If three moles of electrons are passed through molten `RbCl, BrCl_(2)` and `AuCl_(3)` then the ratio of amounts of different substances deposited at the cathodes of respective electrolytic cells is

Options

A. `6 : 3 : 2`
B. `1 : 2 : 3`
C. `3 : 2 : 1`
D. `2 : 3 : 6`

Answer

A

Explanation

The `SI` unit of amount is mole. The quantity of material formed or consumed in elctrolysis is inversely proportional to the number of electrons per mole required to bring about the indicated change in oxidation state Consider the reactions at the cathodes of the three electrolytic cell:
`Rb^(l)+e^(-) rarr Rb(l)`
`Ba^(2+)(l)+2e^(-) rarr Ba(l)`
`Au^(3+)(l)+e^(-) rarr Rb(l)`
`1` mole of electrons cause the formation of `1` mol of `Rb` matel in the electrolusis of molten rubidium chloride. Thus, `3` mol electrons will deposit `3` mol of `Rb` matel.
In the electrolysis of molten `BaCl_(2)`, twice as many electrons per mole are needed to bring about the indicated change in oxidation state, because the charge on the `Ba^(2+)` is twice the charge on the `Rb^(+)` ion. Here `1` mol of electrons deposits only `0.5` mol of `Ba` metal. Thus, `3` mol electrons will deposit `3(0.5)` or `1.5` mol of `Ba` metal.
In the electrolysis of molten `AuCl_(3)`, one mole of electrons deposit only `(1)//(3)` mol of `Au` metal. Thus, `3` mol electrons will deposit `1` mol of `Au` matel.
The ratio of amount (moles) is therefore
`3 : 1.5 : 1`
or `6 : 3 : 2`