Solution : Chapter 03 : Questions No. 13

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For chemical reaction , the concentration of reactant was initial taken as 20 molar per liter , after 30 minutes 50% of it remained. If the same reaction is started with concentration of 40 mol/litre , then after 1/2 hour it's concentration remains 20 mol/litre.
What conclusion will you draw based on above observation, based on this conclusion what will be the order of reaction ?

Answer : 

Based on the given observations, we can draw the following conclusion and determine the order of the reaction:

Conclusion based on observations:

1. Observation 1: When the initial concentration of the reactant is 20 mol/liter, after 30 minutes, 50% of it remains (i.e., 10 mol/liter). This means the half-life (t₁/₂) of the reaction is 30 minutes when the initial concentration is 20 mol/liter.
2. Observation 2: When the same reaction is started with an initial concentration of 40 mol/liter, after 1/2 hour (30 minutes), its concentration remains 20 mol/liter. This means the half-life (t₁/₂) of the reaction is 30 minutes when the initial concentration is 40 mol/liter.

From both observations, it is evident that the **half-life (t₁/₂) of the reaction remains constant (30 minutes) regardless of the initial concentration of the reactant.**

Order of reaction:

The characteristic property of a first-order reaction is that its half-life is independent of the initial concentration of the reactant.

For a zero-order reaction, t₁/₂ is directly proportional to the initial concentration.
For a first-order reaction, t₁/₂ = ln(2) / k (where k is the rate constant), which shows no dependence on the initial concentration.
For a second-order reaction, t₁/₂ is inversely proportional to the initial concentration.

Since the half-life is constant and does not change with the initial concentration, the reaction is a first-order reaction.

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