Q.A current strength of 3.86 A was passed through molten calcium oxide for 41 minutes and 40 seconds. The mass of calcium in grams deposited at the cathode is (atomic mass of Ca is 40 g/mol and 1F = 96500 C).

The charge carried by one mole of electrons (one Faraday) is 96500 C; dividing the given 9650 C by this Faraday constant gives the number of moles of electrons, which is then converted to a number of electrons using Avogadro's number.

Step 1 — moles of electrons: one Faraday, $F = 96500\ C$, is the charge of exactly one mole ($6.022\times10^{23}$) of electrons. The number of moles of electrons corresponding to 9650 C is: $n = \dfrac{9650\ C}{96500\ C\,mol^{-1}} = 0.1\ mol$

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The Faraday constant, $F=N_A\times e\approx 96500\ C\,mol^{-1}$, is the total charge of Avogadro's number of electrons — i.e. the charge carried by one mole of electrons.

$F=N_A\times e$, where $N_A=6.022\times10^{23}\ mol^{-1}$ (Avogadro's number) and $e=1.602\times10^{-19}\ C$ (charge on a single electron); multiplying gives $F\approx96500\ C\,mol^{-1}$. Option (b) describes the charge of a single electron, not a mole of them. Option (c) understates the number of electrons ($6.022\times10^{23}$, not $6.22\times10^{10}$). Option (a) describes the charge needed to deposit one equivalent of substance during electrolysis (which numerically equals 1 Fara …