First Order Reactions (Chemical Kinetics) - Units, Example, FAQs

In this article we will be discussing everything about first order kinetics which includes first order reaction graph, first order reaction example, rate constant of first order reaction, first order reaction units, first order reaction equation, first order reaction formula, first order reaction definition, first order reaction derivation and first order reaction example problems.

What is a First Order Reaction?

The rate of reaction is proportional to concentration of product or reactant raised to certain power. The value of power of concentration of product or reactant is equal to 1 for a first order reaction. In other words, the first order reaction rate depends on concentration of only one species that can be either product or reactant. A reaction can be first order for one species but the overall order may be different. A reaction can be an overall 1st order reaction but the respective products or reactants may have different values of power.

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Rate constant of first order reaction

Since, in 1st order kinetics depends on concentration of only one species, the first order reaction formula can be written as:

Rate α [M]

For a reaction:

n₁M + n₂N ? m₁P + m₂S

This means the rate of reaction is first order with respect to M and zero order for the rest of the species.

By removing sign of proportionality, a constant of proportionality is introduced:

Rate = k₁[M]¹

This constant of proportionality, coefficient k, is called rate constant for the reaction.

Here, it will be termed as rate constant of first order reaction and hence the subscript 1 is used.

The rate constant of reaction depends on temperature but is independent of the concentrations.

For first order kinetics, the unit of rate constant is 1/s or per second or time^-1 (unit of 1st order reaction).

First Reaction Equation

The first order rate equation can be written as:

Rate(R) = k₁[M]¹

The first order reaction equation in differential form can be written as:

Rate(R) = - -d[M]/dt

For a reaction:

n₁M + n₂N ? m₁P + m₂S

Rate(R) = - 1/n1 -d[M]/dt = k₁[M] … (e.q.1)

This is a differential form of the first order rate equation.

The first order reaction derivation is explained below:

E.q.1 can be written as:

d[M/][M] = -k₁n₁.dt

On integrating both side of above equation we get:

We know that1/x = ln(x), therefore,

ln ([M]0/[M]t) = k₁n₁t

ln ([M]t/[M]0) = -k₁n₁t

We know that ln(A/B) = ln(A) – ln(B) therefore,

ln[M]_t – ln[M]₀ = -k₁n₁t

ln[M]_t = ln[M]₀ - k₁n₁t

ln[M]_t = -k₁n₁t + ln[M]₀

For most first order reaction, n₁ = 1 thus,

ln[M]_t = -k₁t + ln[M]₀ … (e.q.2)

First Order Reaction Graph

On comparing e.q.2

ln[M]_t = -k₁t + ln[M]₀

with y=mx+c we get,

mx = -k₁t

c = ln[M]₀

y = ln[M]_t

A straight line first order reaction graph can be plotted:

For determining if a reaction is first order reaction or not, plots the value of ln of concentration against time. If the plot comes out to be a straight line with downward (negative) slope, then the reaction is a first order reaction.

We can also raise e.q.2 to the power e,

e^ln[M]t = e^ln[M]0-k1t

Or [M]_t = [M]₀ e^-kt

The integrated form of first order reaction is used to determine reactant population at any certain time after initiation of reaction.

For determining half-life of first order reaction,

[M]_t1/2 = 1/2 [M]₀

ln([M]₀/[M]0/2) = k₁ t_1/2

2.303 log 2 = k₁ t_1/2

t_1/2 = 0.693/k1

The concentration vs time graph for first order reaction can also be plotted as:

First Order Reaction Units

Since, Rate is defined as any quantity compared against time.

The rate constant of reaction depends on temperature but is independent of the concentrations.

For first order kinetics, the unit of rate constant is 1/s or per second or time^-1.

Read more:

• NCERT solutions for Class 12 Chemistry Chapter 4 Chemical Kinetics
• NCERT Exemplar Class 12 Chemistry solutions Chapter 4 Chemical Kinetics
• NCERT notes Class 12 Chemistry Chapter 4 Chemical Kinetics

First Order Reaction Example

There are many reactions that exhibit first order reactions. Some examples are given below:

• Decomposition of di-tert-butyl

(CH₃)₃COOC(CH₃)₃ →2CH₃COCH₃ + C₂H₆

• Decomposition of dinitropentaoxide

N₂O₅ (g)→ 2NO₂(g) + ½ O₂(g)

• Decomposition of azoisopropane

(CH₃)₂CHN=NCH(CH₃)₂ → N₂ + C₆H₁₄

• Decomposition of thionyl chloride

SO₂CL₂ → SO₂ + Cl₂

• Decomposition of 2,4,6-trinitrobenzoic acid

2,4,6-TRINITROBENZOIC ACID → TRINITROBENZENE + CO₂

• Decomposition of hydrogen peroxide

H₂O₂(aq) → H₂O(l) + ½ O₂(g)

• All radioactive decays

First order reaction example problem

Question.1. The half-life of a first-order reaction is given as 10 seconds at a certain temperature t. What is its rate constant?

Solution

t_1/2 = 0.693/k₁

k₁=0.0693 s^-1

Question.2. The decomposition of hydrogen peroxide is given as H₂O₂(aq) → H₂O(l) + ½ O₂(g), the initial concentration of H₂O₂ is 0.2547 M, and the initial rate of reaction is 9.31×10^–4 M s^–1. What will be [H₂O₂] at t = 35 s?

Solution

We know that,

Rate(R) = - 1/n1 -d[M]/dt = k₁[M]

Therefore,

Rate(R) = - 9.31×10^–4 = Δ [H₂O₂]/ Δt

- 9.31×10^–4 = [H₂O₂]- 0.2547 /35

[H₂O₂] = 0.222115M

Also check-

• NCERT Exemplar Class 11th Chemistry Solutions
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NCERT Chemistry Notes :

• NCERT notes Class 11 Chemistry
• NCERT notes Class 12 Chemistry
• NCERT Notes For All Subjects