The Rate of a Chemical Reaction is a measure of how quickly reactants are transformed into products. It can be expressed in various ways, depending on the specific details of the reaction. Generally, it is defined as the change in concentration of a reactant or product per unit of time.
Mathematically, the Rate of a Reaction (R) can be expressed using the following general formula:
From the graph, it is clear that the concentration of the reactant decreases and that of the product increases as the reaction proceeds and the rate of the change of the concentration of the reactant as well as that of the product is also changing.
Example 1: Suppose the concentration of a reactant A changes from 0.4 M to 0.1 M in a time interval of 20 seconds. The rate of the reaction (r) can be calculated using formula:
r= Δ[A]/Δt
r = (0.1M−0.4M)/20s
r= −0.3M/20s
r=−0.015M/s
Note: The negative sign indicates a decrease in the concentration of the reactant, which is typical for reactants in a chemical reaction.So, in this example, the rate of the reaction is −0.015M/s
Let a simple kinetic reaction,
A → B
The rate in terms of reactant = − d[A]/dt
The rate in terms of product = d[B]/dt
Example 2: In a chemical reaction, N2 + 3H2 → 2 NH3 the rate of (d[NH3]/dt) = 2 × 10−4. How to calculate the value of (−d[H2]/dt) by kinetics equation?
Answer: From the rate equation for the formation of ammonia from nitrogen and hydrogen,
d[H2]/dt = (3/2) × 2 × 10−4 mol lit−1 sec−1
= 3 × 10−4 mol lit−1 sec−1
Example 3: What do you understand by the rate law and rate constant of a reaction?
Answer: The rate of reaction is shown to be dependent on the concentration terms of reactant A and reactant B.
Then, Rate of reaction ∝ [A]α [B]β
or Rate = K [A]α [B]β
This expression is termed Rate law.
Example 4: The rate of formation of NO(g) in the reaction NOBr(g)→ NO(g) Br2(g) is found to be 1.6 × 10-4 M/s. Find the rate of overall reaction rate and rate of consumption of NOBr.
We have : 1.6 × 10-4 M/s.
First write a balanced chemical equation. 2NOBr(g) → 2NO(g) Br2(g)
Now, Rate of overall reaction = = = = 0.8 × 10-4 M/s
Rate of consumption of NOBr = - = 1.6 × 10-4 M/s
The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate equation (rate law) for that particular reaction.
For example consider the reaction : aA+ bB → cC +dD. The differential rate law is written as :
Rate = = = = = kr[A]m[B]n
where kr is called as rate constant of the reaction or velocity constant or specific Reaction rate.
k is a characteristic of a reaction at a given temperature. It changing only when the temperature changes.
The powers m and n are integers or fractions. m is called as order of reaction with respect to A and n is called as order of reaction with respect to B. The overall order of reaction = m + n
Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction.
For example consider the following reaction :
(i) H2(g) Br2(g) → 2 HBr (g) rate = k[H2] [Br2]1/2 (by experiment), order of reaction = 1 + 1/2 = 3/2
(ii) CH3CHO(g) → CH4(g) CO(g), rate = k[CH3CHO]3/2 , order of reaction = 3/2
In general, the rate law for a nth order reaction can be taken as :
where k: rate constant; c : concentration and n : order of reaction
⇒ ⇒ Units of k º (mol/L)1-n (time)-1
Example 5: The rate constant of a reaction is k=3.28×10-4 s-1. Find the order of the reaction.
a) Zero order
b) First order
c) Second order
d) Third order
Answer: b) First order
Explanation: Given, k= 3.28×10-4 s-1
The standard formula for calculating rate constant units is k=(mol L-1)1-ns-1, where ‘n’ is the reaction order. The value of ‘n’ must be 1 for (mol L-1)1-ns-1 to be s-1. As a result, k=3.28×10-4s-1 denotes a first-order reaction.
Molecularity refers to the number of molecules (or ions) that participate as reactants in an elementary reaction.
Rate=k[A][B]
It's important to note that molecularity is a theoretical concept used to describe elementary reactions. In more complex reactions, which involve multiple elementary steps, the reaction order and molecularity may not be the same. Overall reaction orders are determined experimentally, while molecularity is a concept used to describe the individual elementary steps of a reaction mechanism.
