Understanding the Calculation of Mass Deposited or Released in Electrolysis Using Faraday’s Laws

Electrolysis transforms electrical energy into chemical changes by depositing or releasing mass at electrodes. Calculating this mass precisely is crucial for industrial and laboratory applications.

This article explores the detailed methodology behind mass calculation in electrolysis, focusing on Faraday’s Laws. You will find comprehensive formulas, tables, and real-world examples to master this essential electrochemical process.

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Calculate the mass of copper deposited from a 2A current over 30 minutes.
Determine the mass of oxygen gas released during the electrolysis of water with 5A current for 1 hour.
Find the mass of silver dissolved when 0.5A current flows for 45 minutes.
Compute the mass of hydrogen gas produced from electrolysis with 3A current over 20 minutes.

Comprehensive Tables of Common Electrolysis Parameters

Element / Ion	Atomic / Molecular Weight (g/mol)	Valency (n)	Faraday Constant (F) (C/mol e^–)	Equivalent Weight (g/equiv)	Common Electrolysis Applications
Copper (Cu²⁺)	63.55	2	96485	31.775	Electroplating, refining copper
Silver (Ag⁺)	107.87	1	96485	107.87	Silver plating, purification
Aluminum (Al³⁺)	26.98	3	96485	8.993	Aluminum extraction (Hall-Héroult process)
Hydrogen (H⁺)	1.008	1	96485	1.008	Hydrogen gas generation
Oxygen (O^2-)	16.00 (per atom)	4 (for O₂ molecule)	96485	8.00 (per electron)	Oxygen gas evolution in water electrolysis
Nickel (Ni²⁺)	58.69	2	96485	29.345	Nickel plating, battery electrodes
Lead (Pb²⁺)	207.2	2	96485	103.6	Lead refining, battery manufacturing
Chromium (Cr³⁺)	51.996	3	96485	17.332	Chromium plating

Fundamental Formulas for Mass Calculation in Electrolysis

Faraday’s Laws of Electrolysis provide the foundation for calculating the mass of substance deposited or released during electrolysis. The key relationships are derived from the charge passed through the electrolyte and the stoichiometry of the electrochemical reaction.

First Law of Electrolysis

The mass (m) of a substance deposited or liberated at an electrode is directly proportional to the quantity of electric charge (Q) passed through the electrolyte.

m ∝ Q

Second Law of Electrolysis

The masses of different substances deposited or liberated by the same quantity of electricity are proportional to their equivalent weights.

m ∝ E

Combined Faraday’s Law Formula

The quantitative formula combining both laws is:

m = (Q × M) / (n × F)

m = mass of substance deposited or released (grams)
Q = total electric charge passed (coulombs, C)
M = molar mass of the substance (grams per mole, g/mol)
n = number of electrons transferred per ion (valency)
F = Faraday constant ≈ 96485 C/mol e^–

Calculating Electric Charge (Q)

The total charge Q is calculated from current (I) and time (t):

Q = I × t

I = current in amperes (A)
t = time in seconds (s)

Equivalent Weight (E) and Its Role

The equivalent weight is defined as:

E = M / n

Where:

M = molar mass (g/mol)
n = valency (number of electrons transferred)

Equivalent weight represents the mass of substance deposited per mole of electrons transferred.

Mass of Gas Released at Electrodes

For gases evolved during electrolysis (e.g., H₂, O₂), the volume can be related to the charge passed using the ideal gas law and Faraday’s laws.

V = (Q × Vm) / (n × F)

V = volume of gas evolved (liters)
Vm = molar volume of gas at given conditions (typically 22.4 L/mol at STP)
Q, n, and F as defined above

Detailed Explanation of Variables and Typical Values

Current (I): The flow of electric charge, measured in amperes (A). Typical laboratory currents range from milliamperes (mA) to several amperes (A).
Time (t): Duration of current flow, measured in seconds (s). Often recorded in minutes or hours and converted to seconds for calculations.
Molar Mass (M): The mass of one mole of the substance, expressed in grams per mole (g/mol). Values are element-specific and found in the periodic table.
Valency (n): Number of electrons involved in the redox reaction per ion. For example, Cu²⁺ has n=2, Ag⁺ has n=1.
Faraday Constant (F): The charge of one mole of electrons, approximately 96485 coulombs per mole of electrons.
Equivalent Weight (E): The mass of substance deposited per mole of electrons, calculated as M/n.
Volume of Gas (V): For gases, volume is often more practical than mass. Calculated using molar volume and charge passed.

Real-World Applications and Case Studies

Case Study 1: Copper Electroplating

In industrial copper electroplating, precise control of deposited copper mass ensures coating quality and thickness. Suppose a plating bath operates with a current of 3 A for 1 hour. Calculate the mass of copper deposited.

Given:

Current, I = 3 A
Time, t = 1 hour = 3600 s
Molar mass of Cu, M = 63.55 g/mol
Valency, n = 2 (Cu²⁺)
Faraday constant, F = 96485 C/mol

Step 1: Calculate total charge Q

Q = I × t = 3 × 3600 = 10800 C

Step 2: Calculate mass deposited using Faraday’s formula

m = (Q × M) / (n × F) = (10800 × 63.55) / (2 × 96485) ≈ 3.56 g

Therefore, approximately 3.56 grams of copper will be deposited on the cathode after 1 hour.

Case Study 2: Hydrogen Gas Production by Water Electrolysis

Electrolysis of water produces hydrogen and oxygen gases. Calculate the volume of hydrogen gas generated when a current of 5 A is passed for 30 minutes at standard temperature and pressure (STP).

Given:

Current, I = 5 A
Time, t = 30 minutes = 1800 s
Valency for H₂, n = 2 (2 electrons per H₂ molecule)
Faraday constant, F = 96485 C/mol
Molar volume at STP, Vm = 22.4 L/mol

Step 1: Calculate total charge Q

Q = I × t = 5 × 1800 = 9000 C

Step 2: Calculate moles of hydrogen gas produced

nH2 = Q / (n × F) = 9000 / (2 × 96485) ≈ 0.0466 mol

Step 3: Calculate volume of hydrogen gas

V = nH2 × Vm = 0.0466 × 22.4 ≈ 1.04 L

Thus, approximately 1.04 liters of hydrogen gas are produced under STP conditions.

Additional Considerations and Advanced Insights

While Faraday’s laws provide a robust theoretical framework, practical electrolysis involves factors that can affect accuracy:

Current Efficiency: Not all current contributes to the desired electrochemical reaction. Side reactions and losses reduce efficiency, often expressed as a percentage.
Electrode Surface Area and Morphology: Affect deposition rates and uniformity.
Electrolyte Concentration and Temperature: Influence ion mobility and reaction kinetics.
Overpotential and Cell Voltage: Affect energy consumption and reaction rates.

In industrial settings, these parameters are optimized to maximize yield and minimize energy costs. Accurate mass calculations must incorporate current efficiency (η):

m = (η × Q × M) / (n × F)

Where η is the current efficiency (0 < η ≤ 1).

Summary of Key Points for Practical Application

Always convert time to seconds and use amperes for current to calculate charge in coulombs.
Use accurate molar masses and valency values from reliable chemical data sources.
Consider current efficiency for real-world applications to adjust theoretical mass values.
For gas evolution, use molar volume at the specific temperature and pressure conditions.
Validate calculations with experimental data to account for system-specific variables.

Calculation of Mass Deposited or Released in Electrolysis (Faraday’s Laws)