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Rate Law-Law of Mass Action, Statement of Rate Law, Rate Constant, Practice Problems and FAQs
You know that chemical reactions can be slow, medium or fast. But why so? What factors decide the speed of the reaction? Come, we shall find answers to these questions.
The rate of a chemical reaction, at a given temperature, depends upon the concentration of reactants. But, how do we relate the rate and concentration of reactants, mathematically?
Let’s study in detail and try to relate the rate of a reaction to the concentration of reactants.
Table of Contents
- Law of Mass Action
- Statement of Rate Law
- Rate Constant
- Unit of Rate Constant
- Practice Problems
- Frequently Asked Questions-FAQ
Law of Mass Action
The law of mass action states that the rate of any chemical reaction is proportional to the product of the concentrations of reactants, each raised to the power of their stoichiometric coefficient in the balanced chemical equation.
Let’s consider a chemical reaction, aA + bB +cC products
Rate of reaction ∝ [A]a [B]b [C]c
Where a, b and c are the stoichiometric coefficients of reactants A, B and C.
Note:
This law of mass action was useful to get the correct equilibrium equation for a reaction, but it has been studied and now it is proved that this law can only be applied on elementary reactions, for complex reactions we have to study about rate law which ultimately will give the correct relation between the rate of a reaction and concentration.
Statement of Rate law
Rate law is the representation of the rate of reaction in terms of the concentration of the reactants.
Let’s consider a chemical reaction;
aA + bB cC
Rate of a reaction ∝ [A]x[B]y
Rate of a reaction =-dRdt= k [A]x [B]y……….(i)
Where,
- [A] & [B] are the concentrations of the reactants A and B.
- x and y are the orders with respect to the reactants A & B respectively (which may or may not be equal to their stoichiometric coefficients a & b).
- The proportionality constant ‘k’ is the rate constant of the reaction.
The equation (i) is termed as a differential rate equation.
Note:
- Rate law expression for a specific reaction can only be determined experimentally.
- Rate law expression may vary for the same reaction under different conditions like temperature and pressure.
Rate Constant
The rate constant is the proportionality constant which gives the relationship between the molar concentration of the reactants and the rate of a reaction.
The rate constant is denoted by 'k'.
From rate law expression,
Rate of a reaction = k [A]x [B]y
⇒ k = Rate of a reaction [A]x[B]y
The value of rate constant depends on the nature of the reactant, temperature of the reaction and nature of the catalyst.
Unit of rate constant
(∵ unit of rate of a reaction =mol L-1s-1 and unit of concentration =mol L-1)
[∵ Order of the reaction ( n) = x+y ]
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Practice Problems
Q 1. For the reaction, 2N2O5 4NO2 + O2the rate can be expressed in two ways:d[N2O5]dt =k[N2O5] and d[NO2]dt =k'[N2O5]
k and k' are related as:
(A) k =k'
(B) k =2k'
(C) 2k =k'
(D) k =4k'
Answer: (C)
For the given reaction, 2N2O5 4NO2 + O2,the rate of reaction can be expressed as follows in terms of both reactants and products:
Q 2. Considering a reaction:
H2 + I2 2HI
This reaction is a second-order reaction.
The differential rate equation for the reaction H2 + I2 2HI can be expressed as:
Answer: (D)
Rate of a reaction can be expressed as:
Rate of reaction 
∵ The reaction (H2 + I2 2HI) is a second-order reaction.
So, the rate of the reaction would be:
R=k HI2 ...(ii)
From equations (i) and (ii), we get;
Q 3. In the given chemical reaction, CHCl3+ Cl2 CCl4 + HCl, Which of the following statements is correct regarding the rate expression for the reaction?
(A) Rate=k[CHCl3][Cl2]
(B) Rate=k[CHCl3]
(C) Rate =k[Cl2]
(D) Cannot be predicted from given data
Answer: (D)
As we know that rate law expression can only be determined experimentally. ∴ Rate law expression cannot be predicted from the above given data for the mentioned reaction.
Q 4. For the reaction, A+ B products, it is observed that: On tripling the initial concentration of A only, the rate of reaction is tripled and on tripling the initial concentration of both A and B, the rate of a reaction is increased by 27 times.
The rate of reaction can be expressed as:
(A) Rate = k[A][B]
(B) Rate = k[A]2[B]
(C) Rate = k[A][B]2
(D) Rate = k[A]2[B]2
Answer: (C)
Let’s consider for the reaction, A+ B products, rate is:
Rate(R)=k [A]x [B]y.........(i)
On tripling the concentration of A, the rate also gets tripled.
3R = k[3A]x[B]y.........(ii)
On dividing the equation (ii) by (i), we get;
⇒ 3 = 3x
⇒ x = 1
Also, on tripling the concentration of A and B, rate increases by 27 times.
27R = k[3A]x[3B]y.........(iii)
On dividing the equation (iii) by (i), we get;
⇒ 27 = 3x × 3y
Substituting, x = 1
⇒ 27 = 31× 3y
⇒ y = 2
Substituting the values of x and y in equation (i), we get;
Rate(R)=k [A]x [B]y.........(i)
Rate=k [A]1 [B]2
Frequently Asked Questions-FAQs
Q 1. What is meant by the differential rate equation?
Answer: Differential rate laws are used to express the rate of a reaction in terms of the changes in reactant concentrations [d[R]) over a small interval of time (dt)].
It is expressed as:
Differential rate law can also be used to calculate the instantaneous rate of a reaction, which is the rate of reaction defined for an infinitesimally small interval of time.
Q 2. What will be the unit of rate constant in case of gaseous reaction?
Answer: Consider a chemical reaction occurring in the gaseous phase;
xX(g) yY(g)
Rate=k pXn
Where pX is the partial pressure of reactant X and n is the experimentally determined order of this reaction.
Q 3. What is the difference between 'Keq' and 'k'?
Answer: 'Keq' is an equilibrium constant, it tells the net extent of reversible reactions whereas k is the rate constant of the reaction that tells how fast a reaction is proceeding.
Q 4. Does rate constant change with the rate of a reaction?
Answer: For any reaction, aA + bB cC
Rate of reaction ∝ [A]x [B]y
Rate = k [A]x [B]y
k is rate constant.
x and y are the orders with respect to the reactants A & B respectively.
As the concentration of reactants [A] and [B] changes, the rate of reaction changes but the rate constant (k) always remains constant throughout the entire span of reaction at a given temperature.
Related Topic
|
Reaction mechanism |
Rate of a Reaction |
|
Integrated Rate Laws |
Order of a Reaction |
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