Electrolytic Cell Examples and Calculations

Explore practical examples of electrolytic cells and their calculations in electrochemistry.
By Jamie

Understanding Electrolytic Cells

Electrolytic cells are essential components in various industrial processes and scientific applications. They utilize electrical energy to drive non-spontaneous chemical reactions, often employed in electroplating, electrolysis, and the production of chemicals. This article presents three practical examples of electrolytic cells and their calculations, illustrating their real-world applications and the underlying principles.

Example 1: Electrolysis of Water

Context

The electrolysis of water is a fundamental process used to produce hydrogen and oxygen gases. This reaction is significant in the field of renewable energy, particularly in developing hydrogen fuel.

To perform this process, water is split into hydrogen and oxygen gas using an electric current. The overall reaction can be represented as:

2 H₂O (l) → 2 H₂ (g) + O₂ (g)

Example Calculation

In a typical setup, suppose we have a system where 2.0 grams of water is electrolyzed. First, we need to determine how many moles of water are present:

  • Molar mass of H₂O = 18.02 g/mol
  • Moles of water = 2.0 g / 18.02 g/mol = 0.111 moles

According to Faraday’s laws of electrolysis, 1 mole of H₂ requires 2 moles of electrons for its production. Therefore:

  • Moles of electrons required = 0.111 moles H₂ × 2 = 0.222 moles of electrons

Using Faraday’s constant (F = 96485 C/mol), the total charge (Q) required can be calculated:

  • Q = moles of electrons × Faraday’s constant = 0.222 moles × 96485 C/mol = 21406.57 C

Notes

The efficiency of the electrolysis process can vary based on temperature and electrode material. Higher temperatures typically increase reaction rates, improving efficiency.

Example 2: Electroplating a Metal Object

Context

Electroplating is a process in which a thin layer of metal is deposited onto the surface of an object, commonly used to enhance appearance and prevent corrosion. For instance, the electroplating of silver onto a copper object is widely practiced in the jewelry industry.

Example Calculation

Let’s consider electroplating a copper ring with silver. Suppose we want to deposit 5.0 grams of silver on the ring. First, we calculate the moles of silver:

  • Molar mass of Ag = 107.87 g/mol
  • Moles of silver = 5.0 g / 107.87 g/mol = 0.0463 moles

Silver requires one mole of electrons for deposition:

  • Moles of electrons required = 0.0463 moles

Now, the total charge needed:

  • Q = 0.0463 moles × 96485 C/mol = 4465.66 C

Notes

The quality of electroplated layers can be affected by factors such as current density, temperature, and the concentration of the silver solution. Adjusting these parameters can yield different plating results.

Example 3: Production of Chlorine Gas

Context

The electrolysis of brine (sodium chloride solution) is an industrial method for producing chlorine gas, hydrogen gas, and sodium hydroxide, vital for various chemical processes.

Example Calculation

In a brine electrolysis process, if a plant electrolyzes 1000 grams of NaCl, we first determine the moles of NaCl:

  • Molar mass of NaCl = 58.44 g/mol
  • Moles of NaCl = 1000 g / 58.44 g/mol = 17.14 moles

During electrolysis, each mole of NaCl produces one mole of chlorine gas and one mole of hydrogen gas:

  • Moles of chlorine produced = 17.14 moles

To calculate the charge required for producing chlorine gas, note that it takes two moles of electrons to produce one mole of Cl₂:

  • Moles of electrons required = 17.14 moles × 2 = 34.28 moles

Now calculate the total charge:

  • Q = 34.28 moles × 96485 C/mol = 3307909.8 C

Notes

The efficiency of the electrolysis process can depend on the cell design and operational conditions. The separation of gases produced is crucial to prevent recombination and ensure purity in the final products.