A solution of \(\mathrm{CuSO}_{4}\) is electrolyzed for 7 minutes with a current of \(0.6 \mathrm{~A}\). The amount of electricity passed is equal to: (a) \(26 \mathrm{C}\) (b) \(4.2 \mathrm{C}\) (c) \(2.6 \times 10^{-4} \mathrm{~F}\) (d) \(2.6 \times 10^{-3} \mathrm{~F}\)

Faraday's laws of electrolysis are fundamental to understanding how electric current causes chemical changes during electrolysis. The first law states that the amount of chemical change at an electrode during electrolysis is proportional to the quantity of electricity passed through the electrolyte. In other words, the more charge you pass, the more substance is deposited or dissolved at the electrode. This can be expressed mathematically as:
\( m = (Q \times M) / (n \times F) \), where \( m \) is the mass of the substance altered at an electrode, \( Q \) is the total charge passed through the solution, \( M \) is the molar mass of the substance, \( n \) is the number of moles of electrons exchanged, and \( F \) is Faraday's constant, approximately \( 96,485 C/mol \) of electrons.

Implications of Faraday's First Law

Applying Faraday's first law can help predict the results of electrolytic processes such as electroplating or the production of pure metals. This law directly ties the theoretical yield with the practical application of electrolysis in industry.The second law of Faraday states that when the same amount of electric charge is passed through different electrolytes, the mass of substances altered at respective electrodes is directly proportional to their equivalent weights. Equivalent weight is the molar mass divided by the valence of the substance. These laws are crucial not only in theoretical chemistry but also in practical applications such as battery design, electroplating, and electrorefining.

When it comes to electrolysis, being able to calculate the charge is essential. As showcased in the exercise above, the charge passed through an electrolyte can be calculated using the formula
\( Q = I \times t \), where \( Q \) is the charge in coulombs (C), \( I \) is the current in amperes (A), and \( t \) is the time in seconds (s). This formula is a simplified representation that follows from the direct proportionality between the charge and the product of current and time, as noted by Faraday's first law.

Why Charge Calculation Matters

The calculation of charge is central to many electrochemical applications. For instance, in the context of battery charging/discharging, the amount of charge signifies how much energy a battery can store or has delivered. In industrial electrolytic processes, calculating charge helps in determining the efficiency of the process and the quantity of material transformed or produced.

Understanding the relationship between current and time in electrolysis is critical for accurately determining the extent of electrolysis that occurs. The direct proportionality between current and time is encapsulated in the formula for charge:
\( Q = I \times t \). A higher current or longer time will result in a greater charge, thus leading to more substance being electrolyzed.

Practical Example

In a practical scenario, such as the exercise provided, knowing the current supplied and the time it flows allows us to calculate the total charge passed. With a current of \(0.6 \text{ A}\) flowing for 7 minutes, or \(420 \text{ seconds}\), the charge passed is simply a product of these two quantities, equal to \(252 \text{ C}\). This value is critical for determining the overall yield of an electrolytic process, such as the amount of copper deposited from a solution of \(\mathrm{CuSO}_{4}\) during those 7 minutes.