For the first order reaction
`2 N_(2)O_(5)(g) to 4 NO_(2) (g) + O_(2)(g)`

Options

A. The concentration of the reaction decreases exponentially with time
B. The half-life of the reaction decreases with increasing temperature
C. The half-life of the reaction depends on the initial concentration of the reactant
D. The reaction proceeds to 99.6 % completion in eight half-life duration

Explanation

To solve the problem regarding the first-order reaction \( 2 N_{2}O_{5}(g) \rightarrow 4 NO_{2}(g) + O_{2}(g) \), we will analyze the characteristics of first-order reactions and their half-lives.

### Step-by-Step Solution:

1. **Identify the Reaction Order**:
- The reaction given is a first-order reaction. This means that the rate of reaction is directly proportional to the concentration of one of the reactants.

2. **Understanding Half-Life for First-Order Reactions**:
- For first-order reactions, the half-life (t₁/₂) is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where \( k \) is the rate constant. This indicates that the half-life is constant and does not depend on the initial concentration of the reactant.

3. **Concentration Over Time**:
- In a first-order reaction, as time progresses, the concentration of the reactant decreases exponentially. This means that if you plot the concentration of the reactant against time, the graph will show a downward curve.

4. **Analyzing the Statements**:
- **Statement 1**: The concentration of the reactant decreases with time.
- **True**: This is a characteristic of all reactions, especially first-order reactions.
- **Statement 2**: Does half-life decrease?
- **False**: The half-life remains constant for first-order reactions and does not decrease with time.
- **Statement 3**: Does half-life depend on initial concentration?
- **False**: The half-life for first-order reactions is independent of the initial concentration.
- **Statement 4**: The reaction proceeds 99.6% complete in 8 half-life durations.
- **False**: In reality, a first-order reaction approaches completion asymptotically, and it does not reach 99.6% completion in just 8 half-lives.

5. **Conclusion**:
- The correct option regarding the characteristics of the first-order reaction is **Statement 1**: The concentration of the reactant decreases with time.