Calculate the time required to liberate 9g of Aluminium metal, when a current of 18A is passed through it.

To solve this problem, we use Faraday’s First Law of Electrolysis, which states that the mass of a substance deposited during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

1. Analyze the Question

• Mass ($m$): 9g
• Current ($I$): 18A
• Element: Aluminium ($Al$)
• Molar Mass of Al: 27 g/mol
• Valency of Al: 3 (Aluminium forms $Al^{3+}$ ions, so $n = 3$)
• Faraday’s Constant ($F$): 96,500 C/mol

2. Explain the Concept

The formula for Faraday’s Law is:

Where:

• $m$ = mass deposited (g)
• $M$ = molar mass (g/mol)
• $I$ = current (A)
• $t$ = time (seconds)
• $n$ = number of electrons transferred (valency)
• $F$ = Faraday’s constant (96,500 C/mol)

We need to rearrange this formula to solve for time ($t$):

3. Show the Solution

Step 1: Plug the values into the formula

Step 2: Simplify the calculation

Step 3: Convert seconds to minutes Since the options are in minutes, divide by 60:

4. Identify the Answer

Comparing our result to the options provided, 89.35 minutes is approximately 89.34 minutes. This matches option B.

(Note: The slight difference is due to rounding variations in the value of Faraday's constant used in different textbooks, but 89.34 is the intended answer.)

5. Exam Tip

Always remember the "M-I-T-N-F" mnemonic for Faraday's law: Mass = (Molar mass × Current × Time) / (Number of electrons × Faraday constant). Also, always check if your final answer needs to be in seconds or minutes—many students lose marks by forgetting to divide by 60!