deposited to the current, time, molar mass, and number of electrons transferred:
- m = (M * I * t) / (n * F)
Steps for Calculation
There are two ways to approach the calculation:
Method 1: Step-by-Step (using Q and Z)
- Calculate the Charge (Q): Use Q = I * t.
- Calculate the Electrochemical Equivalent (Z): Use Z = M / (n * F).
- Calculate the Mass Deposited (m): Use m = Q * Z.
Example Problem
Let’s say we want to calculate the mass of copper deposited during the electrolysis of copper sulfate (CuSO4) solution. A current of 2 amperes is passed through the solution for 1 hour.
- Calculate Charge (Q):
- I = 2 A
- t = 1 hour = 3600 seconds
- Q = 2 A * 3600 s = 7200 C
- Calculate Electrochemical Equivalent (Z):
- M (copper) = 63.55 g/mol
- n (for Cu2+ + 2e- → Cu) = 2
- F = 96485 C/mol
- Z = 63.55 g/mol / (2 * 96485 C/mol) ≈ 0.000329 g/C
- Calculate Mass Deposited (m):
- Q = 7200 C
- Z ≈ 0.000329 g/C
- m = 7200 C * 0.000329 g/C ≈ 2.37 g
Therefore, approximately 2.37 grams of copper would be deposited during the electrolysis.
Method 2: Direct Calculation (using the combined formula)
- Identify all the variables: Determine the current (I), time (t), molar mass (M), and the number of electrons transferred (n).
- Calculate the Mass Deposited (m): Use the combined formula: m = (M * I * t) / (n * F).
Example Problem (using the combined formula)
Let’s calculate the mass of copper deposited during the electrolysis of copper sulfate (CuSO4) solution. A current of 2 amperes is passed through the solution for 1 hour.
- Identify Variables:
- I = 2 A
- t = 1 hour = 3600 s
- M (copper) = 63.55 g/mol
- n (for Cu2+ + 2e- → Cu) = 2
- F = 96485 C/mol
- Calculate Mass (m):
- m = (63.55 g/mol * 2 A * 3600 s) / (2 * 96485 C/mol)
- m ≈ 2.37 g
Therefore, approximately 2.37 grams of copper would be deposited during the electrolysis.
Advantages of the Combined Formula
- Efficiency: It allows for directly calculating the mass deposited without the intermediate steps of calculating Q and Z.
- Simplicity: It reduces the number of calculations required, minimizing potential rounding errors.