# Rate Constant for First Order Reaction

## Rate Constant for First Order Reaction

The reaction in which rate is determined by the variation of only one concentration term is called first order reaction.Let us consider the following first order reaction-

This is the First order kinetics or rate constant for first order reaction.

## Unit of First-Order Reaction

Time^{−1}or Sec

^{−1}

## First-Order Reaction Graph

Try to Answer:

1. A first order reaction is 20% complete in 10 minutes. Calculate the rate constant of the reaction.

[Hints: k=2.2 × 10

2. Shows that for a first order reaction the time required for 99.9% completion is three times required for the completion of 90% reaction.

1. A first order reaction is 20% complete in 10 minutes. Calculate the rate constant of the reaction.

[Hints: k=2.2 × 10

^{−2}min^{−1}]2. Shows that for a first order reaction the time required for 99.9% completion is three times required for the completion of 90% reaction.

## Half life period (t_{1/2}) for First Order Reaction:

The time during which initial concentration of reactant is reduced to half is called half life period. It is denoted as t_{1/2}

We know that, for first order reaction, the rate constant (k) is-

k = (2.303/t) log(a/a-x) -------1

where a is initial concentration of reactant and (a-x) is concentration after time t.

From equation 1-

t = (2.303/k) log(a/a-x) -------2

Now, when, t = t

_{1/2}then, x = a/2

Now putting the value of t and x in equation 2 we get-

t

_{1/2}= (2.303/k) log2

or, t

_{1/2}= 0.693/k --------3

From the equation 3 we see that

**half life period is inversely proportional to k and independent of initial concentration of the reactant**.

Try to Answer:

Calculate the rate constant if the half-life period for the first order reaction is 1.7 hrs.

[Hints: 0.4076 h

Calculate the rate constant if the half-life period for the first order reaction is 1.7 hrs.

[Hints: 0.4076 h

^{−1}]## Characteristic of a First Order Reaction

The followings are the main characteristics of first order kinetics-1. The unit of rate constant does not contain any concentration term.

2. The half life period of first order reaction is constant and is independent of its initial concentration.

3. When the concentration of the reactant is increased by 'n' times, the rate of reaction is also increased by n times. So, if the concentration of the reactant is doubled, the rate is also doubled.

4. The plot of average rate constant vs. average concentration over a particular time interval is straight line passing through the origin.