To solve the problem, we need to analyze the given reaction and the rates of disappearance and formation of the reactants and products. The reaction is:
\[ 2P + Q \rightarrow 2R + 3S \]
We are given that the rate of disappearance of \( Q \) is \( 2 \times 10^{-2} \) moles \( l^{-1} s^{-1} \).
### 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:
- Rate of disappearance of \( P \):
\[
-\frac{1}{2} \frac{d[P]}{dt}
\]
- Rate of disappearance of \( Q \):
\[
-\frac{d[Q]}{dt}
\]
- Rate of formation of \( R \):
\[
\frac{1}{2} \frac{d[R]}{dt}
\]
- Rate of formation of \( S \):
\[
\frac{1}{3} \frac{d[S]}{dt}
\]
### Step 2: Relate the rates using the given information
We know that the rate of disappearance of \( Q \) is given as:
\[
-\frac{d[Q]}{dt} = 2 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1}
\]
Thus, we can write:
\[
\frac{d[Q]}{dt} = -2 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1}
\]
### Step 3: Calculate the rate of disappearance of \( P \)
Using the stoichiometric coefficients, we relate the rate of disappearance of \( P \) to that of \( Q \):
\[
-\frac{1}{2} \frac{d[P]}{dt} = -\frac{d[Q]}{dt}
\]
Substituting the value of \( \frac{d[Q]}{dt} \):
\[
-\frac{1}{2} \frac{d[P]}{dt} = 2 \times 10^{-2}
\]
Thus, we find:
\[
\frac{d[P]}{dt} = -4 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1}
\]
### Step 4: Calculate the rate of formation of \( R \)
Using the stoichiometric coefficients again:
\[
\frac{1}{2} \frac{d[R]}{dt} = -\frac{d[Q]}{dt}
\]
Substituting the value of \( \frac{d[Q]}{dt} \):
\[
\frac{1}{2} \frac{d[R]}{dt} = 2 \times 10^{-2}
\]
Thus, we find:
\[
\frac{d[R]}{dt} = 4 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1}
\]
### Step 5: Calculate the rate of formation of \( S \)
Using the stoichiometric coefficients:
\[
\frac{1}{3} \frac{d[S]}{dt} = -\frac{d[Q]}{dt}
\]
Substituting the value of \( \frac{d[Q]}{dt} \):
\[
\frac{1}{3} \frac{d[S]}{dt} = 2 \times 10^{-2}
\]
Thus, we find:
\[
\frac{d[S]}{dt} = 6 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1}
\]
### Step 6: Analyze the options
Now we can analyze the options provided in the question:
1. Rate of disappearance of \( P \): \( 4 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1} \) (True)
2. Rate of formation of \( S \): \( 6 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1} \) (True)
3. Rate of formation of \( R \): \( 4 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1} \) (False, it should be \( 2 \times 10^{-2} \))
4. Rate of formation of \( R \): \( 2 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1} \) (True)
### Conclusion
The statement that is **not true** is the one regarding the rate of formation of \( R \) being \( 2 \times 10^{-2} \, \text{moles} \, l^{-1} s^{-1} \).
