A steady electric current of 5.0\text{ A} is passed through molten lead(II) bromide (PbBr_… — JAMB UTME

A steady electric current of $5.0\text{ A}$ is passed through molten lead(II) bromide ( $PbBr_2$ ) for $32\text{ minutes}$ and $10\text{ seconds}$ . What mass of lead, in grams, is deposited at the cathode? [ $\text{Pb} = 207$ , $1\text{ F} = 96\text{ }500\text{ C mol}^{-1}$ ]

Answer: 10.35 g

Answer

The mass of lead deposited at the cathode is

10.35\text{ g}

Passing a steady current of

5.0\text{ A}

for

1930\text{ s}

transfers

9650\text{ C}

of charge, corresponding to

0.10\text{ mol}

of electrons (

0.10\text{ F}

). Since reduction of lead(II) ions (

Pb^{2+} + 2e^- \rightarrow Pb

) requires 2 moles of electrons per mole of lead metal,

0.05\text{ mol}

of lead is deposited. Multiplying by the relative atomic mass of lead (

207\text{ g/mol}

) gives

10.35\text{ g}

Step-by-Step Solution

Convert time from minutes and seconds into total seconds

t = (32 \times 60\text{ s}) + 10\text{ s} = 1930\text{ s}

Time must be expressed in seconds to calculate electric charge in coulombs.

Calculate total quantity of electricity (

Q

) passed

Q = I \times t = 5.0\text{ A} \times 1930\text{ s} = 9650\text{ C}

Electric charge is the product of current in amperes and duration in seconds.

Calculate the moles of electrons transferred

\text{Moles of } e^- = \frac{9650\text{ C}}{96500\text{ C mol}^{-1}} = 0.10\text{ mol e}^-

One Faraday (

96500\text{ C}

) corresponds to one mole of electrons.

Relate moles of electrons to moles of lead metal using the cathode half-reaction

Pb^{2+} + 2e^- \rightarrow Pb(s) \implies \text{Moles of } Pb = \frac{0.10\text{ mol e}^-}{2} = 0.05\text{ mol}

Lead has a valency of 2 in

PbBr_2

, requiring 2 moles of electrons per mole of lead deposited.

Calculate the mass of deposited lead

\text{Mass} = 0.05\text{ mol} \times 207\text{ g mol}^{-1} = 10.35\text{ g}

Mass is obtained by multiplying the amount of substance in moles by its relative atomic mass.

Key Concept

Faraday's Laws of Electrolysis and Quantitative Calculations

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