The Order of reaction gives a relationship between the rate of a chemical reaction and the concentration of the elements taking part in it. Therefore it can be defined as the power dependence of rate on the concentration of all reactants. To determine the reaction order, the power-law form of the rate equation is commonly used. The expression for the rate law is given by r = k[A]x[B]y. In the expression, ‘r’ refers to the rate of reaction, ‘k’ is the rate constant of the reaction, [A] and [B] are the concentrations of the reactants. The exponents of the reactant concentrations x and y are partial orders of the reaction. So, the sum of all the partial orders of the reaction gives the overall order of the reaction. In this topic, we will discuss Zero-order reactions.
What is a Zero Order Reaction?
A reaction in which the concentration of the reactants does not change with respect to time and the concentration rates remain constant throughout is called a zero-order reaction. The rate of these reactions is always equal to the rate constant of the specific reactions because the rate of these reactions is proportional to the zeroth power of reactants concentration.
A Zero-order reaction is always an artifact(made by humans) of the conditions under which the reaction is carried out. Due to this reason, reactions following zero-order reactions are also sometimes referred to as pseudo-zero-order reactions.
Differential and Integral Form of Zero Order Reaction
An equation representing the dependence of the rate of reaction on the concentration of reacting species is termed the differential rate equation. The instantaneous rate of reaction is expressed as the slope of the tangent at any instant of time in the concentration-time graph. It is not easy to determine the rate of reaction from the concentration-time graph. So, we need to integrate the differential rate equation in order to obtain a relation between the concentration at different points and the rate constant. This equation used is known as the integrated rate equation. For reactions of a different order, we observe different integrated rate equations.
In the case of a zero-order reaction, the rate of reaction depends on the zeroth power of the concentration of reactants.
For the reaction given as, A → B (A is reactant and B is product)
Rate = -d[A] / dt = k[A]0
⇒ -d[A] / dt = k
⇒ d[A] = -k dt
Now Integrating both sides, we get:
⇒ [A] = -kt + c
Where c = constant of integration
At time, t = 0, [A] = [A]0
Putting the limits in the above equation we will get the value of c,
⇒ [A]0 = c
Using the value of c in the equation above we get:
⇒ [A] = -kt + [A]0
⇒ [A] = [A]0 - kt
This equation is known as the integrated rate equation for zero-order reactions. We can observe the above equation as an equation of the straight line (y = mx + c) with a concentration of reactant on the y-axis and time on the x-axis. The slope of the straight line gives the value of the rate constant, k.
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Half-Life of a Zero Order Reaction
The half-life of a chemical reaction can be defined as the specific amount of time taken for the concentration of a given reactant to reach 50% of its initial concentration (or the time taken by the reactant concentration to reach half of its initial value). It is denoted by the symbol ‘t1/2’ and is expressed in seconds. It is to be noted that the formula for the half-life of a reaction varies with the order of the reaction.
From the above-integrated equation we have:
[A] = [A]0 - kt
Now replacing t with half-life t1/2 in the above equation:
⇒ 1/2 [A] = [A]0 - k t1/2
⇒ k t1/2 = 1/2 [A]0
⇒ t1/2 = 1/2 k [A]0
⇒ t1/2 = [A]0 / 2k
t1/2 is the half-life of the reaction ( seconds)
[A]0 is the initial reactant concentration (mol.L-1 or M)
k is the rate constant of the reaction ( M(1-n) s-1 where ‘n’ is the reaction order)
From this equation, it can be concluded that the half-life is dependent on the rate constant as well as the reactant’s initial concentration.
For a first-order reaction, the half-life is: t1/2 = 0.693/ k
Examples of Zero Order Reaction
1. The reaction of hydrogen with chlorine also known as a Photochemical reaction.
H2 + Cl2 → 2HCl
Rate = k[H2]0 [Cl2]0
Rate = k
2. Decomposition of nitrous oxide on a hot platinum surface.
N2O → N2 + 1/2 O2
Rate [N2O]0 = k[N2O]0 = k
d [N2O] / dt = k
3. Decomposition of NH3 in the presence of molybdenum or tungsten is a zero-order reaction.
2NH3 → N2 + 3H2