Chemical Kinetics

Consider a **first-order gas-phase decomposition reaction**:

Let the initial pressure of be and the pressure at time be .

As the reaction proceeds, suppose the partial pressure of that decomposes is .

Then, - Pressure of left = - Pressure of formed = - Pressure of formed =

Therefore, the total pressure at time is: which gives

Hence, the pressure of remaining is:

For a first-order reaction, the integrated rate law is:

Substituting :

Therefore, the correct integrated rate law for a first-order gas-phase reaction is:

The rate law equation is given by: where and are the reaction orders with respect to and , respectively.
Step 1: Determine From the first condition: Taking :
Step 2: Determine From the second condition:
Final Rate Law: or

Step 1: Recall the rate law.
The general form of the rate law is: where:

• = rate constant
• = concentration of reactant A
• = order of reaction with respect to A

Step 2: Case of negative order.
If , then the concentration of A appears in the denominator: where represents the absolute value of the negative exponent.

Step 3: Effect of increasing [A].
Since is in the denominator, as the concentration of A increases, the overall rate of the reaction decreases.
Conversely, if decreases, the rate of the reaction increases.

Step 4: Conclusion.
For a reaction with negative order in A, the reactant A behaves like an inhibitor.
Therefore, increasing reduces the reaction rate.

Final Answer:

If , an increase in concentration of A will decrease the rate of the reaction.

Definition: Zero-Order Reaction

A zero-order reaction is a chemical reaction wherein the rate of reaction does not depend on the concentration of the reactants. The rate remains constant over time.

where is the rate constant.

Reaction Analysis

Step 1: Write the overall reaction.

To get the overall reaction, add the elementary steps and cancel out species that appear on both sides.

Step 2: Identify the reaction intermediate.

A reaction intermediate is a species that is formed in one step of a reaction and consumed in a subsequent step. It does not appear in the overall balanced equation.

In this mechanism, NOCl (g) is formed in Step 1 and consumed in Step 2. Therefore, NOCl is the reaction intermediate.