The rate of disapperance of Q in the reaction `2P+Q to 2R+3S` is `2 times 10^-2` moles `l^-1 s^-1`. Which of the following statement is not true?

Options

A. `-(d[P])/(dt)=4 times 10^-2 moles l^-1 s^-1`
B. `+(d[S])/(dt)=6times 10^-2 moles l^-1 s^-1`
C. `+1/2 (d[R])/(dt)=2 times 10^-2 moles l^-1 s^-1`
D. `+(d[R])/(dt)=2 times 10^-2 moles l^-1 s^-1`

Answer

To solve the problem, we need to analyze the reaction and the given rate of disappearance of Q. The reaction is:

\[ 2P + Q \rightarrow 2R + 3S \]

We are given that the rate of disappearance of Q is:

\[ -\frac{d[Q]}{dt} = 2 \times 10^{-2} \, \text{moles} \, \text{l}^{-1} \, \text{s}^{-1} \]

### Step 1: Write the rate expressions for the reaction.

From the stoichiometry of the reaction, we can express the rates of disappearance and formation as follows:

- For P:
\[ -\frac{1}{2} \frac{d[P]}{dt} \]

- For Q:
\[ -\frac{d[Q]}{dt} \]

- For R:
\[ \frac{1}{2} \frac{d[R]}{dt} \]

- For S:
\[ \frac{1}{3} \frac{d[S]}{dt} \]

### Step 2: Relate the rates to the given rate of disappearance of Q.

Since we know that:

\[ -\frac{d[Q]}{dt} = 2 \times 10^{-2} \]

We can find the rates of disappearance of P and formation of R and S.

### Step 3: Calculate the rate of disappearance of P.

From the stoichiometric relationship:

\[ -\frac{1}{2} \frac{d[P]}{dt} = -\frac{d[Q]}{dt} \]

Substituting the value of \(-\frac{d[Q]}{dt}\):

\[ -\frac{1}{2} \frac{d[P]}{dt} = 2 \times 10^{-2} \]

Thus,

\[ \frac{d[P]}{dt} = -4 \times 10^{-2} \, \text{moles} \, \text{l}^{-1} \, \text{s}^{-1} \]

### Step 4: Calculate the rate of formation of R.

From the stoichiometric relationship:

\[ \frac{1}{2} \frac{d[R]}{dt} = -\frac{d[Q]}{dt} \]

Substituting the value of \(-\frac{d[Q]}{dt}\):

\[ \frac{1}{2} \frac{d[R]}{dt} = 2 \times 10^{-2} \]

Thus,

\[ \frac{d[R]}{dt} = 4 \times 10^{-2} \, \text{moles} \, \text{l}^{-1} \, \text{s}^{-1} \]

### Step 5: Calculate the rate of formation of S.

From the stoichiometric relationship:

\[ \frac{1}{3} \frac{d[S]}{dt} = -\frac{d[Q]}{dt} \]

Substituting the value of \(-\frac{d[Q]}{dt}\):

\[ \frac{1}{3} \frac{d[S]}{dt} = 2 \times 10^{-2} \]

Thus,

\[ \frac{d[S]}{dt} = 6 \times 10^{-2} \, \text{moles} \, \text{l}^{-1} \, \text{s}^{-1} \]

### Step 6: Evaluate the statements.

Now we can evaluate the statements based on our calculations:

1. **Statement 1**: \(-\frac{d[P]}{dt} = 4 \times 10^{-2}\) (True)
2. **Statement 2**: \(\frac{d[S]}{dt} = 6 \times 10^{-2}\) (True)
3. **Statement 3**: \(\frac{1}{2} \frac{d[R]}{dt} = 2 \times 10^{-2}\) (True)
4. **Statement 4**: \(\frac{d[R]}{dt} = 2 \times 10^{-2}\) (False, it should be \(4 \times 10^{-2}\))

### Conclusion

The statement that is not true is **Statement 4**.

---