The rate constant of the reaction `A rarr B` is `0.6 xx 10^(-3)` mole per second. If the concentration of `A` is `5 M`, then concentration of `B` after `20` minutes is:

Options

A. `0.36 M`
B. `0.72 M`
C. `1.08 M`
D. `3.60 M`

Explanation

To solve the problem, we need to determine the concentration of substance B after 20 minutes given the rate constant and the initial concentration of substance A. The reaction is a zero-order reaction, which means the rate of reaction is constant and does not depend on the concentration of the reactant.

### Step-by-Step Solution:

1. **Identify the Reaction Order**:
The rate constant (k) is given as \(0.6 \times 10^{-3}\) moles per second. Since the units of k are in moles per second, this indicates that the reaction is zero-order.

**Hint**: The unit of the rate constant can help determine the order of the reaction.

2. **Write the Zero-Order Rate Equation**:
For a zero-order reaction, the concentration of A at time t is given by the equation:
\[ [A]_t = [A]_0 - kt \]
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 from Minutes to Seconds**:
The time given is 20 minutes. We need to convert this to seconds:
\[ t = 20 \text{ minutes} \times 60 \text{ seconds/minute} = 1200 \text{ seconds} \]

**Hint**: Always ensure that the time unit matches the unit of the rate constant.

4. **Substitute Values into the Equation**:
Now, we can substitute the values into the zero-order rate equation:
\[ [A]_t = [A]_0 - kt \]
Given:
- \([A]_0 = 5 \text{ M}\)
- \(k = 0.6 \times 10^{-3} \text{ moles/second}\)
- \(t = 1200 \text{ seconds}\)

Substituting these values:
\[ [A]_t = 5 - (0.6 \times 10^{-3} \text{ moles/second} \times 1200 \text{ seconds}) \]

5. **Calculate the Change in Concentration**:
Calculate \(kt\):
\[ kt = 0.6 \times 10^{-3} \times 1200 = 0.72 \text{ M} \]
Now substitute this back into the equation:
\[ [A]_t = 5 - 0.72 = 4.28 \text{ M} \]

6. **Determine the Concentration of B**:
Since the reaction \(A \rightarrow B\) indicates that for every mole of A that reacts, one mole of B is produced, the concentration of B formed (\([B]\)) is equal to the decrease in concentration of A:
\[ [B] = [A]_0 - [A]_t = 5 - 4.28 = 0.72 \text{ M} \]

### Final Answer:
The concentration of B after 20 minutes is \(0.72 \text{ M}\).

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