Question

How is the amount of current flowing through an electrolytic cell related to the amount of product produced in the redox reaction?

Short answer

The amount of current flowing through an electrolytic cell is directly proportional to the amount of product produced; more current or longer electrolysis time results in more product.

Step-by-step solution

Understand the Relation via Faraday’s Laws of Electrolysis

Faraday's First Law of Electrolysis states that the amount of substance produced or consumed at each electrode during electrolysis is directly proportional to the amount of electricity that passes through the electrolyte. This implies that the greater the current (or the longer the time for which it flows), the greater will be the amount of substance produced. Faraday's Second Law states that the amount of different substances produced by the same quantity of electricity passing through the electrolytic solution is proportional to their equivalent weights.

Express the Mathematical Relationship

The quantitative aspects of Faraday's laws are given by the equation \( m = (Q \times M) / (n \times F) \), where \( m \) is the mass of the substance produced at the electrode, \( Q \) is the total electric charge passed through the solution, \( M \) is the molar mass of the substance, \( n \) is the number of moles of electrons required to produce one mole of the substance, and \( F \) is Faraday's constant (approximately \( 96,485 \) coulombs per mole of electrons). Since \( Q \) is equal to current \( I \) times time \( t \), \( Q = I \times t \), the equation can also be written as \( m = (I \times t \times M) / (n \times F) \).

Apply the Concept

To relate the current to the amount of product produced, we see from the equation in Step 2 that the mass of the product \( m \) varies directly with the current \( I \) and the time \( t \). This means that if the current or time increases, the mass of the product also increases proportionally, assuming that all other factors (molar mass \( M \), number of moles of electrons \( n \), and Faraday's constant \( F \)) remain constant.

Key concepts

Electrolytic Cell Current

Understanding the role of current in an electrolytic cell is crucial for grasping the essentials of electrochemistry. Let's simplify this concept. An electrolytic cell is a device that drives a chemical reaction through the introduction of electrical energy. The current, which is the flow of electric charge, plays a pivotal part in this process.

Think of the electrolytic cell as a party, where the current is the guest of honor, whose arrival triggers all the activities (reactions). More guests mean more action. Similarly, the more current you introduce, the more substance you'll get as the reaction proceeds. Why? Faraday's first law points out that the amount of substance formed or decomposed at an electrode is directly linked to the amount of electric charge (or current) passed through the electrolyte.

For instance, if a current of 2 amps is passed for 1 hour, it will produce twice the amount of a substance compared to a current of 1 amp passed for the same duration. Remember, it's not just the magnitude of current but also how long it's maintained that dictates the quantity of the product formed.

Redox Reaction Products

In every electrolytic cell, redox reactions are the superstars. These reactions involve the transfer of electrons between substances. 'Redox' stands for reduction (gaining electrons) and oxidation (losing electrons). The products of these reactions depend on the substances present and their ability to gain or lose electrons.

During a redox process in an electrolytic cell, a substance at the cathode gains electrons (it is reduced), while a substance at the anode loses electrons (it is oxidized). The nature of these products varies and is determined by the type of material undergoing electrolysis as well as the electrolyte in use. For example, electrolyzing aqueous sodium chloride (table salt) yields hydrogen gas at the cathode and chlorine gas at the anode.

Interesting Products of Redox Reactions

• Electroplating metals for corrosion resistance or aesthetic purposes.
• Producing gases like hydrogen and oxygen for industrial use.
• Refining metals, such as copper and aluminum, to a higher purity.

This variation ensures that with different setups, you can produce an assortment of products in an electrolytic cell—just like how mixing different ingredients in a recipe can give you a diverse range of dishes.

Quantitative Electrolysis Relationships

To build a bridge between theory and reality in electrolysis, we dive into the quantitative relationships, which are the numerical aspects of these reactions. Faraday's laws set the stage, offering the mathematical tools to predict the mass of a substance produced or consumed at an electrode based on the current flowing through the cell.

The key equation stemming from Faradays' laws is: \( m = \frac{I \times t \times M}{n \times F} \), where each symbol represents a vital piece of the electrolysis puzzle. Here's a breakdown:

• \( m \) - Mass of the substance produced at the electrode (grams)
• \( I \) - Current flowing through the cell (amperes)
• \( t \) - Time the current flows (seconds)
• \( M \) - Molar mass of the substance (grams per mole)
• \( n \) - Number of moles of electrons needed to produce one mole of substance
• \( F \) - Faraday's constant (approximately 96,485 coulombs per mole of electrons)

This equation is like a recipe that predicts how much product you will end up with based on how much current you 'cook' with and for how long. It quantitatively expresses the direct proportionality between the mass of the product and the current used, considering the time of the reaction and the substance's properties. Hence, understanding this relationship is pivotal for students as it allows them to calculate the expected outcome (yield) of an electrolysis process.