Problem 96 - A Complete Resource Book in Chemistry for JEE Main

Question

When \(\mathrm{X}\) amperes of current is passed through molten \(\mathrm{AlCl}_{3}\) for \(96.5\) seconds, \(0.09\) grams of aluminium is deposited. What is the value of \(X\) ? (a) 10 (b) 20 (c) 30 (d) 40

Step-by-Step Solution

Answer

Option (a) 10 amperes is the value of X.

Step 1: Determine Moles of Aluminium

Firstly, calculate the number of moles of aluminium deposited using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of aluminium (Al) is approximately 27 g/mol. \[ \text{moles of Al} = \frac{0.09}{27} \approx 0.00333 \text{ moles} \]

Step 2: Understand the Electrochemical Reaction

The reaction for aluminum deposition in electrolysis is:\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \]This tells us that depositing one mole of aluminum requires three moles of electrons.

Step 3: Calculate Total Charge Required

Using Faraday’s laws of electrolysis, 1 mole of electrons corresponds to a charge of 96500 Coulombs (Faraday's constant). Therefore, for 0.00333 moles of aluminum using 3 moles of electrons per mole of Al:\[ \text{Total charge} = 0.00333 \times 3 \times 96500 \approx 963.65 \text{ Coulombs} \]

Step 4: Use Current Formula to Find X

Current is the total charge passed divided by the time spent in seconds. Given that the time is 96.5 seconds, apply:\[ \text{Current} (I) = \frac{\text{Total charge}}{\text{Time}} = \frac{963.65}{96.5} \approx 10 \text{ Amperes} \]

Key Concepts

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis are fundamental principles that help us understand how electrolysis works. These laws were formulated by Michael Faraday, a pioneer in electrochemistry. They help us calculate the amount of substance produced or consumed during an electrolysis process.
When we pass electrical current through a compound, it causes a chemical reaction. The Laws of Electrolysis quantify this process by relating the amount of electric current to the amount of substance deposited.

• First Law: The mass of a substance deposited or released at an electrode is directly proportional to the quantity of electric charge passed through the electrolyte.
• Second Law: When the same quantity of electricity flows through different electrolytes in series, the masses of the substances deposited are proportional to their equivalent weights.

In simpler terms, these laws imply that the more current we pass through an electrolyte solution, the more material will be deposited. The laws are helpful in predicting the results of an electrolysis process. For instance, if we know the current and the time, we can find out how much material will be deposited.

Current Calculation

Calculating electrical current during electrolysis is essential to understanding how much charge flows through an electrolyte. Electrolysis makes use of electric current to drive a non-spontaneous chemical reaction.
Electric current, measured in amperes, represents the flow of electric charge in a circuit. During electrolysis, this charge is transferred in the form of electrons.
The formula used for current calculation in electrolysis is:

• \[I = \frac{Q}{t}\]
• Where \(I\) is the current in amperes, \(Q\) is the total charge in coulombs, and \(t\) is the time in seconds.

By understanding the total charge needed for the reaction, and the duration of the current flow, you can determine the current required to cause the electrolysis process. This is exactly what was demonstrated in the given exercise, where the calculated charge helped us determine the current of approximately 10 amperes.

Moles and Molar Mass Calculation

Understanding the concept of moles and molar mass is crucial in chemistry, especially when dealing with chemical reactions and electrolysis.
Moles help us to express amounts of a chemical substance. It provides a bridge between the atomic world (atoms, molecules) and the real-world amount of substance we can measure.
To calculate moles, we use the formula:

• \[\text{moles} = \frac{\text{mass}}{\text{molar mass}}\]
• Mass is the substance's mass in grams, and molar mass is the mass of one mole of the substance in grams per mole \(\text{g/mol}\).

For instance, in the exercise, we determined the moles of aluminum deposited using its known molar mass (27 g/mol) and the given mass (0.09 g). This calculation allows us to understand how much of a substance participates in the electrolysis process. It’s an essential step in determining the total charge needed, thanks to Faraday's laws, which is further used to find the current.