Calculate the number of Faradays required to discharge 6g of ion X3+ if the cost to discharge 10g of X3+ is ₦20.00.

First, find the moles of X:

$$\text{Moles of X} = \frac{\text{Mass of X}}{\text{Atomic mass of X}} = \frac{10 \text{ g}}{27 \text{ g/mol}}$$

The discharge reaction for $\text{X}^{3+}$ is:

$$\text{X}^{3+} + 3\text{e}^- \to \text{X}$$

This means 3 Faradays (3F) are required to discharge 1 mole of X.
So, the Faradays required for 10g of X is:

$$\text{Faradays for X} = \text{Moles of X} \times \text{Charge of X}^{3+}$$ $$\text{Faradays for X} = \frac{10}{27} \text{ mol} \times 3 \text{ F/mol} = \frac{30}{27} \text{ F} = \frac{10}{9} \text{ F}$$

We are given that the cost to discharge 10g of $\text{X}^{3+}$ (which is $\frac{10}{9}$ F) is ₦20.00.

$$\text{Cost per Faraday} = \frac{\text{Total cost}}{\text{Total Faradays}} = \frac{\text{₦}20.00}{\frac{10}{9} \text{ F}}$$ $$\text{Cost per Faraday} = \text{₦}20.00 \times \frac{9}{10} \text{ F}^{-1} = \text{₦}2 \times 9 \text{ F}^{-1} = \text{₦}18.00/\text{F}$$

First, find the moles of Y:

$$\text{Moles of Y} = \frac{\text{Mass of Y}}{\text{Atomic mass of Y}} = \frac{6 \text{ g}}{24 \text{ g/mol}} = \frac{1}{4} \text{ mol} = 0.25 \text{ mol}$$

The discharge reaction for $\text{Y}^{2+}$ is:

$$\text{Y}^{2+} + 2\text{e}^- \to \text{Y}$$

This means 2 Faradays (2F) are required to discharge 1 mole of Y.
So, the Faradays required for 6g of Y is:

$$\text{Faradays for Y} = \text{Moles of Y} \times \text{Charge of Y}^{2+}$$ $$\text{Faradays for Y} = \frac{1}{4} \text{ mol} \times 2 \text{ F/mol} = \frac{2}{4} \text{ F} = \frac{1}{2} \text{ F} = 0.5 \text{ F}$$

Using the cost per Faraday calculated in Step 2:

$$\text{Cost for Y} = \text{Faradays for Y} \times \text{Cost per Faraday}$$ $$\text{Cost for Y} = 0.5 \text{ F} \times \text{₦}18.00/\text{F} = \text{₦}9.00$$

The cost to discharge 6g of ion $\text{Y}^{2+}$ is ₦9.00.

The final answer is $\text{₦9.00}$.