When electric current is passed through acidified water for 1930 s, 1120 mL of `H_(2)` gas is collected (at STP) at the cathode. What is the current passed in amperes?

Options

A. `0.05`
B. `0.50`
C. `5.0`
D. `50`

Explanation

To solve the problem of finding the current passed in amperes when electric current is passed through acidified water for 1930 seconds, resulting in the collection of 1120 mL of hydrogen gas at STP, we can follow these steps:

### Step 1: Convert the volume of hydrogen gas to moles
At STP (Standard Temperature and Pressure), 1 mole of gas occupies 22,400 mL. Therefore, we can calculate the number of moles of hydrogen gas (H₂) collected.

\[ \text{Number of moles of } H_2 = \frac{\text{Volume of } H_2}{\text{Molar volume at STP}} = \frac{1120 \, \text{mL}}{22400 \, \text{mL/mol}} = 0.05 \, \text{mol} \]

### Step 2: Determine the charge required to produce the moles of hydrogen
According to Faraday's laws of electrolysis, the charge (Q) required to produce a certain amount of substance is given by:

\[ Q = n \cdot F \]

Where:
- \( n \) = number of moles of electrons transferred
- \( F \) = Faraday's constant (approximately 96500 C/mol)

For the electrolysis of water, the reaction produces 1 mole of H₂ gas for every 2 moles of electrons (since 2 electrons are required to produce 1 mole of H₂). Therefore, for 0.05 moles of H₂:

\[ n = 2 \times 0.05 = 0.1 \, \text{mol of electrons} \]

Now, calculate the charge:

\[ Q = 0.1 \, \text{mol} \times 96500 \, \text{C/mol} = 9650 \, \text{C} \]

### Step 3: Calculate the current using the formula
The current (I) can be calculated using the formula:

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

Where:
- \( Q \) = total charge in coulombs
- \( t \) = time in seconds

Substituting the values we have:

\[ I = \frac{9650 \, \text{C}}{1930 \, \text{s}} \approx 5 \, \text{A} \]

### Conclusion
The current passed is approximately **5 amperes**.

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