To solve the problem of determining the time required to produce 450 mL of hydrogen at NTP using an electrolytic cell with an average current of 2 A, we can follow these steps:
### Step 1: Determine the number of moles of hydrogen produced
At NTP (Normal Temperature and Pressure), 1 mole of gas occupies 22,400 mL. Therefore, we can calculate the number of moles of hydrogen (H₂) produced from the given volume:
\[
\text{Number of moles} = \frac{\text{Volume}}{22,400 \, \text{mL}} = \frac{450 \, \text{mL}}{22,400 \, \text{mL/mol}} \approx 0.0201 \, \text{mol}
\]
### Step 2: Identify the electrochemical reaction
The electrochemical reaction for the production of hydrogen gas is:
\[
2H^+ + 2e^- \rightarrow H_2
\]
This indicates that 2 moles of electrons are required to produce 1 mole of hydrogen gas.
### Step 3: Calculate the total charge required
Using Faraday's law, the charge (Q) required to produce a certain number of moles of hydrogen can be calculated using the formula:
\[
Q = n \times F
\]
Where:
- \( n \) is the number of moles of electrons required,
- \( F \) is Faraday's constant (approximately 96500 C/mol).
Since 2 moles of electrons are needed to produce 1 mole of hydrogen, for 0.0201 moles of hydrogen, the number of moles of electrons required is:
\[
n = 2 \times 0.0201 \approx 0.0402 \, \text{mol}
\]
Now, calculate the total charge:
\[
Q = 0.0402 \, \text{mol} \times 96500 \, \text{C/mol} \approx 3889.3 \, \text{C}
\]
### Step 4: Calculate the time required using the current
The relationship between charge, current, and time is given by:
\[
Q = I \times t
\]
Where:
- \( Q \) is the total charge,
- \( I \) is the current (2 A),
- \( t \) is the time in seconds.
Rearranging the formula to find time:
\[
t = \frac{Q}{I} = \frac{3889.3 \, \text{C}}{2 \, \text{A}} \approx 1944.65 \, \text{s}
\]
### Step 5: Convert time from seconds to hours
To convert seconds to hours:
\[
t \text{ (in hours)} = \frac{1944.65 \, \text{s}}{3600 \, \text{s/hour}} \approx 0.54 \, \text{hours}
\]
### Final Answer
The time required to produce 450 mL of hydrogen at NTP is approximately **0.54 hours**.
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