Example 6: From the rate laws for the reactions given below, determine the order with respect to each species and the overall order:
(i) 2HCrO4- + 6I- + 14H → 2Cr3 + 3I2+8H2O, Rate = k[HCrO4-] [I-]2 [H ]2
(ii) H2O2 +2I- +2H → I2 +2H2O, Rate = k[H2O2] [I-]
Sol. (i) The order of the reaction with respect to [HCrO4-] is 1; with respect to [I-] is 2 and with respect to [H ] is 2. The overall order of the reaction is 1 +2 +2 = 5
(ii) The order of the reaction with respect to [H2O2] is 1 and with respect to [I-] is 1. The overall order of the reaction is 1 +1= 2.
- In (i) stoichiometric coefficient of I- is 6 whereas the power coefficient (n) in the rate law is 2.
- Reaction (i) may not take place in a single step. It may not be possible for all the 22 molecules to be in a state to collide with each other simultaneously. Such a reaction is called a complex reaction.
- A complex reaction takes place in a series of a number of elementary reactions.
Integrated rate equations are mathematical expressions that relate the concentrations of reactants and/or products to time for a chemical reaction.
These equations are obtained by integrating the rate laws, which describe how the rate of a reaction depends on the concentrations of reactants.
The rate law for zero order reactions (n = 0) is written as :
-
-
[A]o - [A] = kt
=
Time in which half of initial amount is left.
[A]o [A]o/2
t = o t = t1/2
k =
t1/2 =
Thus, for a Zero order reaction, half-life is directly proportional to the initial concentration of the reactant.
Clearly, zero-order reactions are those, whose rates are not affected by change in concentrations of reactants (i.e., independent of concentration). The rates of such reactions only depend upon temperature. Most of photochemical reactions are zero order reactions. Other examples are : decomposition of HI over the surface of gold and NH3 over tungsten.
(1) Photochemical Reactions, Photosynthesis
(2) CH4 Cl2
Cl - Cl Cl
CH4 + Cl CH3Cl + H
A product
t = o [A]o -
t = t [A] [P]
ln [A]o/[A] = kt
t = t1/2 [A] = [A]o/2
=
[A] = where , n = number of half lifes.
Rate constant of a first order reaction can also be calculated by measuring the concentration of the reactants at two time instants (if the initial concentration is not known).
If A1 and A2 are the reactant's concentrations at two time instants 't1' and 't2' respectively, then we have :
...(iii)
and ... (iv)
Subtracting (iv) from (iii), we get :
Thus, k can be evaluated.
Example: For a reaction 2NO(g) + 2H2(g) → N2(g) + 2H2O (g) ; the following data were obtained.
| [NO] (mol/L) | [H2](mol/L) | Rate (mol/L/s) |
1. | 5 X 10-3 | 2.5 X 10-3 | 3 X 10-5 |
2. | 15 X 10-3 | 2.5 X 10-3 | 9 X 10-5 |
3. | 15 X 10-3 | 10 X 10-3 | 3.6 X 10-4 |
(a) Calculate the order of reaction.
(b) Find the rate constant.
(c) Find the initial rate if [NO] = [H2] = 8.0 x 10-3 M
Sol: Assuming rate law can be expressed as follows :
rate = k[NO]x [H2]y
By analyzing the data :
From observation 1 and 2, we see that [H2] is constant and when [NO] is tripled, the rate is also tripled.
⇒ rate (r) ∝ [NO] ⇒ x = 1
From observations 2 and 3, we see that [NO] is constant; when [H2] is increased four times, the rate also increases four times :
rate ∝ [H2] ⇒ y = 1
⇒ r = k [NO] [H2O]
⇒ The order of reaction w.r.t No and H2 is 1 and the overall order of reaction is 1 1 = 2.
Initial rate = k[NO][H2] = 2.4 x (8 x 10-3)2 = 1.536 x 10-4 mol/L/s.
- = k[A]2
k =
[A]t = , k = 2/[A]o - 1/[A]o
t1/2 =
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1. What is the Rate of a Reaction? |
2. What is Rate Law? |
3. What is Order of a Reaction? |
4. What is Molecularity of a Reaction? |
5. What are Integrated Rate Equations? |
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