A first order reaction is completed 90%in 60 mintue. Calculate it's half life period?

Question

Answer

Calculating the Half-life of a First Order Reaction

In order to calculate the half-life of a first order reaction, we need to understand the concept of a first order reaction and how it relates to the rate constant.

First Order Reaction

A first order reaction is a type of chemical reaction where the rate of the reaction is directly proportional to the concentration of only one reactant. The rate equation for a first order reaction is given by:

Rate = k[A]

Where [A] is the concentration of the reactant and k is the rate constant.

Half-life of a First Order Reaction

The half-life of a reaction is the time it takes for the concentration of the reactant to decrease by half. For a first order reaction, the half-life can be calculated using the following equation:

t_1/2 = (0.693) / k

Where t_1/2 is the half-life and k is the rate constant.

Given Information

In this case, we are given that the reaction is completed 90% in 60 minutes. This means that the remaining concentration of the reactant is 10% of the initial concentration.

We can use this information to determine the value of the rate constant and then calculate the half-life of the reaction.

Calculation

Since the reaction is 90% completed in 60 minutes, this means that the remaining concentration of the reactant is 10% of the initial concentration.

Let's assume that the initial concentration of the reactant is [A]₀.

Therefore, the remaining concentration after 60 minutes is 0.1[A]₀.

Using the rate equation for a first order reaction:

Rate = k[A]

At t = 60 minutes, the rate of the reaction is equal to the rate constant (k) multiplied by the remaining concentration (0.1[A]₀):

k * 0.1[A]₀ = k[A]

Since the concentration of the reactant cancels out, we can conclude that:

k * 0.1 = k

This implies that 0.1 = 1, which is not possible. Therefore, we need to assume that the remaining concentration after 60 minutes is actually 0.1 times the initial concentration.

Let's assume that the remaining concentration after 60 minutes is 0.1[A]₀.

Therefore, the initial concentration of the reactant is [A]₀ = (0.1[A]₀) / 0.1 = [A]₀.

Now

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