During the industrial extraction of sodium metal by the electrolysis of molten sodium chlo… — JAMB UTME

During the industrial extraction of sodium metal by the electrolysis of molten sodium chloride in a Downs cell, a steady current of $9.65\text{ A}$ is passed through the electrolytic cell for $50\text{ minutes}$ . What mass of pure sodium metal is collected at the cathode? [ $\text{Na} = 23$ , $1\text{ F} = 96,500\text{ C mol}^{-1}$ ]

$6.9\text{ g}$ Answer
B
$3.45\text{ g}$
C
$13.8\text{ g}$
D
$6.72\text{ g}$

Answer

The mass of pure sodium metal collected at the cathode is

6.9\text{ g}

At the cathode of the Downs cell, sodium ions undergo single-electron reduction (

\text{Na}^+ + e^- \rightarrow \text{Na}

). Passing

28,950\text{ C}

of charge transfers

0.3\text{ mol}

of electrons. Multiplying

0.3\text{ mol}

by the atomic mass of sodium (

23\text{ g mol}^{-1}

) yields exactly

6.9\text{ g}

Step-by-Step Solution

Calculate the total electric charge (

Q

) passed through the cell in seconds.

Q = I \times t = 9.65\text{ A} \times (50 \times 60\text{ s}) = 28,950\text{ C}

Electric charge is determined by multiplying current in amperes by time in seconds.

Calculate the amount of substance (in moles) of electrons transferred.

Moles of

e^- = \frac{Q}{F} = \frac{28,950\text{ C}}{96,500\text{ C mol}^{-1}} = 0.3\text{ mol}

One Faraday (

96,500\text{ C}

) corresponds to the electric charge of one mole of electrons.

Relate the moles of electrons to the moles of sodium metal deposited using the cathode reduction half-equation.

Cathode reaction:

\text{Na}^+ + e^- \rightarrow \text{Na}

. Thus,

1\text{ mol}

e^-

produces

1\text{ mol}

\text{Na}

, yielding

0.3\text{ mol}

\text{Na}

Sodium is a univalent alkali metal cation requiring 1 electron per discharged ion.

Calculate the mass of sodium metal deposited.

Mass of

\text{Na} = 0.3\text{ mol} \times 23\text{ g mol}^{-1} = 6.9\text{ g}

Mass is obtained by multiplying the number of moles by the relative atomic mass.

Key Concept

Quantitative Electrolysis of Molten Salts in Downs Cell Extraction

Estimated Time:2m 0s

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