The cost of discharging 6.0g of a divalent metal, X from its salt is ₦12.00. What is the cost of discharging…

To solve this problem, we use Faraday’s Laws of Electrolysis, which state that the mass ($m$) of a substance deposited is proportional to the quantity of electricity ($Q$) passed through the electrolyte.

1. Analyze the Question

• Metal X (Divalent): Mass ($m_x$) = 6.0g, Molar mass ($M_x$) = 63, Valency ($n_x$) = 2. Cost = ₦12.00.
• Metal Y (Trivalent): Mass ($m_y$) = 9.0g, Molar mass ($M_y$) = 27, Valency ($n_y$) = 3. Cost = ?

2. Explain the Concept

The quantity of electricity ($Q$) required to deposit a mass ($m$) is given by:

Where:

• $n$ = valency (number of electrons involved)
• $F$ = Faraday's constant
• $M$ = Molar mass

Since the cost is proportional to the quantity of electricity used, we can say:

Where $k$ is a constant representing the cost per unit of electricity.

3. Show the Solution

Step 1: Calculate the quantity of electricity for Metal X ($Q_x$)

We know that $Q_x$ costs ₦12.00. Therefore, the cost per Faraday ($k$) is:

Step 2: Calculate the quantity of electricity for Metal Y ($Q_y$)

Step 3: Calculate the cost for Metal Y

4. Identify the Answer

The cost of discharging 9.0g of metal Y is ₦63.00. This corresponds to option C.

5. Exam Tip

When dealing with electrolysis cost problems, always remember the "Faraday equivalent" formula: $Q = \frac{m \times n}{M}$. By calculating the number of Faradays required for each metal first, you simplify the problem into a basic ratio calculation, which saves time and reduces errors in the exam hall.