Question

What do you understand by order of reaction? What is the difference between the first order and zero order reaction? Following data was obtained on first order thermal decomposition of \(N_2O_5\) (g) at fixed volume: 2N\(_2\)O\(_5\) (g) \(\rightarrow\) 2N\(_2\)O\(_4\) (g) + O\(_2\) (g)

Hint:

The rate constant of a first-order reaction can be calculated by using the rate of pressure change for gas-phase reactions.

Answer 1

Step 1: Understanding the Order of Reaction.
The order of a reaction is the sum of the powers of the concentration terms in the rate law expression. A first-order reaction has a rate that is directly proportional to the concentration of one reactant, while a zero-order reaction has a rate that is independent of the concentration of the reactant.
Step 2: First Order Reaction vs Zero Order Reaction.
- First Order Reaction: The rate of reaction depends on the concentration of one reactant raised to the first power. The rate law is: \[ \text{Rate} = k[A] \] where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant. The half-life of a first-order reaction is constant, independent of the concentration. - Zero Order Reaction: The rate of reaction is constant and does not depend on the concentration of the reactant. The rate law is: \[ \text{Rate} = k \] The half-life of a zero-order reaction is directly proportional to the initial concentration of the reactant.
Step 3: Calculate the Velocity Constant.
Using the data provided: - Initial pressure at time \( t = 0 \) is 0.5 atm, - Pressure after 100 seconds is 0.512 atm. The change in pressure is \( \Delta P = 0.512 - 0.5 = 0.012 \) atm. For a first-order reaction, the velocity constant \( k \) can be calculated using: \[ k = \frac{\text{Change in pressure}}{t} = \frac{0.012}{100} = 1.2 \times 10^{-4} \, \text{s}^{-1} \]