## Zero order Reaction in Chemical Kinetics

**Zero order** chemical kinetics deals with learning of the speed and mechanism of chemical reaction in terms of reactants and products. In chemical equilibrium, only the initial and final states are considered and the energy relation between reactant and products governed by thermodynamics where the time and intermediate states are not concerned. Therefore, Zero order kinetics define the rate of chemical reaction in terms of reactant and product per unit time and rate of reactions independent with the decrease or increase the concentration of reacting species. Therefore the zero order kinetics are rare in reality, the enzyme catalyst reaction is an example of this type of kinetic reaction with respect to the substrate. In catalyzed reactions of chemical science, the transformation takes place on the surface of the catalyst or the walls of the container.

### Kinetic Reaction in terms of Reactant Product

In kinetics, the rate of a chemical reaction generally expressed in terms of reactant and product atoms in the molecules. Therefore, the concentration of reactant decrease and reactant increase. When these decrease or increase concentration expressed per unit time, we find the rate laws in chemical kinetics.

A → Product

Rate of reaction = – d[A]/dt = k [A]^{n}

Some surface reactions the rate has been found to be independent of concentration. These reactions are known as the zero order kinetics reaction.

### Zero-order Kinetics Reactionin Terms of Product

Rate laws of zero order chemical kinetics define the dependence of the concentration of the reacting species. Whereas the integrated law provides the increase or decreases the concentration of reacting species at any time from the start of the reactions. Let us take a chemical reaction with the initial concentration of reactant = a and product = 0. After time t concentration of reactant = (a – x) and product = x. Therefore concentration decrease after t time = x.

The rate in terms of product,

dx/dt = k_{0
}where k₀ = rate constant.

or, dx = k_{0}dt

When we integrating the above equation within limits, produce the rate equation for the reactions, x = k_{0}t + c, where c = integration constant. But when t = 0, that is the initial state of the reaction, x = 0. Therefore, the integration constant of this rate equation also zero.

∴ x = k_{0}t

This is the relationship between decreases of concentration of the reactant within the time for zero order kinetic.

Question: When the rate of the reaction equal to the rate constant. What is the order of the reaction?

Answer: Zero order reaction.

### Rate of Reaction in terms of Reactant

Let the initial concentration of reactant = [A]_{0} and after t time = [A], thus the rate equation in terms of reactant,

– d[A]/dt = k_{0} × [A]^{0} = k_{0}

Negative sign because the concentration decreases with time and initial concentration reactant [A]_{0} = 0.

or, – d[A] = k_{0}dt

Integrating the above equation

∫d[A] = k_{0} ∫dt

∴ – [A] = k_{0}t + c

where c = integration constant.

If the initial concentration of the reactant = [A]_{0} when time = 0, that is the initial time, – [A]_{0 }= 0 + c and [A] = – [A]_{0}. Therefore the integrated rate equation for the zero order kinetic

– [A] = k_{0}t – [A]_{0}

or, [A]_{0} – [A] = k_{0}t

This is another form of the rate equation of the kinetic reaction.

### Unit of the Rate Constant in Kinetics

The rate equation in terms of chemical product

– d[A]/dt = k_{0} × [A]^{n}

∴ Unit of k_{n} = unit of conc/(unit of conc)n × unit of time

= (unit of conc)^{1-n}/unit of time

Unit molar conc = mol lit^{-1} and time = sec.

Hence the unit rate constant for the zero order kinetics

(mol lit^{ -1})^{1 -0}/ sec

= mol lit^{-1} sec^{-1}

### Half-life of Zero Order Reaction

Half-life means 50% of reactants disappear in that time interval. But when t = t_{½}, that is the half-life of the reaction completed, the concentration of the reactant, [A] = [A]/2.

Therefore, [A]/2 = k_{0} × t_{½}

∴ t_{½} = [A]/2k

Hence the half-life of the zero order kinetics depends on the initial concentration of the reactant.

Question: The half-life of zero order = x. If the reaction completed on t_{1} time, what is the relation between x and t_{1}?

Answer: t_{½} = x = a/2k and completion time t_{1} = a/k. Therefore, x/t_{1} = (a/2k) × (k/a) and t_{1} = 2x.

### Order of Enzyme-Catalyzed Kinetic Reaction

Enzymes are complex protein produces from the living organisms of our environment. These are responsible for catalyzing infinite types of chemical changes occurring in our living system. For example, catalase obtained from living plant cells catalyzes the decomposition of hydrogen peroxide, yeast contains various enzymes, among which maltase converts maltose into glucose and zymase and zymase further converted glucose into eathy alcohol. All the reactions will be zero order for a given amount of enzyme with respect to the substrate. Heterogeneous catalyzed reactions are also the zero order kinetics.

### Examples of Zero Order Kinetic Reaction

- Dissociation of hydrogen iodide in the gold surface with high pressure is zero order reaction because the rate equation is derived from the experiment result. But when two molecules having sufficient energy to come together, the hydrogen and iodine bond dissociation to form the new bonds between the hydrogen atom and iodine atom. Since the reaction is the bimolecular chemical reaction.

2HI(gas) → H_{2}(gas) + I_{2} (gas)

Rate of reaction = k × [HI]^{0} = k

2N_{2}O (gas) → 2N_{2}(gas) + O_{2}(gas)

Rate of reaction = k [N_{2}O]^{0} = k

### Concentration and Zero order Kinetics

- The rate of the reactions is independent of concentration.
- Half-life is proportional to the initial concentration of the reactant.
- The rate of zero order kinetics in chemical science is always equal to the rate constant at all concentrations.