An electrolytic cell is constructed for preparing hydrogen. For an average current of 2 ampere in the circuit, the time required to produce 450 mL of hydrogen at NTP is approximately

Options

A. 1/2 hour
B. 1 hour
C. 2 hours
D. 5 hours

Answer

To solve the problem of determining the time required to produce 450 mL of hydrogen gas at NTP using an electrolytic cell with a current of 2 amperes, we can follow these steps:

### Step 1: Calculate the number of moles of hydrogen gas produced
At NTP (Normal Temperature and Pressure), 1 mole of any gas occupies 22,400 mL. Therefore, to find the number of moles in 450 mL of hydrogen gas, we can use the formula:

\[ \text{Number of moles} = \frac{\text{Volume of gas (mL)}}{\text{Molar volume at NTP (mL/mol)}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{450 \text{ mL}}{22400 \text{ mL/mol}} \approx 0.0201 \text{ moles} \]

### Step 2: Determine the charge required to produce the hydrogen
The balanced reaction for the formation of hydrogen gas (H₂) from hydrogen ions (H⁺) is:

\[ 2 \text{H}^+ + 2e^- \rightarrow \text{H}_2 \]

This indicates that to produce 1 mole of H₂, 2 moles of electrons are required. Therefore, for 0.0201 moles of H₂, the moles of electrons required is:

\[ \text{Moles of electrons} = 2 \times 0.0201 \approx 0.0402 \text{ moles} \]

Now, we can calculate the total charge (Q) required using Faraday's constant (approximately 96500 C/mol):

\[ Q = \text{Moles of electrons} \times \text{Faraday's constant} \]
\[ Q = 0.0402 \text{ moles} \times 96500 \text{ C/mol} \approx 3889 \text{ C} \]

### Step 3: Calculate the time required using the current
We know that current (I) is defined as the charge (Q) per unit time (t):

\[ I = \frac{Q}{t} \]

Rearranging this gives:

\[ t = \frac{Q}{I} \]

Substituting the values we have:

\[ t = \frac{3889 \text{ C}}{2 \text{ A}} \approx 1944.5 \text{ seconds} \]

### Step 4: Convert time from seconds to hours
To convert seconds to hours, we use the conversion factor:

\[ \text{Time (hours)} = \frac{\text{Time (seconds)}}{3600} \]

Calculating this gives:

\[ \text{Time (hours)} = \frac{1944.5}{3600} \approx 0.54 \text{ hours} \]

### Final Answer
The time required to produce 450 mL of hydrogen at NTP is approximately **0.54 hours**.