Question

Write a mathematical formula for mole ratio. How long will it take to produce 2.415g of Ag metal from its salt solution by passing a current of 3A? Molar mass of Ag= 107.9 g mol^-1.

Answer 1

A mathematical formula for mole ratio:

Mole ratio = `"Moles of product formed in half-reaction"/"Moles of electrons required in half-reaction"`

Given: Mass of silver deposited (W) = 2.415 g, Current (I) = 3 A, Molar mass of silver = 107.9 g mol^–1

To find: Time (t)

Formulae: 

1. Mole ratio = `"Moles of product formed in half-reaction"/"Moles of electrons required in half-reaction"`
2. W = `("I" ("A") xx "t"("s"))/(96500 ("C"//"mole e"^-)) xx "mole ratio" xx "molar mass"`

Calculation:

Stoichiometry: \[\ce{Ag^+_{ (aq)} + e^- -> Ag_{(s)}}\]

Using formula (1),

Mole ratio = `(1  "mol")/(1  "mole e"^-)`

Using formula (2),

W = `("I" ("A") xx "t"("s"))/(96500 ("C"//"mole e"^-)) xx "mole ratio" xx "molar mass of Ag"`

`2.415 cancel("g") = (3 "A" xx "t")/(96500 ("C"//cancel("mol")"e"^-)) xx (1 cancel("mol"))/(1 cancel ("mol") "e"^-) xx 107.9 "g"  cancel("mol"^-1)`

t = `(2.415 xx 96500 ("C" = cancel("A")"s"))/(3 cancel("A") xx 107.9)` = 720 s = 12 min.

Time taken to produce 2.415 g of Ag at the cathode is 12 min.