Determine the time needed to liberate 1.0 litre of hydrogen at STP in an electrolytic cell using a current of 5.0 A .

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 29 minutes

The reaction for the liberation of hydrogen gas at the cathode is:

2H^{+} + 2e^{-} \rightarrow H_2

From the stoichiometry,

2 \text{ moles}

of electrons (

2 \text{ F}

of charge) are required to produce

1 \text{ mole}

of

H_2

gas.

At STP,

1 \text{ mole}

of an ideal gas occupies

22.4 \text{ L}

.

Number of moles of

H_2

in

1.0 \text{ L}

is

\dfrac{1.0}{22.4} \text{ mol}

.

Charge required,

Q = 2 \times \dfrac{1.0}{22.4} \times 96500 \text{ C} = \dfrac{96500}{11.2} \text{ C}

.

Using the formula

Q = I \times t

, where

I = 5.0 \text{ A}

:

t = \dfrac{Q}{I} = \dfrac{96500}{11.2 \times 5.0} \text{ s} = \dfrac{19300}{11.2} \text{ s} \approx 1723.2 \text{ s}

Converting time into minutes:

t = \dfrac{1723.2}{60} \text{ minutes} \approx 28.72 \text{ minutes}

This is approximately

29 \text{ minutes}

.

Determine the time needed to liberate 1.0 litre of hydrogen at STP...