In the following reaction `A rarr B+C`, rate constant is `0.001Ms^(-1)`. If we start with `1M` of A then , cond, of A and B after 10 minutes are respectively.

Options

A. `0.5M , 0.5M`
B. `0.6 M,0.4M`
C. `0.4M,0.6M`
D. none of these

Explanation

To solve the problem, we need to determine the concentrations of A and B after 10 minutes for the reaction \( A \rightarrow B + C \) given that the rate constant \( k = 0.001 \, \text{M s}^{-1} \) and the initial concentration of A is \( 1 \, \text{M} \).

### Step-by-Step Solution:

1. **Identify the Order of the Reaction:**
The rate constant \( k \) is given as \( 0.001 \, \text{M s}^{-1} \). Since the units of the rate constant suggest that this is a zero-order reaction (units of concentration/time), we can conclude that the reaction is zero-order.

**Hint:** Check the units of the rate constant to determine the order of the reaction.

2. **Use the Zero-Order Rate Equation:**
For a zero-order reaction, the concentration of the reactant at time \( t \) is given by:
\[ [A]_t = [A]_0 - kt \]
where:
- \([A]_t\) is the concentration of A at time \( t \),
- \([A]_0\) is the initial concentration of A,
- \(k\) is the rate constant,
- \(t\) is the time in seconds.

3. **Convert Time to Seconds:**
The time given is 10 minutes. We need to convert this to seconds:
\[ t = 10 \, \text{minutes} \times 60 \, \text{seconds/minute} = 600 \, \text{seconds} \]

**Hint:** Always convert time to the appropriate units that match the rate constant.

4. **Substitute Values into the Equation:**
Now we can substitute the values into the zero-order equation:
\[ [A]_t = 1 \, \text{M} - (0.001 \, \text{M s}^{-1} \times 600 \, \text{s}) \]
\[ [A]_t = 1 \, \text{M} - 0.6 \, \text{M} = 0.4 \, \text{M} \]

5. **Calculate the Concentration of B:**
Since the stoichiometry of the reaction shows that for every mole of A that reacts, one mole of B and one mole of C are produced, the amount of A that has reacted (let's call it \( x \)) is equal to the concentration of B and C formed:
\[ x = [A]_0 - [A]_t = 1 \, \text{M} - 0.4 \, \text{M} = 0.6 \, \text{M} \]
Therefore, the concentration of B and C is:
\[ [B] = x = 0.6 \, \text{M} \]
\[ [C] = x = 0.6 \, \text{M} \]

6. **Final Concentrations:**
After 10 minutes, the concentrations of A and B are:
- Concentration of A: \( 0.4 \, \text{M} \)
- Concentration of B: \( 0.6 \, \text{M} \)

### Final Answer:
The concentrations of A and B after 10 minutes are \( 0.4 \, \text{M} \) and \( 0.6 \, \text{M} \) respectively.

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