For the reaction,
`4P+Q rarr 2R+2S`,
Which of the following statement(s) is /are true?
Rate of appearance of S is doubled the rate of the disappearance of Q.
Rate of disappearance of Q is one fourth the rate of disappearance of P.
Rate of formation of R is equal to the rate of formation of S.
Choose the correct ooption.

Options

A. I and II
B. II and III
C. I and III
D. All of these

Answer

To analyze the given reaction and determine the truth of the statements, we start with the balanced chemical equation:

\[ 4P + Q \rightarrow 2R + 2S \]

### Step 1: Write the rate expressions for the reactants and products.

For the reaction, we can express the rates of disappearance of reactants and the rates of appearance of products as follows:

- Rate of disappearance of \( P \):
\[ -\frac{1}{4} \frac{d[P]}{dt} \]

- Rate of disappearance of \( Q \):
\[ -\frac{1}{1} \frac{d[Q]}{dt} \]

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

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

### Step 2: Analyze the first statement.

The first statement claims that the rate of appearance of \( S \) is double the rate of disappearance of \( Q \).

From the rate expressions, we have:
\[ \frac{d[S]}{dt} = \frac{1}{2} \frac{d[Q]}{dt} \]

This implies that:
\[ \frac{d[S]}{dt} = 2 \left(-\frac{d[Q]}{dt}\right) \]

Thus, the first statement is **true**.

### Step 3: Analyze the second statement.

The second statement claims that the rate of disappearance of \( Q \) is one-fourth the rate of disappearance of \( P \).

From the rate expressions, we have:
\[ -\frac{d[Q]}{dt} = \frac{1}{1} \frac{d[Q]}{dt} \]
and
\[ -\frac{1}{4} \frac{d[P]}{dt} \]

This implies:
\[ -\frac{d[Q]}{dt} = \frac{1}{4} \left(-\frac{d[P]}{dt}\right) \]

Thus, the second statement is **true**.

### Step 4: Analyze the third statement.

The third statement claims that the rate of formation of \( R \) is equal to the rate of formation of \( S \).

From the rate expressions, we have:
\[ \frac{d[R]}{dt} = \frac{1}{2} \frac{d[R]}{dt} \]
and
\[ \frac{d[S]}{dt} = \frac{1}{2} \frac{d[S]}{dt} \]

This implies:
\[ \frac{d[R]}{dt} = \frac{d[S]}{dt} \]

Thus, the third statement is **true**.

### Conclusion

All statements are true. Therefore, the correct option is that all the statements are correct.

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