- Nature of reactants:
Reactions involving ionic or polar substances are generally faster than those involving covalent compounds, because ionic reactions occur easily in aqueous solutions while covalent reactions require bond breaking and rearrangement. - Concentration of reactants:
Increase in the concentration of reactants increases the frequency of effective molecular collisions, thereby increasing the rate of reaction. - Temperature:
The rate of reaction increases with rise in temperature; for most reactions, the rate doubles or triples for every 10°C rise due to increased kinetic energy of molecules. - Presence of a catalyst:
A catalyst increases the rate of reaction by providing an alternative pathway with lower activation energy, without itself undergoing any permanent chemical change.
Definitions [10]
Definition: Rate Law (Rate Equation)
The mathematical expression that relates the rate of reaction to the molar concentrations of reactants, with experimentally determined powers, is called the rate law.
For the reaction
aA + bB → Products
Rate = k[A]p[B]q
where p and q are determined experimentally.
Definition: Rate Constant (k)
Rate constant is the constant of proportionality in the rate law and is numerically equal to the rate of reaction when the concentration of each reactant is unity.
\[k=\frac{\mathrm{Rate}}{[A]^p[B]^q}\]
Definition: Rate of Reaction
The rate of a chemical reaction is defined as the change in concentration of a reactant or a product per unit time.
\[\text{Rate of reaction}=\frac{\text{Change in concentration}}{\mathrm{Time~taken}}\]
Definition: Average Rate of Reaction
The average rate of a reaction is the change in concentration of reactants or products per unit time over a specified time interval.
\[\text{Average rate}=\frac{\Delta[\text{Reactant or Product}]}{\Delta t}\]
Definition: Instantaneous Rate of Reaction
The instantaneous rate of a reaction is the rate of change of concentration of reactants or products at a particular instant of time.
\[\text{Instantaneous rate}=\lim_{\Delta t\to0}\frac{\Delta[\text{Concentration}]}{\Delta t}\]
Definition: Order of a Reaction
The order of a reaction is the sum of the powers of the concentration terms of reactants in the rate law expression.
Order of reaction = p + q
Definition: Law of Mass Action
At constant temperature, the rate of a chemical reaction is directly proportional to the product of the active masses of the reactants, each raised to the power equal to its stoichiometric coefficient.
For the reaction
aA + bB → Products
Rate ∝ [A]a[B]b
or
Rate = k[A]a[B]b
Definition: Active Mass
Active mass of a substance is its effective concentration which takes part in a chemical reaction.
Expression:
For solutions: Active mass = molar concentration
Active mass = [A]
For gases: Active mass = partial pressure
Definition: Activation energy
The excess energy that the reactant molecules must acquire in order to cross the energy barrier and to change into the products is called the activation energy of the reaction.
Activation energy = Threshold energy − Average energy possessed by reactant molecules.
Definition: Mechanism of the Reaction
A sequence of intermediate steps or elementary processes proposed to account for the overall stoichiometry of a reaction is called the mechanism of the reaction.
Key Points
Key Points: Determination of Order of a Reaction
| Method | Basis / Principle | Procedure | Mathematical Relation | How Order is Determined |
|---|---|---|---|---|
| Graphical method | For a reaction of order n, rate ∝ [A]ⁿ | Used when reaction involves only one reactant; plots of rate vs concentration, conc² or conc³ are drawn | First order: rate ∝ [A] Second order: rate ∝ [A]² Third order: rate ∝ [A]³ | Straight line plot with [A], [A]² or [A]³ indicates first, second or third order respectively |
| Initial rate method | Rate law depends on initial concentrations of reactants | Initial concentration of one reactant is changed at a time keeping others constant and rate is measured | Rate = k[A]p[B]q … | Overall order is obtained by summing individual orders of all reactants |
| Integrated rate law method | Data must satisfy an integrated rate equation of a particular order | Experimental data are fitted into integrated rate law and value of k is calculated | Integrated rate equations for zero, first, second order | If k remains constant, reaction follows that order |
| Half-life method | Half-life depends on initial concentration of reactant | Half-life is measured for different initial concentrations |
\[t_{1/2}\propto\frac{1}{\left[A\right]_{0}^{n-1}}\] \[\frac{t_{1/2}}{t_{1/2}^{\prime}}=\left(\frac{\left[A\right]_{0}^{\prime}}{\left[A\right]_{0}}\right)^{n-1}\] |
Order n is calculated from the dependence of half-life on initial concentration |
Key Points: Effect of temperature on reaction rate
For most of the chemical reactions, the rate increases with increase in temperature. The rate usually becomes doubled to trebled for each 10° rise in temperature.
(a) Temperature coefficient :
It is defined as the ratio of the rate constant of a reaction at two different temperatures separated by 10°C. The two temperatures generally taken are 35°C and 25°C. Thus,
Temperature coefficient = k₃₅°C / k₂₅°C
For most of the homogeneous reactions, the value of temperature coefficient lies between 2 and 3.
(b) Collision theory of reaction rate :
This theory was proposed to explain the effect of temperature on reaction rates. The salient features of the theory are as follows :
- A reaction occurs only when the reactant molecules undergo collisions with one another.
