To solve the problem, we need to determine the concentration of B after 100 seconds and 200 seconds for the reaction \( A \overset{k_r=0.6 \, \text{M min}^{-1}}{\rightarrow} 2B \), starting with an initial concentration of A at 1 M.
### Step 1: Understand the Reaction and Rate Constant
The reaction is a zero-order reaction because the rate constant \( k_r \) is given in units of M/min. For a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants.
### Step 2: Write the Zero-Order Rate Equation
For a zero-order reaction, the concentration of the reactant decreases linearly over time. The equation for the concentration of A at time \( t \) is given by:
\[
[A] = [A]_0 - k_r \cdot t
\]
where:
- \([A]_0\) is the initial concentration of A,
- \(k_r\) is the rate constant,
- \(t\) is the time in minutes.
### Step 3: Calculate Concentration of A after 100 seconds
Convert 100 seconds to minutes:
\[
t = \frac{100 \, \text{seconds}}{60 \, \text{seconds/minute}} \approx 1.67 \, \text{minutes}
\]
Now substitute the values into the equation:
\[
[A] = 1 \, \text{M} - (0.6 \, \text{M/min}) \cdot (1.67 \, \text{min})
\]
\[
[A] = 1 \, \text{M} - 1.002 \, \text{M} \approx -0.002 \, \text{M}
\]
Since concentration cannot be negative, this means that all of A has reacted, and we need to find the concentration of B produced.
### Step 4: Calculate Concentration of B after 100 seconds
Since the stoichiometry of the reaction shows that 1 mole of A produces 2 moles of B, the concentration of B produced can be calculated as:
\[
[B] = 2 \times (1 - [A]_0) = 2 \times (1 - 0) = 2 \, \text{M}
\]
### Step 5: Calculate Concentration of A after 200 seconds
Convert 200 seconds to minutes:
\[
t = \frac{200 \, \text{seconds}}{60 \, \text{seconds/minute}} \approx 3.33 \, \text{minutes}
\]
Now substitute the values into the equation:
\[
[A] = 1 \, \text{M} - (0.6 \, \text{M/min}) \cdot (3.33 \, \text{min})
\]
\[
[A] = 1 \, \text{M} - 1.998 \, \text{M} \approx -0.998 \, \text{M}
\]
Again, since concentration cannot be negative, all of A has reacted.
### Step 6: Calculate Concentration of B after 200 seconds
Using the same stoichiometry:
\[
[B] = 2 \times (1 - [A]_0) = 2 \times (1 - 0) = 2 \, \text{M}
\]
### Final Answers
- Concentration of B after 100 seconds: **2 M**
- Concentration of B after 200 seconds: **2 M**
