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

Electrolysis mass calculation quantifies substance deposited during electrochemical reactions precisely. This article explores Faraday’s Laws and their application in electrolysis mass determination.

Discover detailed formulas, extensive tables of common values, and real-world examples to master the calculation of deposited mass in electrolysis processes.

• Calculate the mass of copper deposited when 5 amperes flow for 30 minutes in a copper sulfate solution.
• Determine the mass of silver deposited from a 2-ampere current over 45 minutes using Faraday’s laws.
• Find the mass of hydrogen gas evolved at the cathode when 3 amperes pass through water for 1 hour.
• Compute the mass of aluminum deposited during electrolysis with a current of 10 amperes for 2 hours.

Comprehensive Tables of Common Electrolysis Parameters

Fundamental Formulas for Mass Calculation in Electrolysis

Faraday’s laws of electrolysis provide the theoretical foundation for calculating the mass of a substance deposited or liberated at an electrode during electrolysis. The primary formula is derived from the relationship between electric charge and the amount of substance transformed.

Faraday’s First Law of Electrolysis

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

Mass (m) ∝ Charge (Q)

Faraday’s Second Law of Electrolysis

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

Key Formula for Mass Calculation

m = (Q × M) / (n × F)

• m = mass of substance deposited (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^–

The total charge Q can be calculated from current and time:

Q = I × t

• I = current (amperes, A)
• t = time (seconds, s)

Equivalent Weight

The equivalent weight (E) is defined as:

E = M / n

Where:

• M = molar mass (g/mol)
• n = number of electrons involved in the redox reaction

Thus, the mass can also be expressed as:

m = (Q × E) / F

Additional Considerations

• Current Efficiency (η): In practical applications, not all current contributes to the desired reaction. Efficiency factor (0 < η ≤ 1) accounts for side reactions.
• Adjusted Mass Formula:

m = (η × I × t × M) / (n × F)

Where η is the current efficiency expressed as a decimal.

Detailed Explanation of Variables and Typical Values

• Mass (m): The amount of substance deposited or liberated, measured in grams (g). This is the primary output of the calculation.
• Charge (Q): The total electric charge passed through the electrolyte, measured in coulombs (C). Calculated as current multiplied by time.
• Current (I): The flow of electric charge, measured in amperes (A). Typical electroplating currents range from milliamperes to several amperes depending on scale.
• Time (t): Duration of current flow, measured in seconds (s). Often given in minutes or hours and converted accordingly.
• Molar Mass (M): The mass of one mole of the substance, in grams per mole (g/mol). Values are element or compound specific.
• Valency (n): Number of electrons transferred per ion in the redox reaction. For example, Cu²⁺ has n=2.
• Faraday Constant (F): The charge of one mole of electrons, approximately 96485 C/mol e^–. This is a universal constant.
• Current Efficiency (η): Fraction of current effectively used for the desired electrochemical reaction. Typically ranges from 0.7 to 1.0 in industrial processes.

Real-World Applications and Case Studies

Case Study 1: Copper Electroplating

In industrial copper electroplating, precise control of deposited mass ensures coating quality and thickness. Suppose a plating bath uses a current of 5 A for 30 minutes to deposit copper on a metal surface.

Given:

• Current, I = 5 A
• Time, t = 30 minutes = 1800 seconds
• Molar mass of copper, M = 63.55 g/mol
• Valency, n = 2 (Cu²⁺)
• Faraday constant, F = 96485 C/mol
• Current efficiency, η = 0.95 (95%)

Calculate the total charge:

Q = I × t = 5 × 1800 = 9000 C

Calculate the mass deposited:

m = (η × Q × M) / (n × F) = (0.95 × 9000 × 63.55) / (2 × 96485)

Calculate numerator:

0.95 × 9000 × 63.55 = 543,622.5

Calculate denominator:

2 × 96485 = 192,970

Mass deposited:

m = 543,622.5 / 192,970 ≈ 2.82 g

This means approximately 2.82 grams of copper will be deposited on the cathode after 30 minutes under these conditions.

Case Study 2: Hydrogen Gas Evolution in Water Electrolysis

Electrolysis of water produces hydrogen gas at the cathode. Suppose a current of 3 A is passed through water for 1 hour. Calculate the mass of hydrogen gas evolved.

Given:

• Current, I = 3 A
• Time, t = 1 hour = 3600 seconds
• Molar mass of hydrogen, M = 2.016 g/mol (H₂)
• Valency, n = 2 (2 electrons per H₂ molecule)
• Faraday constant, F = 96485 C/mol
• Current efficiency, η = 1 (assuming ideal conditions)

Calculate total charge:

Q = I × t = 3 × 3600 = 10800 C

Calculate mass of hydrogen gas evolved:

m = (η × Q × M) / (n × F) = (1 × 10800 × 2.016) / (2 × 96485)

Calculate numerator:

10800 × 2.016 = 21772.8

Calculate denominator:

2 × 96485 = 192970

Mass evolved:

m = 21772.8 / 192970 ≈ 0.113 g

Therefore, approximately 0.113 grams of hydrogen gas is produced after 1 hour at 3 amperes.

Additional Insights and Practical Considerations

• Temperature and Concentration Effects: Electrolyte temperature and ion concentration influence reaction rates and current efficiency.
• Electrode Surface Area: Larger electrode areas can sustain higher currents without excessive polarization, affecting deposition rates.
• Side Reactions: Competing reactions such as oxygen evolution or hydrogen evolution can reduce current efficiency.
• Measurement Accuracy: Precise current and time measurement are critical for accurate mass calculation.
• Industrial Relevance: Faraday’s laws underpin processes like metal refining, electroplating, battery manufacturing, and hydrogen production.

Recommended External Resources for Further Study

• Chemguide: Faraday’s Laws of Electrolysis – Detailed explanation and examples.
• Engineering Toolbox: Electrolysis and Faraday’s Law – Practical engineering applications.
• American Chemical Society: Electrolysis Fundamentals – Academic resource on electrochemical principles.
• NIST Physical Constants – Authoritative source for constants like Faraday’s constant.

Summary of Key Points

• Faraday’s laws provide a quantitative basis for calculating mass deposited during electrolysis.
• The mass depends on total charge, molar mass, valency, and Faraday’s constant.
• Current efficiency and practical conditions affect real-world outcomes.
• Extensive tables of common substances aid quick reference and calculation.
• Real-world examples demonstrate application in electroplating and gas evolution.

Mastering these calculations is essential for professionals in electrochemistry, materials science, and industrial manufacturing to optimize processes and ensure quality control.