Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 moles of H₂ gas at the cathode is (1 Faraday = 96500 C mol^-1)

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38.6 × 10⁴ sec

9.65 × 10⁴ sec

28.95 × 10⁴ sec

19.3 × 10⁴ sec

answer is B.

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Detailed Solution

When dilute aqueous solution is electrolysed, at cathode, Hydrogen gas and at anode, Oxygen gas are liberated.
$2 H_{2} O + 2 e^{-} \to H_{2} .$
For liberation of 1 mole of H₂, 2 moles of e^- are required .
0.01 moles of H₂ will require 2 X 0.01 = 0.02 moles of electrons or 0.02 faradays.
Charge required = i X t
$Time (t) = \frac{Charge}{Current}$
i= 10 mill ampere = 10 X 10^-3 ampere.
$t = \frac{0.02 X 96500}{10 X 10^{- 3}} = 19.3 X 10^{4} seconds .$