First-Order Reactions

Chemistry, by its nature, is all about different reactions and changes. In chemistry, various chemical reactions occur, which are studied with the help of its branch called Chemical Kinetics. The word kinetics is derived from the Greek word ‘kinesis’ which means movement. Chemical kinetics is all about the rate of reactions and the speed of reactions. The rate of the reaction is generally expressed as the decrease of reactants and increase in the concentration of the products. The concentrations are taken in gm-moles/litre, hence the rate is moles/litre/second. The types of orders chemical kinetics have are:- zero-order reaction, first-order reaction, second-order reaction, or mixed order.

In first-order reactions, the rate depends on the first power of concentration of a single reactant. A first-order reaction is represented by:   

 A → B

t=0         C0           –

t=t          C       x

where A is the reactant and B is the product. In first-order reactions, the rate of reaction is directly proportional to the concentration of one of the reactants. The differential equation for first-order reaction or the first-order reaction equation is:

 –dcdt=KC

in which ‘c’ is the concentration of the reactant at any time ‘t’ and k is the velocity constant or specific rate reaction

If the concentration of c is doubled, the rate of reaction also doubles. If the concentration of c is increased by factor 10 or other, the rate of reaction also gets increased by the factor of 10 or the other. Because the units of the reaction rate are always moles per litre per second. First-order reactions depend only on the concentration of one reactant.

Half-life of first-order reactions

The half – life of any reaction is defined as the time taken by the reactant to reduce its concentration to one-half of its initial concentration.  Therefore [C]o=[C]/2.

To determine the half-life of a reaction, we need to know the following:

• Order of the reaction

• Rate constant K, or any information to determine it

If two reactions have same order, then

The half-life will be longer for the slower reaction of two reactions that have the same order or the half-life will be shorter for the faster reaction of two reactions having the same order.

The half-life of the first-order reaction is constant under a given set of reaction conditions, This is not true for second and zero-order reactions. The concentration of reactant is independent of the half-life of the first-order reaction. Thus the half-life of the First-order reaction is 

ln2k=0.693k.

Pseudo first order-reactions

A Pseudo first-order reaction is a second-order or bimolecular reaction, which is prepared or made to behave like a first-order reaction. This reaction occurs when the reactant is in excess or is maintained at a concentration as compared with the other substance, one of the reactants is the catalyst. Examples of Pseudo first-order reactions are:

Hydration of alkyl halide 

CH3I (aq) + H2O (l)  →CH3OH (aq) + H+ (aq) + I– (aq)

Hydrolysis of cane sugar

C12H22O11 + H2O → C6H12O6 + C6H12O

Hydrolysis of ester

CH3COOC2H5 + H2O  → CH3COOH + C2H5OH

Hydrolysis of ethyl acetate

CH3COOC2H5 + H2O  → CH3COOH + C2H5OH

The reactant in pseudo-first-order reactions should be isolated.

Unit of rate constant for first-order reactions

In Chemical kinetics rate constant is defined as the proportionality constant, which explains the rate of reaction and the relationship between the molar concentration of the reactants. Rate constants are specific for a particular reaction. They are measured by the concentration of species over time in the laboratory. The rate of reaction is the change in concentration with time.

Rate of reaction= mol/liter/sec

Rate = k[A]

Where k is rate constant

mol/lit/sec = k(mol/lit)

k=1/sec

Thus, the unit of the rate constant for first-order reactions is 1/sec or s-1.

Examples of first-order reactions

First-order reaction equations are very common. Here are some examples of first-order reactions:-

• When trimethyl bromomethane is being reacted with sodium hydroxide, it gives trimethyl methanol and sodium bromide.

(CH3)3CBr + NaOH → (CH3)3COH + NaBr

• The decomposition of hydrogen peroxide gives water and oxygen.

2H2O2 → H2O + O2

• Methyl acetate Hydrolysis in the presence of mineral acids

CH3COOCH3 + H2O → CH3COOH + CH3OH

• Hydrogenation of the ethene.

C2H4 + H2 → C2H6 (g)

• Decomposition of ammonium nitrate in presence of an aqueous solution.

NH4NO2 (aq.) → N2 + 2H2O

Conclusion 

The first-order reaction formula is -d[A]/dT = k[A]1 

– Where k is the rate constant whose unit is sec inverse.

– [A] is the concentration of first-order reactant ‘A’.

– d[A]/dt denotes the change in concentration of the first order reactant ‘A’ in the time interval ‘dt’.

 The order of the first-order reaction is equal to 1(one). The main difference between first-order reactions and other-order reactions is that for first order kinetics we can write order equivalent to the sum of the Stoichiometric Coefficient but this is not applicable for other order. The first-order reaction equation is – dA/dt= kA.