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Order of Reaction is a parameter that depicts the relationship between the Rate of a Chemical Reaction and the concentration of species taking part in the reaction. The order of a reaction is determined by obtaining the rate equation of the reaction. Let’s discuss the order of reaction, its type, methods along with few important questions.
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Key Terms: Rate of Reaction, Chemical Reactions, temperature, reactant, rate constant, rate equation
Order of Reaction
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Order of reaction represents the number of reactants whose concentration directly affects the rate of reaction. Given below are some of the characteristics of order of reaction:
- The order of a reaction is the power dependence of the reaction rate on the reactants’ concentration.
- It shows the concentrations of the species that affect the reaction rate.
- The exponentials of the reactants in the rate equation are summed up to determine the order of the reaction.
- The concentration of the reactants is considered for the order of the reaction.
- The concentration of the products is not the governing factor for determining the order of the reaction.
- The order of a reaction can be zero, integer, or fraction.
- The negative value of the integer for order of reaction depicts an inverse relationship of effect between the concentration of the reactants and the rate of a reaction.
- The positive value of the integer for order of reaction depicts a direct relationship of effect between the concentration of the reactants and the rate of a reaction.
- The value of the order of the reaction as zero depicts that there is no relationship of effect between the concentration of the reactants and the rate of a reaction.
- The fractional value of the order of the reaction depicts a complex relationship of effect between the concentration of the reactants and the rate of a reaction.
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Difference between Molecularity and Order of Reaction
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Both Molecularity and Order of Reaction provide information about chemical reactions, but they are very different from each other. Molecularly depicts the number of molecules involved in the reaction, while the order of reaction tells about the relationship between the concentration of reactants and the rate of reaction. The table below summarises the differences between molecularity and order of the reaction.
| Molecularity | Order of Reaction |
|---|---|
| It refers to the number of molecules involved in the rate-determining step. | It depicts the relationship between the concentration of reactants and the rate of reaction. |
| Only the rate-determining step is taken into account for calculating molecularity. | Every step of a reaction is examined while determining the order of the reaction. |
| There is no dependence on temperature and pressure. | There is a dependence on temperature, pressure, and concentration. |
| It cannot be a negative number. | It can be a negative number. |
| It can be calculated from a balanced chemical equation. | It is calculated experimentally. |
Different Values of Order of Reaction
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The value of Order of Reaction can be in the form of integers, zeros, or fractions. Below you can find a graph detailing the reaction rates for different reaction orders.
Reaction Rates for different Reaction Orders
According to the dependence of the reaction rate on the concentration, chemical reactions can be divided into the following types.
- Zero-order reactions
- First-order reactions
- Pseudo-first-order reactions
- Second-order reactions
Zero-order reaction
The zero-order reaction is a reaction in which the reactants' concentration does not change over time and the concentration rate remains constant throughout. The rate of reaction is independent of the concentration of the reactants. A reaction of zero-order is always an artifact of the conditions under which the reaction occurs. Because of that, reactions after zero-order reactions are sometimes also called pseudo-zero-order reactions.
Example: Reactions include the enzyme-catalyzed oxidation of CH3CH2OH (ethanol) to CH3CHO (acetaldehyde).
First-order reaction
The reaction rate depends only on the concentration of one reactant in these reactions. The reaction can contain numerous reactants, but only the concentration of one reactant affects the reaction rate. There will be no effect on the order of reaction of other reactants. The reaction rate in a first-order reaction is proportional to the concentration of the reactant.
Example: 2H2O2 → 2H2O + O2
Rate = k[H2O2]
Pseudo-first-order reaction
In a pseudo-first-order reaction, the concentration of one reactant remains constant. The reactant with the constant concentration is either present in excess with respect to the other reactant or is a catalyst.
Example: (CH3)2COO + 2H2O → CH3COOH + CH3CHO
Rate = k[CH3COOCH3]
Second-order reaction
Reactions of the Second Order can be characterized in the corresponding rate of the chemical reaction as chemical reactions, whereby the total of the exponents is equal to two. A rate such as r = k[A]2, and R = k[A][B] can be indicated.
The reactions of the second order are chemical reactions that either depends on the concentrations of two reactants of the first order or the concentration of one reactant of the second order.
Example – 2NO2 → 2NO + O2
Rate = k[NO2]2
CH3COOC2H5 + OH- CH3COO- + C2H5OH
Rate = k[CH3COOC2H5] [OH-]
Methods to determine the Order of Reaction
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There are several methods that can be followed to determine the order of the reaction. Some of these methods are described below-
1. Initial Rate Method
-
Obtain the natural log expression of the power law as ln r= ln k + x ln[A] + y ln[B]+…
- For every reactant, the partial order is calculated. This is done by changing the concentrations of the reactants in question and keeping the concentration of other reactants constant.
