Chemical Kinetics in Physical Chemistry

Chemical kinetics and half-life formulas deal with the rate change of reactants and products of reactions per unit time in physical chemistry. Hence rate law in chemical kinetics studies provides formulas, mechanisms, and molecular pathways of kinetic reaction in chemistry.

In physical chemistry, on the basis of speed of reactions are three types

  1. Very fast reaction
  2. very slow reaction
  3. Moderate speed reaction

But very fast where oxidation number of reactant and product same or very slow reactions can not study under chemical kinetic only a moderate rate of reaction discus. All the redox reaction is going fast and the formation of HCl in dark conditions is a slow reaction.

Hydrolysis of ester, decomposition of N2O5, the reaction between PO4 and I, etc are the examples of moderate rate reaction.

Studies of chemical kinetics formulas in chemistry and rate law for reactants and products in kinetic reactions

Importance of Kinetic Reaction

There is two main importance for studies the rate reaction in chemical kinetics

  1. The first is the practical importance for able to predict how quickly a reaction mixture moves to equilibrium. Thus it depends only on the external factor which used to proceeding the reaction.
  2. The second is the theoretical importance of kinetics reactions is to define the chemical formulas and mechanisms in physical chemistry. Thus we can analyze the chemical reaction to many elementary steps.

Reactants and Products in Kinetic Chemistry

The rate of chemical reaction in kinetics depends on the change of concentration of reactants and products at any instant of time.

Let a simple kinetic reaction
A → B

The rate in terms of reactant = – d[A]/dt
But rate in terms of reactant = – d[B]/dt

Negative signs used to show the decrease of concentration of reactants with time. But the rate is always a positive quantity and it decreases with time.

A complication arises if we consider the reaction

A + 2B → 3C + D

The above reaction rate of decrease of B is twice the rate of decrease of A. To resolve this complication we mention the rate of reaction in terms of a particular component. Thus the best way to write the rate of kinetic reaction

    \[ \boxed{Rate =\pm \frac{1}{\gamma _{i}}\frac{d[C]}{dt}}{dt}} \]

where γi = stoichiometric coefficient of the balanced equation and positive sign used for products and negative sign for reactants in physical chemistry. Thus the rate equation for the above reaction

    \[ \boxed{-\frac{d[A]}{dt} =-\frac{1}{2}\frac{d[B]}{dt} =\frac{1}{3}\frac{d[C]}{dt} =\frac{d[D]}{dt}} \]

Question

In a chemical reaction, N2 + 3H2 → 2NH3  the rate of (d[NH3]/dt) = 2×10-4. Calculate the value of (-d[H2]/dt).

Answer

From the rate equation for the above reaction

∴ dH2/dt = (3/2) × 2 × 10-4 mol lit-1 sec-1
= 3 × 10-4 mol lit-1 sec-1

Units of the Rate Change in Chemical Kinetics

In physical chemistry, the rate of reactions defined as the rate of change of concentration of reactants and products at any instant of time.

Unit of rate = unit of concentration/unit of time

Thus the units of the rate of the reaction
mol lit-1sec-1
and mol m-3 sec-1

Factors Affecting the Rate of Reaction

There are several factors affecting the rate of a chemical reaction. Out of this some important factor are

  1. Active mass or concentration of the reactants and products derived by mass action law chemistry.
  2. The temperature of the equation derived in the Arrhenius equation.
  3. Presence of catalyst in a chemical reaction.
  4. Degree of fineness of reactants.
  5. Absorption of radiation of suitable frequency derived in the photochemical reaction.

Rate Law in Chemical Kinetics

Dependence of reaction rate with the concentration of reactants we express rate equation or rate law. Mass action law guides the basis of the formulation of rate equations. But the rate equation can only be formulated on the basis of experimental data.

Thus decomposition of hydrogen peroxide represented as

2H2O2 → 2H2O + O2

From the mass action law and kinetic rate equation
– d[H2O2]/dt = k [H2O2]2

But the experiment shows the rate equation is

– d[H2O2]/dt = k [H2O2]

The single power of concentration controlled the decomposition of hydrogen peroxide. Thus this reaction is 1st order because of only one concentration term used in the rate equation. K = const, called rate constant of a specific reaction.

Thus for a general reaction,

aA + bB → cC + dD

Rate of reaction = k × CAm × CBn

Where values of m and n depend on the experimental data. It does not depend on the values of a and b.

Units of the Rate Constant in Kinetics

If a kinetic reaction expressed as,
A → Product

The rate equation for this reaction
– d[A]/dt = k [A]n
where n= order of the reaction

∴ Units of rate constant (k) in kinetics
= (unit of concentration)1-n/unit of time

Order of reaction Unit of the rate constant
Zero-order mol lit-1 sec-1
first-order sec-1
second-order lit mol-1 sec-1

Half-life Formula in Chemical Reaction

When the chemical reaction proceeds the concentration of reactant decreases and productivity increases. But after a certain period of time the value of the reactant one haft of initial concentration. This study is the basis for the formulas of half-life in chemical kinetic.

The integrated rate law for the zero-order kinetics

x = k0 × t
but when t=t½ , x = x/2
∴ t½ = x/2k
where x = initial conc. of reactant.

Importance of Rate Law

The importance of rate law serves mainly three purpose

  1. It permits to predicts the rate at a given concentration from the knowledge of rate constant.
  2. Rate laws help to build up the possible mechanism of a chemical reaction.
  3. From the rate law studies, we can clarify the kinetics of the chemical reaction as first, second, or third-order kinetic.