Chemical Kinetics

 

Chemical Kinetics

 Chemical kinetics

 Chemical kinetics is the branch of chemistry that studies the rates and mechanisms of chemical reactions. It is concerned with the way in which the rate of a reaction depends on various factors, such as the concentration of reactants, temperature, pressure, and catalysts. 

Rate of a Chemical Reaction

The rate of a reaction can be defined as the change in concentration of a reactant or product in unit time. 

1. Average rate of reaction

2. Instantaneous rate of reaction

1.  Average rate of reaction

The average rate of a chemical reaction is the change in the concentration of a reactant or product per unit of time. It is usually expressed in terms of the amount of substance that reacts or is produced per unit time, such as moles per second. 

If  `[R]_1`  and `[P]_1`  are the concentrations of `R` and `P` respectively at time `t_1` and `[R]_2`  and `[P]_2`  are their concentrations at time `t_2`  then,

`\Delta t = t_2 - t_1`

`\Delta [R] = [R]_2 - [R]_1`

`Delta [P] = [P]_2 - [P]_1`

👉 The square brackets in the above expressions are used to express molar concentration.

Rate of disappearance of R

`= `Decrease in the concentration of R / Time taken 

`= - \frac{\Delta [R]}{\Delta t}` 

Rate of appearance of P

`=` Increase in concentration of P/ Time taken 

`= + \frac{\Delta [P]}{\Delta t}`

👉 Average rate depends upon the change in concentration of reactants or products and the time taken for that change to occur.

Units of rate of a reaction

If concentration is in `mol L^{–1}` and time is in seconds then the units will be `mol L^{-1}s^{ –1}`. 

2. Instantaneous rate of reaction

The instantaneous rate of reaction is the rate at which a chemical reaction occurs at a specific moment in time. It represents the change in concentration of a reactant or product per unit of time at that particular instant.

To express the rate at a particular moment of time we determine the instantaneous rate. It is obtained when we consider the average rate at the smallest time interval say `dt` ( i.e. when `∆t` approaches zero). 

Hence, mathematically for an infinitesimally small `dt` instantaneous rate is given by

Geometrically  👉 The slope of this tangent gives the instantaneous rate.

Example

From the concentrations of `C_4H_9Cl` (butyl chloride) at different times given below, calculate the average rate of the reaction:

`C_4H_9Cl + H_2O → C_4H_9OH + HCl`

Solution

It can be seen (Table ) that the average rate falls from `1.90 × 10^{-4} mol L^{-1}s^{-1}` to `0.4 × 10^{-4} mol L^{-1}s ^{-1}`. However, average rate cannot be used to predict the rate of a reaction at a particular instant as it would be constant for the time interval for which it is calculated.

👉 The slope of this tangent gives the instantaneous rate.

 

Stoichiometric coefficients

Stoichiometric coefficients, also known as stoichiometric numbers or stoichiometric ratios, are numerical values that represent the relative quantities of substances involved in a chemical reaction. They are used to balance chemical equations and indicate the mole ratios between reactants and products.

Stoichiometric coefficients of the reactants and products are same

Where stoichiometric coefficients of the reactants and products are same, then rate of the reaction is given as

`Hg(l) + Cl_2 (g) → HgCl_2 (s)` 

Rate of reaction

 `= - \frac{\Delta [Hg]}{\Delta t} = -\frac{\Delta [Cl_2]}{\Delta t} = \frac{\Delta [HgCl_2]}{\Delta t}`    

i.e., rate of disappearance of any of the reactants is same as the rate of appearance of the products.

Stoichiometric coefficients of the reactants and products are not same

Two moles of `HI` decompose to produce one mole each of `H_2` and `I_2`

`2HI(g) → H_2 (g) + I_2 (g)` 

Rate of reaction `= -1/2\frac{\Delta [HI]}{\Delta t } = \frac{\Delta [H_2]}{\Delta t} = \frac{\Delta [I_2]}{\Delta t}`

Rate Law

Rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.

Consider a general reaction

`aA + bB → cC + dD`

where `a, b, c` and `d` are the stoichiometric coefficients of reactants and products. 

The rate expression for this reaction is

Rate `∝ [A]^x [B]^y`

where exponents `x` and `y` may or may not be equal to the stoichiometric coefficients (`a` and `b`) of the reactants.  Above equation can also be written as

Rate `= k [A]^x [B]^y`  

 `-\frac{d[R]}{dt} = k [A]^x[B]^y`

This form of equation is known as differential rate equation, where `k` is a proportionality constant called rate constant. 

For example:

`2NO(g) + O_2 (g) → 2NO_2 (g)` 

It is obvious, after looking at the results, that when the concentration of `NO` is doubled and that of `O_2`  is kept constant then the initial rate increases by a factor of four from `0.096` to `0.384  mol L^{–1} s^{–1}`. This indicates that the rate depends upon the square of the concentration of NO. When concentration of `NO` is kept constant and concentration of `O_2`  is doubled the rate also gets doubled indicating that rate depends on concentration of `O_2` to the first power.

Hence, the rate equation for this reaction will be

Rate `= k[NO]^2 [O_2]`

The differential form of this rate expression is given as

`-\frac{d[R]}{dt} =  k[NO]^2 [O_2]`

Now, we observe that for this reaction in the rate equation derived from the experimental data, the exponents of the concentration terms are the same as their stoichiometric coefficients in the balanced chemical equation. 

Some other examples are given below:

In these reactions, the exponents of the concentration terms are not the same as their stoichiometric coefficients. Thus, we can say that:

👉 Rate law for any reaction cannot be predicted by merely looking at the balanced chemical equation, i.e., theoretically but must be determined experimentally. 

 Order of a Reaction

The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction

Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero order reaction means that the rate of reaction is independent of the concentration of reactants.

Molecularity of a Reaction

The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. 

Unimolecular Reaction

When one reacting species is involved, for example, the decomposition of ammonium nitrate. 

`NH_4NO_2 → N_2 + 2H_2O` 

Bimolecular reaction

Bimolecular reactions involve simultaneous collision between two species, for example, dissociation of hydrogen iodide.

`2HI → H_2 + I_2`

Trimolecular or termolecular reaction

Trimolecular or termolecular reactions involve simultaneous collision between three reacting species, for example, `2NO + O_2 → 2NO_2`

Summary 

Chemical Kinetics 👉The branch of chemistry which deals with the rates of chemical reactions and the mechanism by which they occur, is called chemical kinetics.

Rate of reactions 👉 The change of concentration of any one of the reactants or products at a given time interval (average) or given time (instantaneous). 

Hypothetical reaction:

`A \rightarrow B`

Average rate of reaction (reactant) `= - \frac{\Delta [A]}{\Delta t}`

Average rate of reaction (product) `= \frac{\Delta [B]}{\Delta t}`

Instantaneous rate of reaction (reactant) `=  - \frac{d [A]}{dt}`

Instantaneous rate of reaction (product) `=   \frac{d [B]}{ dt}`

For a general reaction

`aA + bB \rightarrow cC + dD`

Rate of reactions (instantaneous) `=` 

`-1/a \frac{d[A]}{dt} = -1/b \frac{d[B]}{dt} = 1/c \frac{d[C]}{dt} = 1/d \frac{d[D]}{dt}`

References:

1. NCERT Chemistry Part 1 Class 12