A factory produces 40 kg of Calcium in two hours by electrolysis. How much Aluminium can be produced by the same current in two hours ? (At. wt. of $Ca=40.$ $Al=27$)

Question

Accepted Answer

To determine how much Aluminium can be produced by the same current in two hours, we need to consider the electrochemical equivalent of both Calcium and Aluminium. The electrochemical equivalent is determined by the atomic weight divided by the valency of the element.

1. **Calcium (Ca):**
   - Atomic weight = 40
   - Valency = 2 (since Calcium forms Ca²⁺ ions)
   - Electrochemical equivalent of Calcium = 40/2 = 20

2. **Aluminium (Al):**
   - Atomic weight = 27
   - Valency = 3 (since Aluminium forms Al³⁺ ions)
   - Electrochemical equivalent of Aluminium = 27/3 = 9

Given that 40 kg of Calcium is produced in two hours, we can use the ratio of electrochemical equivalents to find out how much Aluminium can be produced by the same current in the same time period.

The amount of substance produced is directly proportional to its electrochemical equivalent. Therefore, the ratio of the mass of Aluminium produced to the mass of Calcium produced is equal to the ratio of their electrochemical equivalents:

$$
\frac{\text{Mass of Aluminium}}{\text{Mass of Calcium}} = \frac{\text{Electrochemical equivalent of Aluminium}}{\text{Electrochemical equivalent of Calcium}}
$$

Substituting the values:

$$
\frac{\text{Mass of Aluminium}}{40} = \frac{9}{20}
$$

Solving for the mass of Aluminium:

$$
\text{Mass of Aluminium} = 40 \times \frac{9}{20} = 18 \text{ kg}
$$

Thus, 18 kg of Aluminium can be produced by the same current in two hours, which corresponds to Option 2.

**Explanation for Incorrect Options:**

- **Option 1 (22 kg):** This option is incorrect because it overestimates the amount of Aluminium that can be produced. The calculation based on electrochemical equivalents shows that only 18 kg can be produced.

- **Option 3 (9 kg):** This option is incorrect because it underestimates the amount of Aluminium that can be produced. The correct calculation shows that 18 kg can be produced.

- **Option 4 (27 kg):** This option is incorrect because it significantly overestimates the amount of Aluminium that can be produced. The calculation based on the electrochemical equivalents clearly indicates that only 18 kg can be produced.

Therefore, the correct answer is Option 2, which is supported by the calculations based on the electrochemical equivalents of Calcium and Aluminium.