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