First, let's determine the amount of oxygen generated during the electrolysis in terms of moles. We are given a volume of $$100 \mathrm{~ml}$$ which is equivalent to $$0.1 \mathrm{~L}$$.

At standard temperature and pressure (STP), 1 mole of any ideal gas occupies $$22.4 \mathrm{~L}$$. Therefore, the number of moles of oxygen gas ($$ \mathrm{O}_2 $$) can be calculated as:

$$ n = \frac{Volume \, of \, gas \, at \, STP}{Molar \, volume \, at \, STP} = \frac{0.1 \, L}{22.4 \, L/mol} \approx 0.004464 \, mol $$

In the electrolysis of water, the reaction at the anode (for oxygen) is:

$$ 2\mathrm{H_2O(l)} \rightarrow \mathrm{O_2(g)} + 4\mathrm{H^+(aq)} + 4e^- $$

According to the balanced chemical equation, $$ 1 \, mol $$ of $$ \mathrm{O}_2 $$ requires $$ 4 \, mol $$ of electrons. Therefore, the amount of charge needed to produce $$ 0.004464 \, mol $$ of $$ \mathrm{O}_2 $$ can be calculated using Faraday's first law of electrolysis, which states that the amount of substance liberated at an electrode is directly proportional to the quantity of electricity passed through the electrolyte. This gives us:

$$ Q = n \times F \times z $$

Where:

$$ n $$ is the number of moles of $$ \mathrm{O}_2 $$,
$$ F $$ is the Faraday constant ($$ 96500 \, C/mol $$ of electrons), and
$$ z $$ is the number of moles of electrons per mole of $$ \mathrm{O}_2 $$ (which is 4).

Let’s calculate the total charge ($$ Q $$):

$$ Q = 0.004464 \, mol \times 96500 \, C/mol \times 4 = 1721.792 \, C $$

To find the current in amperes, we use the relation between the charge ($$ Q $$), current ($$ I $$), and time ($$ t $$):

$$ I = \frac{Q}{t} $$

We are given that the time duration is 2 hours, so converting this to seconds gives us:

$$ t = 2 \, hours \times 3600 \, seconds/hour = 7200 \, seconds $$

Now we can calculate the required electric current ($$ I $$):

$$ I = \frac{1721.792 \, C}{7200 \, s} \approx 0.2391 \, A $$

This value aligns very closely with Option D, which is $$ 0.2393 \, A $$. Hence, the correct answer is:

Option D: 0.2393 A

Electrochemistry

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