A reaction `X_2(g)rarr Z(g) +1/2Y(g)` exhibits an increase in pressure from 150 mm to 170 mm in 10 minutes. The rate of disappearance of `X_2` in mm per minute is

Options

A. 2 mm per minute
B. 8 mm per minute
C. 4 mm per minute
D. 6 mm per minute

Answer

To solve the problem, we need to determine the rate of disappearance of \( X_2 \) based on the change in pressure during the reaction. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Reaction
The reaction given is:
\[ X_2(g) \rightarrow Z(g) + \frac{1}{2}Y(g) \]

### Step 2: Initial and Final Pressure
- Initial pressure of \( X_2 \) = 150 mm
- Final pressure after 10 minutes = 170 mm

### Step 3: Change in Pressure
The increase in pressure is calculated as:
\[ \text{Increase in Pressure} = \text{Final Pressure} - \text{Initial Pressure} = 170 \, \text{mm} - 150 \, \text{mm} = 20 \, \text{mm} \]

### Step 4: Relate Pressure Change to Reaction Progress
Let \( p \) be the pressure of \( X_2 \) that has reacted after 10 minutes. According to the stoichiometry of the reaction:
- For every 1 mole of \( X_2 \) that reacts, the pressure decreases by \( p \).
- The products \( Z \) and \( Y \) contribute to the pressure increase:
- Pressure contribution from \( Z \) = \( p \)
- Pressure contribution from \( Y \) = \( \frac{p}{2} \)

### Step 5: Set Up the Equation
The total pressure after 10 minutes can be expressed as:
\[ \text{Final Pressure} = \text{Initial Pressure} - p + p + \frac{p}{2} \]
Substituting the known values:
\[ 170 = 150 - p + p + \frac{p}{2} \]
This simplifies to:
\[ 170 = 150 + \frac{p}{2} \]

### Step 6: Solve for \( p \)
Rearranging the equation gives:
\[ 170 - 150 = \frac{p}{2} \]
\[ 20 = \frac{p}{2} \]
Multiplying both sides by 2:
\[ p = 40 \, \text{mm} \]

### Step 7: Calculate the Rate of Disappearance
The rate of disappearance of \( X_2 \) can be calculated as:
\[ \text{Rate} = \frac{\text{Change in Pressure}}{\text{Time}} = \frac{p}{10 \, \text{minutes}} = \frac{40 \, \text{mm}}{10 \, \text{minutes}} = 4 \, \text{mm/min} \]

### Final Answer
The rate of disappearance of \( X_2 \) is:
\[ \boxed{4 \, \text{mm/min}} \]