A : The decomposition of gaseous `N_2O_5` follows first order kinetics.
R : The plot of log of its partial pressure versus time is linear with slope , `-k/(2.303)` and having intercept equal to log P.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements , then mark (4)

Answer

To solve the given question, we need to analyze both the assertion and the reason provided.

**Assertion (A):** The decomposition of gaseous N₂O₅ follows first order kinetics.

**Reason (R):** The plot of log of its partial pressure versus time is linear with slope, -k/(2.303), and having intercept equal to log P.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The decomposition of N₂O₅ can be represented as:
\[ 2N₂O₅(g) \rightarrow 4NO₂(g) + O₂(g) \]
We need to determine if this reaction follows first-order kinetics.

2. **Determining the Order of Reaction**:
The order of a reaction can be determined experimentally, but for a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant. In this case, the rate law can be expressed as:
\[ \text{Rate} = k[N₂O₅] \]
Since the rate depends linearly on the concentration of N₂O₅, we can conclude that the reaction is indeed first order.

3. **Using the Integrated Rate Law for First-Order Reactions**:
For a first-order reaction, the integrated rate law is given by:
\[ \log \left( \frac{P_0}{P_t} \right) = \frac{k}{2.303} t \]
where \( P_0 \) is the initial partial pressure of N₂O₅, and \( P_t \) is the partial pressure at time \( t \).

4. **Rearranging the Equation**:
Rearranging the equation gives:
\[ \log P_t = \log P_0 - \frac{k}{2.303} t \]
This equation is in the form of \( y = mx + c \), where:
- \( y = \log P_t \)
- \( m = -\frac{k}{2.303} \) (slope)
- \( c = \log P_0 \) (intercept)

5. **Conclusion**:
The plot of \( \log P_t \) versus time \( t \) will indeed be linear, with a slope of \(-\frac{k}{2.303}\) and an intercept of \(\log P_0\). Therefore, both the assertion and the reason are true.

### Final Answer:
Both the assertion and the reason are true, and the reason correctly explains the assertion. Thus, the correct option is **1**.

---