Find the time requried to liberate 1.0 litre of hydrogen at STP in an electrolytic cell by a current of `5.0 A`.

Explanation

To solve the problem of finding the time required to liberate 1.0 litre of hydrogen at STP in an electrolytic cell by a current of 5.0 A, we can follow these steps:

### Step 1: Calculate the number of moles of hydrogen gas (H2) in 1.0 litre.
At STP (Standard Temperature and Pressure), 1 mole of a gas occupies 22.4 litres. Therefore, the number of moles of hydrogen in 1.0 litre can be calculated as:

\[ \text{Number of moles} = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{1.0 \, \text{litre}}{22.4 \, \text{litres/mole}} = \frac{1}{22.4} \, \text{moles} \]

### Step 2: Calculate the mass of hydrogen gas (H2).
The molar mass of hydrogen (H2) is approximately 2 g/mol. Therefore, the mass of hydrogen can be calculated as:

\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} = \left(\frac{1}{22.4}\right) \times 2 \, \text{g} = \frac{2}{22.4} \, \text{g} \]

### Step 3: Calculate the electrochemical equivalent (Z) of hydrogen.
The electrochemical equivalent (Z) is given by the formula:

\[ Z = \frac{\text{Equivalent weight}}{\text{Faraday's constant}} \]

The equivalent weight of hydrogen is 1 g/equiv, and Faraday's constant is approximately 96500 C/equiv. Therefore:

\[ Z = \frac{1 \, \text{g/equiv}}{96500 \, \text{C/equiv}} = \frac{1}{96500} \, \text{g/C} \]

### Step 4: Use the formula to find the time (T).
The formula relating mass (M), electrochemical equivalent (Z), current (I), and time (T) is:

\[ M = Z \times I \times T \]

Rearranging this formula to find time gives:

\[ T = \frac{M}{Z \times I} \]

Substituting the values we have:

- Mass \( M = \frac{2}{22.4} \, \text{g} \)
- Electrochemical equivalent \( Z = \frac{1}{96500} \, \text{g/C} \)
- Current \( I = 5.0 \, \text{A} \)

So,

\[ T = \frac{\frac{2}{22.4}}{\left(\frac{1}{96500}\right) \times 5} \]

### Step 5: Calculate the time (T).
Calculating the denominator:

\[ Z \times I = \left(\frac{1}{96500}\right) \times 5 = \frac{5}{96500} \]

Now substituting back into the equation for T:

\[ T = \frac{\frac{2}{22.4}}{\frac{5}{96500}} = \frac{2 \times 96500}{22.4 \times 5} \]

Calculating the values:

\[ T = \frac{193000}{112} \approx 1725.00 \, \text{seconds} \]

### Step 6: Convert seconds to minutes.
To convert seconds to minutes, divide by 60:

\[ T \approx \frac{1725.00}{60} \approx 28.75 \, \text{minutes} \approx 29 \, \text{minutes} \]

### Final Answer:
The time required to liberate 1.0 litre of hydrogen at STP by a current of 5.0 A is approximately **29 minutes**.

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