If the cost of electricity required to discharge 10g of an ion X\(^{3+}\) is N20.00,...

If the cost of electricity required to discharge 10g of an ion X\(^{3+}\) is N20.00, how much would it cost to discharge 6g of ion Y\(^{2+}\)?

[1 faraday = 96,500C, atomic masses are X = 27, Y = 24]

X\(^{3+}\) + 3e\(^-\) \(\to\) X

3F = 27g

xF = 10g

\(\frac{x}{3} = \frac{10}{27} \implies x = \frac{10}{9} F\)

\(\frac{10}{9}\)F \(\equiv\) N20.00

1F is equivalent to x

\(\frac{1}{\frac{10}{9}} = \frac{x}{20}\)

\(\frac{9}{10} = \frac{x}{20} \implies x = N18.00\)

1F is equivalent to N18.00.

Y\(^{2+}\) + 2e\(^-\) \(\to\) Y

2F = 24g

xF = 6g

x = \(\frac{6 \times 2}{24} = \frac{1}{2} F\)

1F = N18.00

\(\frac{1}{2}\)F = \(\frac{1}{2} \times N18.00\)

= N9.00

There is an explanation video available below.

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