- With the partial order of A, the power-law equation of the rate expression becomes- ln r = x ln[A] + C, where C is constant.
- The slope obtained by taking ln r as a function of ln[A] is a partial order, given by x.
2. Integral Method
- This method verifies the reaction order obtained by the initial rates method.
- The integral form of the rate law is compared with the measured concentrations of the reactants.
- The verification of the rate law for the first-order reaction is done by checking if the value of ln[A] is a linear function of time.
- Integrated rate equation of a first-order reaction: In[A] = -kt + In [A]0
3. Differential Method
- This method is the easiest method to determine the order of the reaction.
- The expression of rate for a reaction is first written by R= k[A]x [B]y
- The final order of the reaction is given by x+y.
Rate Constant
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The constant of proportionality between the reactants concentration and the rate of a chemical reaction is known as rate constant.
It is denoted by the symbol ‘k’. It is also known as the reaction rate constant or reaction rate coefficient.
In other words, the rate constant is the ratio of the rate of reaction and the molar concentration of the reactants.
The units of rate constant depend on the type of order of reaction, that is, zero order, first order, second order, third order reaction.
The following table gives the units of rate constant and the type of order of the reaction:
| Order of the Reaction | Unit of the Rate Constant |
|---|---|
| Zero-order reaction | Mol L-1 s-1 |
| First-order reaction | s-1 |
| Second-order reaction | mol-1s-1 |
| Third-order reaction | mol-2 s-1 |
The rate constant is determined by the following two methods:
- By using the order of the reaction and the molar concentration of the reactants in the equation.
k = Rate / [A]a[B]b
Where,
k is the rate constant
[A] and [B] are the molar concentration of reactants A and B
a and b are the order of the reaction.
- By Arrhenius equation as, k=Ae-Ea/RT
Where,
A is the frequency of particle collision
Ea is the activation energy
R is the universal gas constant
T is the absolute temperature
Things to Remember
- The relationship between the rate of a chemical reaction and the concentration of the reactants is known as the order of reaction.
- Order of reaction represents the number of reactants whose concentration directly affects the rate of reaction.
- Molecularly depicts the number of molecules involved in the reaction, while the order of reaction depicts the relationship between the concentration of reactants and the rate of reaction.
- Order of reaction is of four types: Zero-order reaction, First-order reaction, Pseudo-first order reaction and second-order reaction.
- Order of reaction can be determined by Initial Rate Method, Integral Method and Differential Method.
Also Read:
Previous Year Questions
Ques : Define ‘ Order of a reaction.’ (All India 2011, 1 Mark)
Ans: The order of the reaction can be defined as the sum of powers of the concentration of the reactants in the rate law expression.
Ques: (i) If the rate constant of a reaction is k = 3 × 10-4 s-1, then identify the order of the reaction.
(ii) Write the unit of rate constant for a zero-order reaction. (Comptt. All India 2013, 2 Marks)
Ans: (i) For k = 3 × 10-4 s-1. The S.I. unit is s-1. s-1 is the unit for the rate constant of the first-order reaction. So, it is a first-order reaction.
(ii) MolL-1s-1 is unit of rate constant for a zero-order reaction.
Ques : A reaction is of second order with respect to a reactant. How will the rate of reaction be affected if the concentration of this reactant is (i) doubled, (ii) reduced to half? (Delhi 2009, 2 Marks)
Ans: Since Rate = K[A]2
For a second-order reaction,
Let [A] = a then Rate = Ka2
(i) If [A] = 2a then Rate = K (2a)2 = 4 Ka2
∴Rate of reaction becomes 4 times
(ii) If [A] = a/2, then Rate = K (a/2)2 = Ka2/4
∴ Rate of reaction will be ¼ th .
Ques : Define the following :
(i) Order of a reaction
(ii) Activation energy of a reaction (All India 2009, 2 Marks)
Ans: (i) Order of a reaction :
- It is the sum of powers of molar concentrations of reactants in the rate equation of the reaction.
- The value of the order of reaction may be a whole number, zero, fractional, positive, or negative.
- It is experimentally calculated.
- It is meant for the reaction and not for its individual steps.
(ii) Activation energy of a reaction: The minimum extra amount of energy required by the reactants to form the activated complex is called activation energy.
Ques : A reaction is of first-order in reactant A and of second-order in reactant B. How is the rate of this reaction affected when (i) the concentration of B alone is increased to three times (ii) the concentrations of A as well as B are doubled? (Delhi 2010, 2 Marks)
Ans: r = K[A]1 [B]2
(i) When the concentration of B increases to 3 times,
r = KA(3B)2
∴ r = 9KAB2 = 9 times
When the concentration of B increases to 3 times, the rate of reaction becomes 9 times
(ii) the concentrations of A as well as B are doubled
r = K(2A) (2B)2
∴ r = 8KAB2 = 8 times
When the concentrations of A as well as B are doubled, the rate of reaction becomes 9 times.
