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Differential and integral forms of zero-order reaction are the mathematical expressions derived from differential rate law to study the kinetics of reactions; for instance, how the reactions are reacting and the rate and time period of reactions. Differential and integral forms can be derived for any order of the reactions.
Zero order reactions
Zero order reactions are those which are not affected by the change in concentration of reactants. A zero order reaction is independent of the concentration of reactants. These reactions are equal to the rate constant since the concentration of reactants has zeroth power in the rate law expression.
Rate = k[A]0 ( K = rate constant )
Rate = k ([A] = Reactant concentration )
Derivation of differential and integral form of zero
Differential and integral forms of zero-order can easily be derived from the differential rate law expression of a zero-order reaction.
Differential forms of the zero order reaction
The differential rate law is the mathematical expression that shows how the rate of a reaction depends on the concentration.
For zero order reaction, differential rate law expression is,
The rate refers to the rate of reaction, K is rate constant, unit of the rate constant is molL-1s-1 or Ms-1.
We can derive the integral form of rate law expression for zero order reaction by using differential rate law expression.
Consider the zero order reaction,
A → Product
From the differential rate law expression of zero order reactions:
Integrating the above equation on both side with considering that initially or at time(t) = zero, that amount of reactant A is [A0] and after time (t) the remaining amount is [A], so
Integrated rate law expression helps us to calculate the concentration of a reactant at any particular time period from starting the reaction.
Graphical representations of differential and integral forms of zero order reaction
In the differential rate law of zero order reaction, the rate of the reaction does not depend on the concentration of any reactant, so plotting the graph between the rate of the reaction and concentration of the reactant will be a straight constant line as, as shown in the figure shown below.
Integrated form of zero order reaction,
By comparing this equation to that of a straight line (y = mx + c), a [A] versus t graph may be plotted to get a straight line with a slope of ‘-k’ and an intercept of [A0], as illustrated below. The slope of the graph is negative because the concentration of reactant A decreases with time.
The half-life of the zero-order reaction
As we can see, half-life of the zero-order reaction does not depend on the concentration of the reactant also; it only depends on the rate constant of the zero-order reaction
Examples of the zero order reaction
The photochemical reaction of hydrogen with chlorine.
2 On the molybdenum and tungsten surface, the decomposition of NH3 is an example of zero order kinetics.
3. A zero-order reaction in the human liver is ethanol oxidation to acetaldehyde, catalysed by the enzyme alcohol dehydrogenase. At high ethanol concentrations, this reaction is also a zero-order reaction.
4. The decomposition of N2O on the Pt surface is also a zero-order kinetics reaction.
5. Reverse Haber bosch process ( reverse process for the production of ammonia (NH3) from N2 and H2
Conclusion
The zero order reactions are those which are not affected by the change in concentration of reactants. A zero order reaction is independent of the concentration of reactants.
Differential and integral forms of zero order can easily be derived from the differential rate law expression of a zero-order reaction. The differential rate law is the mathematical expression that shows how the rate of a reaction depends on the concentration.
