Problem 70 - A Complete Resource Book in Chemistry for JEE Main

Question

The charge required to deposit \(40.5 \mathrm{~g}\) of \(\mathrm{Al}\) (atomic mass \(=27.0 \mathrm{~g}\) ) from the fused \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is (a) \(0.434 \times 10^{5} \mathrm{C}\) (b) \(4.34 \times 10^{5} \mathrm{C}\) (c) \(3.34 \times 10^{5} \mathrm{C}\) (d) \(43.4 \times 10^{5} \mathrm{C}\)

Step-by-Step Solution

Answer

The charge required is \(4.34 \times 10^5 \text{ C}\), option (b).

Step 1: Calculate Moles of Aluminium

To find the moles of aluminium, use the formula: moles = \( \frac{\text{mass}}{\text{atomic mass}} \). So, substitute the values for mass as 40.5 g and atomic mass as 27.0 g/mol: \[ \text{moles of Al} = \frac{40.5}{27.0} = 1.5 \text{ moles} \]

Step 2: Determine Electrons per Mole of Al

The reaction for aluminium during electrolysis is \( \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \). This means that 3 moles of electrons are required to produce 1 mole of aluminium.

Step 3: Calculate Total Moles of Electrons Required

Since 1 mole of aluminium requires 3 moles of electrons, for 1.5 moles of aluminium, the moles of electrons needed are: \[ \text{moles of electrons} = 1.5 \times 3 = 4.5 \text{ moles} \]

Step 4: Convert Moles of Electrons to Coulombs

According to Faraday's law, 1 mole of electrons corresponds to approximately 96500 Coulombs (Faraday's constant). Therefore, 4.5 moles of electrons will be: \[ \text{charge (C)} = 4.5 \times 96500 = 434250 \text{ C} \]

Step 5: Compare with Given Options

The calculated charge of 434250 C is equal to \(4.34 \times 10^5 \text{ C}\). Thus, the correct option is (b) \(4.34 \times 10^5 \text{ C}\).

Key Concepts

Faraday's Laws

Faraday's Laws of Electrolysis are crucial in understanding how electrical energy causes chemical changes. There are two primary laws:

• First Law: The amount of substance deposited at an electrode during electrolysis is directly proportional to the quantity of electricity (or charge) that passes through the electrolyte. In simple terms, the more charge you use, the more substance you can deposit.
• Second Law: When the same amount of electricity is passed through different electrolytes, the mass of substance deposited is proportional to the equivalent weight of the substance. This suggests that different substances will deposit in amounts based on their chemical equivalency.

These laws are particularly helpful in calculating the charges required to deposit certain masses of substances during electrolysis. Understanding Faraday's laws can help predict how much of a material will be transformed, and how much charge is needed for specific reactions.

Electrolysis

Electrolysis is a technique used to drive a non-spontaneous chemical reaction with the help of an electric current. It involves the following key components:

• An electrode: There's a cathode (negative) and an anode (positive) where the reaction takes place. At the cathode, reduction occurs, while oxidation occurs at the anode.
• Electrolyte: This can be a fused substance or an aqueous solution that contains free ions and conducts electricity.

During electrolysis of aluminum from its fused salt, electric current is applied to separate the ions. Only the aluminum ions are reduced, forming aluminum metal. The driving of the current facilitates the movement of ions toward the electrodes, achieving the desired reaction.

Moles and Atomic Mass

In chemistry, understanding moles and atomic mass is key to making calculations for reactions.

• Atomic Mass: This is the weight of a single atom of a chemical element, typically measured in atomic mass units (amu). For instance, aluminum's atomic mass is 27.0 amu.
• Mole: A mole is a fundamental unit in chemistry used to express amounts of a chemical substance, defined as exactly 6.02214076×10^23 (Avogadro's number) particles, be it atoms, molecules, ions, or electrons.

To determine the number of moles in a given mass, you can use the formula \( \text{moles} = \frac{\text{mass}}{\text{atomic mass}} \). For example, with aluminum, if you have 40.5 grams, you simply divide by its atomic mass (27.0 g/mol) to find that it equates to 1.5 moles. This is crucial for understanding how much material is needed or produced in a reaction.