For a hypothetical reaction,
`A+3BrarrP DeltaH=-2x Kj//"mole"` of A` &
`M` rarr `2Q+R` DeltaH=+x kJ//"mole"` of M
These reactions are carried simultaneously in a reactor such that temperature is not changing If rate of disppearance of B is y `sec^(-1)` then rate of formation (in M`sec^(-1))` of Q is :

Options

A. `(2)/(3)y`
B. `(3)/(2)y`
C. `(4)/(3)y`
D. `(3)/(4)y`

Answer

To solve the problem, we need to analyze the two given reactions and their stoichiometry to find the rate of formation of Q based on the rate of disappearance of B.

### Step-by-Step Solution:

1. **Identify the Reactions**:
- Reaction 1: \( A + 3B \rightarrow P \) with \( \Delta H = -2x \, \text{kJ/mole of A} \)
- Reaction 2: \( M \rightarrow 2Q + R \) with \( \Delta H = +x \, \text{kJ/mole of M} \)

2. **Understanding the Rates**:
- The rate of disappearance of B is given as \( y \, \text{sec}^{-1} \).
- From Reaction 1, the stoichiometry shows that for every 3 moles of B that disappear, 1 mole of A reacts. Therefore, the rate of disappearance of B can be expressed as:
\[ \text{Rate of disappearance of B} = -\frac{1}{3} \frac{d[B]}{dt} \]
- Let’s denote the rate of disappearance of B as \( \text{Rate}_1 \), so:
\[ \text{Rate}_1 = y = -\frac{1}{3} \frac{d[B]}{dt} \]

3. **Relating the Rates**:
- For Reaction 2, the formation of Q is related to the stoichiometry:
\[ \text{Rate of formation of Q} = +\frac{1}{2} \frac{d[Q]}{dt} \]
- Let’s denote the rate of formation of Q as \( \text{Rate}_2 \):
\[ \text{Rate}_2 = +\frac{1}{2} \frac{d[Q]}{dt} \]

4. **Setting Up the Equation**:
- From the stoichiometry of both reactions, we can relate the rates:
\[ \text{Rate}_1 = 3 \cdot \text{Rate}_2 \]
- Substituting the expressions for the rates:
\[ y = 3 \cdot \left(\frac{1}{2} \frac{d[Q]}{dt}\right) \]
- Rearranging gives:
\[ \frac{d[Q]}{dt} = \frac{2y}{3} \]

5. **Final Calculation**:
- Therefore, the rate of formation of Q is:
\[ \text{Rate of formation of Q} = \frac{2y}{3} \, \text{M sec}^{-1} \]

### Conclusion:
The rate of formation of Q is \( \frac{2y}{3} \, \text{M sec}^{-1} \).