Question

The following data were obtained during the first order thermal decomposition of \( \text{N}_2\text{O}_5(g) \) at constant volume:

Hint:

For first-order reactions, remember that the relationship between pressure and time is logarithmic. This makes it easier to calculate the rate constant using simple logarithmic equations.

Answer 1

For a first-order reaction, the rate law is given by: \[ \ln \left(\frac{P_0}{P}\right) = k \cdot t \] Where \( P_0 \) is the initial pressure, \( P \) is the pressure at time \( t \), and \( k \) is the rate constant. Using the provided data, we can calculate the rate constant \( k \) using the formula for the first-order reaction. After substituting the values for \( P_0 \), \( P \), and \( t \), the rate constant \( k \) is obtained as 0.0033 s\(^{-1}\).