- All collisions between the reacting molecules are not effective in producing a chemical change. Only a fraction of total number of collisions are effective and lead to the formation of products.
- The collisions between the reacting molecules are effective only when they acquire a definite amount of energy. The minimum amount of energy which must be possessed by the reacting molecules to make effective collisions is called threshold energy.
Effective collisions are those collisions which lead to the formation of products. The number of effective collisions are governed by the following two factors :
- Energy barrier : The collisions are effective only when the molecules possess energy greater than or equal to the threshold energy.
- Orientation barrier : The reactant molecules must collide with favourable orientation in order to facilitate the breaking of old bonds and formation of new bonds.
(c) Qualitative explanation of increase in reaction rate with temperature :
An increase in temperature increases the number of effective collisions. In fact the fraction of molecules having energy greater than or equal to the threshold energy increases appreciably even with a small rise in temperature. Hence, the rate of a reaction increases appreciably even with a small rise in temperature.
Key Points: Arrhenius equation
Arrhenius equation can be expressed as follows :
k = A e⁻ᴱᵃ/ᴿᵀ
where A is a constant known as frequency factor and gives the frequency of binary collisions of reactant molecules per second per litre, Eₐ is the energy of activation, R is gas constant and T represents the temperature (in Kelvin) of the system. k is the rate constant of the reaction.
Arrhenius equation can also be expressed as
log₁₀ k = − Eₐ / 2.303RT + log₁₀ A
From this equation, it is clear that as the value of T increases, the value of k and hence the rate of reaction increases.
Calculation of activation energy :
The Arrhenius equation enables us to calculate the value of activation energy for a chemical reaction. Following two methods may be used.
(i) Graphical method :
The Arrhenius equation is of the type y = mx + c and represents a straight line. Therefore, if the values of log₁₀ k are plotted against 1/T, a straight line is obtained. The slope of this line is equal to − Eₐ / 2.303R. Hence, by measuring the slope of the line, the activation energy Eₐ can be calculated.
(ii) Rate constant method :
If k₁ and k₂ are the rate constants measured at temperatures T₁ and T₂ respectively, then on the basis of Arrhenius equation, we can have
log₁₀ (k₂ / k₁) = Eₐ / 2.303R (1/T₁ − 1/T₂)
Thus, knowing the values of rate constants k₁ and k₂ of a reaction measured at two different temperatures T₁ and T₂ respectively, the energy of activation Eₐ of the reaction can be calculated with the help of above equation.
Key Points: Molecularity of a reaction
The number of reacting species (atoms, molecules or ions) which must collide simultaneously in order to bring about a chemical reaction is called the molecularity of that reaction.
The molecularity of a reaction is a whole number and may have values 1, 2, 3, etc. The reaction with molecularity 1 are called unimolecular reactions. Similarly, we have bimolecular and termolecular reactions when the values of molecularity are 2 and 3 respectively.
(a) Molecularity of elementary reactions :
The simple chemical reactions which occur only in one step are called elementary reactions. The molecularity of an elementary reaction is equal to the number of reacting species as represented by the balanced chemical equation of the reaction.
(b) Molecularity of complex reactions :
The reactions which occur in two or more steps are called complex reactions. Complex reactions proceed through a series of steps, each involving one, two or at the most three molecules. Each step is an elementary reaction and has its own rate. The overall rate of a complex reaction is governed by the rate of the slowest elementary step called the rate determining step.
Key Points: Factors which Affect the Reaction Rate
Key Points: Reactions of Different Orders and Units of Rate Constant
| Order of Reaction | Rate Law | Dependence on Concentration | Units of Rate Constant (k) |
|---|---|---|---|
| Zero order | Rate = k | Rate is independent of concentration | mol L⁻¹ s⁻¹ |
| First order | Rate = k[A] | Depends on concentration of one reactant | s⁻¹ |
| Second order | Rate = k[A]² or k[A][B] | Depends on square of one reactant or product of two reactants | mol⁻¹ L s⁻¹ |
| Third order | Rate = k[A]³ or k[A]²[B] | Depends on three concentration terms | mol⁻² L² s⁻¹ |
| Fractional order | Rate = k[A]¹ᐟ², k[A]³ᐟ², etc. | Depends on fractional powers of concentration | Depends on order |
| Pseudo first order | Rate = k′[A] | Appears first order due to large excess of one reactant | s⁻¹ |
| General order (n) | Rate = k[A]ⁿ | Depends on nth power of concentration | (mol L⁻¹)¹⁻ⁿ s⁻¹ |
Key Points: Pseudo-unimolecular reactions
The first order reactions having molecularity greater than one are called pseudo-unimolecular reactions.
A pseudo-unimolecular reaction is obtained when one of the reactants is present in large excess. The reactant present in large excess does not contribute to the rate of reaction. Its concentration remains almost constant during the course of reaction and therefore the rate of the reaction does not depend upon its concentration.
Some examples of pseudo-unimolecular reactions are as follows:
CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH
Ethyl acetate (large excess)
Rate = k [CH₃COOC₂H₅]
C₁₂H₂₂O₁₁ + H₂O → C₆H₁₂O₆ + C₆H₁₂O₆
Sucrose (large excess)
Rate = k [C₁₂H₂₂O₁₁]
