`"A "+2" B" to 3" C"+2" D"`. The rate of disappearance of B is `1xx10^(-2)" mol lit"^(-1)"sec"^(-1)`. What will be (i) Rate of the reaction (ii) Rate of change in concentration of A and C ?

Answer

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

\[ A + 2B \rightarrow 3C + 2D \]

Given:
- The rate of disappearance of B is \( \frac{d[B]}{dt} = -1 \times 10^{-2} \, \text{mol L}^{-1} \text{s}^{-1} \).

### Step 1: Determine the Rate of Reaction

The rate of reaction can be expressed in terms of the change in concentration of the reactants and products. For the reaction:

\[ -\frac{1}{1} \frac{d[A]}{dt} = -\frac{1}{2} \frac{d[B]}{dt} = \frac{1}{3} \frac{d[C]}{dt} = \frac{1}{2} \frac{d[D]}{dt} \]

From the rate of disappearance of B, we can express the rate of reaction (\( r \)) as follows:

\[ r = -\frac{1}{2} \frac{d[B]}{dt} \]

Substituting the given rate of disappearance of B:

\[ r = -\frac{1}{2} \times (-1 \times 10^{-2}) = \frac{1}{2} \times 10^{-2} = 0.5 \times 10^{-2} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Step 2: Rate of Change in Concentration of A

Using the stoichiometry of the reaction, we can find the rate of change in concentration of A:

\[ -\frac{d[A]}{dt} = r \]

Thus, the rate of change in concentration of A is:

\[ \frac{d[A]}{dt} = -r = -0.5 \times 10^{-2} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Step 3: Rate of Change in Concentration of C

Using the stoichiometry of the reaction again, we can find the rate of change in concentration of C:

\[ \frac{d[C]}{dt} = 3r \]

Substituting the value of \( r \):

\[ \frac{d[C]}{dt} = 3 \times (0.5 \times 10^{-2}) = 1.5 \times 10^{-2} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Summary of Results

1. **Rate of the reaction**: \( 0.5 \times 10^{-2} \, \text{mol L}^{-1} \text{s}^{-1} \)
2. **Rate of change in concentration of A**: \( -0.5 \times 10^{-2} \, \text{mol L}^{-1} \text{s}^{-1} \)
3. **Rate of change in concentration of C**: \( 1.5 \times 10^{-2} \, \text{mol L}^{-1} \text{s}^{-1} \)