Calculate the time required to liberate 9g of Aluminium metal, when a current of 18A is passed through it. (1F = 96500C , Al = 27)

Answer Details

This is a Faraday's law of electrolysis problem. The relationship between mass deposited, current, and time is:

\[m = \frac{M \times I \times t}{n \times F}\]

where \(m\) = mass deposited (g), \(M\) = molar mass, \(I\) = current (A), \(t\) = time (s), \(n\) = number of electrons transferred per ion, and \(F\) = Faraday constant (96500 C/mol).

For aluminium: \(\text{Al}^{3+} + 3e^- \rightarrow \text{Al}\), so \(n = 3\), \(M = 27\), \(m = 9\) g, \(I = 18\) A.

Rearranging for time:

\[t = \frac{m \times n \times F}{M \times I}\]

\[t = \frac{9 \times 3 \times 96500}{27 \times 18}\]

\[t = \frac{2\,605\,500}{486}\]

\[t = 5360.49 \text{ seconds}\]

Converting to minutes:

\[t = \frac{5360.49}{60} = 89.34 \text{ minutes}\]

The time required is 89.34 minutes.