Consider a reaction `A(g)overset(k=0.1 M min^(-1))to2B(g)`. If initial concentration of A is 0.5 M then select correct graph.

Options

A.
B.
C.
D.

Answer

To solve the problem, we need to analyze the reaction and its kinetics step by step.

### Step 1: Identify the Reaction Order
The reaction given is:
\[ A(g) \overset{k=0.1 \, \text{M min}^{-1}}{\rightarrow} 2B(g) \]

The rate constant \( k \) has units of \( \text{M min}^{-1} \). This suggests that the reaction is a zero-order reaction because the unit of the rate constant for a zero-order reaction is \( \text{M} \cdot \text{time}^{-1} \).

### Step 2: Write the Rate Law Expression
For a zero-order reaction, the rate law can be expressed as:
\[ \text{Rate} = k \]
And the concentration of the reactant \( A \) over time can be described by the equation:
\[ [A] = [A_0] - kt \]
Where:
- \( [A_0] \) is the initial concentration of \( A \)
- \( k \) is the rate constant
- \( t \) is time

### Step 3: Substitute Known Values
Given:
- \( [A_0] = 0.5 \, \text{M} \)
- \( k = 0.1 \, \text{M min}^{-1} \)

Substituting these values into the equation gives:
\[ [A] = 0.5 - (0.1 \cdot t) \]

### Step 4: Calculate Concentration of A at Different Times
1. **At \( t = 0 \) min:**
\[ [A] = 0.5 - (0.1 \cdot 0) = 0.5 \, \text{M} \]

2. **At \( t = 5 \) min:**
\[ [A] = 0.5 - (0.1 \cdot 5) = 0.5 - 0.5 = 0 \, \text{M} \]

3. **At \( t = 10 \) min:**
\[ [A] = 0.5 - (0.1 \cdot 10) = 0.5 - 1 = -0.5 \, \text{M} \]
(This is not possible, indicating that the reaction will stop before reaching this time.)

### Step 5: Determine Concentration of B
Since the stoichiometry of the reaction shows that 1 mole of \( A \) produces 2 moles of \( B \):
- At \( t = 5 \) min, when \( [A] = 0 \):
\[ [B] = 2 \times (0.5) = 1 \, \text{M} \]

### Step 6: Analyze the Graphs
We need to select the correct graph based on the concentration of \( B \):
- At \( t = 0 \): \( [B] = 0 \, \text{M} \)
- At \( t = 5 \): \( [B] = 1 \, \text{M} \)
- At \( t > 5 \): \( [B] \) remains constant at \( 1 \, \text{M} \) because \( A \) is fully consumed.

### Conclusion
The correct graph should show:
- An increase in the concentration of \( B \) from \( 0 \) to \( 1 \, \text{M} \) at \( t = 5 \) minutes.
- A plateau at \( 1 \, \text{M} \) for \( t > 5 \) minutes.