When an electric current is passed through acidified water, `112ml` of `H_(2)` gas at `NTP` is collected at the cathode is `965` seconds. The current passed in amperes is

Options

A. 1
B. 0.5
C. 0.1
D. 2

Explanation

To find the current passed in amperes when 112 ml of hydrogen gas is collected at the cathode after passing an electric current through acidified water for 965 seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction at the cathode when hydrogen ions are reduced to hydrogen gas can be represented as:
\[ 2H^+ + 2e^- \rightarrow H_2 \]
This shows that 2 moles of electrons are required to produce 1 mole of hydrogen gas.

2. **Calculate the Number of Moles of Hydrogen Gas**:
At NTP (Normal Temperature and Pressure), 1 mole of any gas occupies 22.4 liters (or 22400 ml). Therefore, the number of moles of hydrogen gas collected can be calculated as:
\[ \text{Number of moles of } H_2 = \frac{\text{Volume of } H_2}{22400 \text{ ml}} = \frac{112 \text{ ml}}{22400 \text{ ml}} = 0.005 \text{ moles} \]

3. **Determine the Number of Electrons Transferred**:
Since 2 moles of electrons are required to produce 1 mole of hydrogen gas, the total number of moles of electrons transferred is:
\[ \text{Number of moles of electrons} = 2 \times \text{Number of moles of } H_2 = 2 \times 0.005 = 0.01 \text{ moles} \]

4. **Calculate the Total Charge (Q)**:
The total charge can be calculated using Faraday's constant, which is approximately 96500 coulombs per mole of electrons:
\[ Q = \text{Number of moles of electrons} \times \text{Faraday's constant} = 0.01 \text{ moles} \times 96500 \text{ C/mole} = 965 \text{ C} \]

5. **Calculate the Current (I)**:
Current can be calculated using the formula:
\[ I = \frac{Q}{t} \]
where \( Q \) is the total charge and \( t \) is the time in seconds. Substituting the values:
\[ I = \frac{965 \text{ C}}{965 \text{ s}} = 1 \text{ A} \]

### Final Answer:
The current passed is **1 ampere**.