An aqueous solution of chromium(III) tetraoxosulfate(VI) is electrolyzed using inert plati… — JAMB UTME

An aqueous solution of chromium(III) tetraoxosulfate(VI) is electrolyzed using inert platinum electrodes. A steady current of $5.00\text{ A}$ is passed through the electrolyte for $96.5\text{ minutes}$ . If the cathodic current efficiency for chromium deposition is $75.0\%$ , calculate the mass, in grams, of chromium metal deposited at the cathode. [Molar mass of $\text{Cr} = 52.0\text{ g/mol}$ , $1\text{ F} = 96500\text{ C/mol}$ ]

Answer: 3.9 g

Answer

3.90\text{ g}

To find the mass of chromium deposited, calculate total charge (

Q = I \times t = 5.00 \times 5790 = 28950\text{ C}

), adjust for

75.0\%

current efficiency (

Q_{\text{eff}} = 21712.5\text{ C}

), convert to Faradays (

0.225\text{ F}

), divide by the valency of 3 for

\text{Cr}^{3+}

to find moles of chromium (

0.075\text{ mol}

), and multiply by molar mass (

52.0\text{ g/mol}

) to yield

3.90\text{ g}

Step-by-Step Solution

Convert the electrolysis time into seconds

t = 96.5 \times 60 = 5790\text{ s}

Standard SI unit of time (seconds) is required for charge calculation (

Q = I \times t

Calculate the total charge transferred

Q = 5.00\text{ A} \times 5790\text{ s} = 28950\text{ C}

Determines total quantity of electricity delivered by the current source.

Apply the current efficiency percentage

Q_{\text{eff}} = 28950\text{ C} \times 0.750 = 21712.5\text{ C}

Only 75% of the total current is utilized specifically for reducing chromium ions.

Convert effective charge into moles of electrons

n_e = \frac{21712.5\text{ C}}{96500\text{ C/mol}} = 0.225\text{ mol } e^-

Faraday's constant gives the charge carried per mole of electrons.

Relate moles of electrons to moles of chromium deposited

n_{\text{Cr}} = \frac{0.225}{3} = 0.075\text{ mol}

Reduction of one mole of

\text{Cr}^{3+}

requires three moles of electrons (3 Faradays).

Calculate the mass of chromium deposited

m = 0.075\text{ mol} \times 52.0\text{ g/mol} = 3.90\text{ g}

Mass is obtained by multiplying the number of moles by the molar mass.

Key Concept

Faraday's Laws of Electrolysis and Current Efficiency

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