Ques : What do you understand by the ‘order of a reaction’ ?Identify the reaction order from each of the following units of reaction rate constant: (i) mol L-1 s-1 (ii) L mol-1 s-1 (Delhi 2012, 2 Marks)
Ans: Order of reaction: The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction.
r = K[A]x[B]y, Order = x + y
(i) mol L-1 s-1- Zero order
(ii) L mol-1 s-1 - Second order
Ques : A first order gas phase reaction: A2B2(g) → 2A(g) + 2B(g) at the temperature 400°C has the rate constant k = 2.0 × 10-4 sec-1. What percentage of A2B2 is decomposed on heating for 900 seconds? (Antilog 0.0781 = 1.197) (Comptt. All India 2013, 3 Marks)
Ans: Since the reaction is of the first order
Ques : Write the differences between ‘order of reaction’ and ‘molecularity of reaction’. (Delhi 2014, 3 Marks)
Ans: The difference between ‘order of reaction’ and ‘molecularity of reaction’ is given below:
| Molecularity of Reaction | Order of Reaction |
|---|---|
| It refers to the number of molecules involved in the rate-determining step. | It depicts the relationship between the concentration of reactants and the rate of reaction. |
| Only the rate-determining step is taken into account for calculating molecularity. | Every step of a reaction is examined while determining the order of the reaction. |
| There is no dependence on temperature and pressure. | There is a dependence on temperature, pressure, and concentration. |
| It cannot be a negative number. | It can be a negative number. |
| It can be calculated from a balanced chemical equation. | It is calculated experimentally. |
Ques : (a) With the help of a labeled diagram explain the role of activated complex in a reaction.
(b) A first-order reaction is 15% completed in 20 minutes. How long will it take to complete 60% of the reaction? (Comptt. Delhi 2012, 5 Marks)
Ans: (a) In order to convert the reactants into products, the reactants have to cross an energy barrier as shown in the diagram
This diagram is obtained by plotting a graph between potential energy and reaction coordinates. It is believed that when the molecules of reactant absorb energy, their bonds are loosened and new bonds are formed between them. The intermediate complex thus formed is called the activated complex. It is unstable and immediately gets dissociated to form stable products.
(b) For the first-order reaction
Ques : (a) For a reaction A + B → P, the rate is given by Rate = k[A] [B]2
(i) How is the rate of reaction affected if the concentration of B is doubled?
(ii) What is the overall order of reaction if A is present in large excess?
(b) A first-order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction. (log 2 = 0.3010) (Delhi 2015, 5 Marks)
Ans: (a) For the reaction A + B → P rate is given by
Rate = k[A]1[B]2
(i) r1 = k[A]1 [B]2
r2 = k[A]1[2B]2
r2 = k[A]1[2B]2 = 4k[A]1[B]2
r1 = 4r2, rate will increase four times of actual rate.
(ii) When A is present in a large amount, the order with respect to A is zero.
Hence overall order = 0 + 2 = 2, second order reaction.
Sample Questions
Ques: Find the order of the reaction 2NO2 → 2NO+ O2 (1 Mark)
Ans: The rate of reaction 2NO2 → 2NO+ O2 is given by,
Rate=k[NO2 ]2
The above rate equation is in the form k[A]2
So, the order of the reaction is second order.
Ques: Find the order and molecularity of the equation N2O5 → N2 O4 + ½ O2 (1 Mark)
Ans: The rate of reaction equation N2O5 → N2 O4 + ½ O2 is given by,
Rate =k[N2O5 ]
The above rate equation is in the form k[A]
So, the order is 1 and molecularity is 1.
Ques: Find the rate constant unit of the reaction 2NO2 → 2NO+ O2 (1 Mark)
Ans: The rate of the reaction 2NO2 → 2NO+ O2 is given by,
Rate=k[ NO2]2
Since it is a second-order reaction, the unit of the rate constant is mol-1 s-1
Ques: Find the order and molecularity of the equation 2HI → H2 + I2 (1 Mark)
Ans: The rate of reaction equation2HI → H2 + I2 is given by,
Rate =k[HI]2
The above rate equation is in the form k[A]2
So, the order is 2 and molecularity is 2.
Ques: Find the rate constant unit for the reaction 2NO+O2→ 2NO2 (1 Mark)
Ans: The rate of the reaction 2NO+O2 → 2NO2 is given by,
Rate=k[NO]2 [O2 ]
Since it is a third-order reaction, the unit of the rate constant is mol-2 s-1.
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