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 question regarding the decomposition of gaseous \( N_2O_5 \) and its kinetics, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding First-Order Kinetics**:
The decomposition of \( N_2O_5 \) is stated to follow first-order kinetics. This means that the rate of reaction is directly proportional to the concentration (or partial pressure) of \( N_2O_5 \).

2. **Writing the Rate Law**:
For a first-order reaction, the rate law can be expressed as:
\[ \text{Rate} = -\frac{d[P]}{dt} = k[P] \]
where \( k \) is the rate constant and \( [P] \) is the concentration (or partial pressure) of \( N_2O_5 \).

3. **Integrating the Rate Law**:
The integrated rate law for a first-order reaction is given by:
\[ \ln[P_t] = \ln[P_0] - kt \]
where \( [P_t] \) is the partial pressure at time \( t \) and \( [P_0] \) is the initial partial pressure.

4. **Converting to Logarithm Base 10**:
To convert the natural logarithm to base 10, we use the relationship:
\[ \ln[P_t] = 2.303 \log[P_t] \]
Thus, we can rewrite the integrated rate law as:
\[ 2.303 \log[P_t] = 2.303 \log[P_0] - \frac{k}{2.303} t \]

5. **Identifying the Slope and Intercept**:
From the equation \( 2.303 \log[P_t] = 2.303 \log[P_0] - \frac{k}{2.303} t \), we can identify:
- The slope \( m = -\frac{k}{2.303} \)
- The intercept \( c = 2.303 \log[P_0] \)

6. **Conclusion**:
The plot of \( \log[P_t] \) versus time \( t \) will be linear, with a negative slope of \( -\frac{k}{2.303} \) and an intercept equal to \( \log[P_0] \). This confirms that the statement in the question is correct.

### Final Answer:
Both statements A and R are correct, and R is the correct explanation for A.

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