For a reaction `P + Q to 2R + S`. Which of the following statements is incorrect?

Options

A. Rate of disappearance of P = Rate of appearance of S
B. Rate of disappearance of Q = `2 xx` Rate of appearance of R
C. Rate of disappearance of P = Rate of disappearance of Q
D. Rate of disappearance of Q = `(1)/(2) xx` Rate of appearance of R

Answer

To solve the question regarding the reaction \( P + Q \rightarrow 2R + S \) and identify the incorrect statement among the options, we will analyze the rates of disappearance and appearance of the reactants and products.

### Step 1: Write the Rate Expressions
For the reaction \( P + Q \rightarrow 2R + S \), we can express the rates of disappearance and appearance as follows:

- Rate of disappearance of \( P \):
\[ -\frac{d[P]}{dt} \]
- Rate of disappearance of \( Q \):
\[ -\frac{d[Q]}{dt} \]
- Rate of appearance of \( R \):
\[ \frac{1}{2} \frac{d[R]}{dt} \]
- Rate of appearance of \( S \):
\[ \frac{d[S]}{dt} \]

### Step 2: Relate the Rates
From the stoichiometry of the reaction, we can relate the rates as follows:

1. The rate of disappearance of \( P \) is equal to the rate of disappearance of \( Q \):
\[ -\frac{d[P]}{dt} = -\frac{d[Q]}{dt} \]
2. The rate of disappearance of \( P \) is half the rate of appearance of \( R \):
\[ -\frac{d[P]}{dt} = \frac{1}{2} \frac{d[R]}{dt} \]
3. The rate of disappearance of \( Q \) is also half the rate of appearance of \( R \):
\[ -\frac{d[Q]}{dt} = \frac{1}{2} \frac{d[R]}{dt} \]

### Step 3: Analyze the Statements
Now, we will analyze the statements provided in the options:

1. **Statement A**: The rate of disappearance of \( P \) is equal to the rate of appearance of \( S \).
- This is **correct** because both sides of the equation balance out.

2. **Statement B**: The rate of disappearance of \( Q \) is equal to \( 2 \times \) the rate of appearance of \( R \).
- This is **incorrect** because the rate of disappearance of \( Q \) is actually half the rate of appearance of \( R \).

3. **Statement C**: The rate of disappearance of \( P \) is equal to the rate of disappearance of \( Q \).
- This is **correct** as per the stoichiometry of the reaction.

4. **Statement D**: The rate of disappearance of \( Q \) is equal to half the rate of appearance of \( R \).
- This is **correct** as established in the rate relationships.

### Conclusion
The incorrect statement is **Statement B**.