A gaseous reaction : `2A(g) + B(g) to 2C(g)`, Show a derease in pressure from 120 mm to 100 mm in 10 minutes. The rate of appearance of C is

Options

A. 2 mm/min
B. 4 mm/min
C. 10 mm/min
D. 12 mm/min

Explanation

To solve the problem, we need to determine the rate of appearance of product C in the given reaction:

**Reaction:**
\[ 2A(g) + B(g) \rightarrow 2C(g) \]

**Given:**
- Initial pressure = 120 mm
- Final pressure = 100 mm
- Time = 10 minutes

### Step-by-Step Solution:

1. **Calculate the Change in Pressure:**
\[ \Delta P = P_{\text{initial}} - P_{\text{final}} = 120 \, \text{mm} - 100 \, \text{mm} = 20 \, \text{mm} \]

2. **Calculate the Rate of Pressure Change:**
The rate of change in pressure over time can be calculated as:
\[ \text{Rate} = \frac{\Delta P}{\Delta t} = \frac{20 \, \text{mm}}{10 \, \text{minutes}} = 2 \, \text{mm/min} \]

3. **Relate the Rate of Pressure Change to the Rate of Appearance of C:**
In the reaction, for every 2 moles of C produced, the pressure decreases by 20 mm (since 2 moles of gas are consumed). Therefore, the rate of appearance of C can be expressed as:
\[ \text{Rate of appearance of C} = \frac{1}{2} \times \text{Rate of pressure change} \]

4. **Substituting the Rate of Pressure Change:**
\[ \text{Rate of appearance of C} = \frac{1}{2} \times 2 \, \text{mm/min} = 1 \, \text{mm/min} \]

### Final Answer:
The rate of appearance of C is \( 1 \, \text{mm/min} \).