The temperature dependence of rate of a chemical reaction
can be accurately explained by Arrhenius equation. It was first proposed by
Dutch chemist J.H. Vant’s Hoff but
Swedish chemist Arrhenius provides its physical justification and
interpretation.

**Where**K= Rate constant

A= Arrhenius constant or
frequency factor or pre exponential factor

R= Universal gas constant =25/3
joule per mole per second

Ea=
Activation Energy

T= temperature

-Ea/RT= Boltzmann factor or fraction of molecule having equal

**or**greater than Activation energy**or**fraction of molecule that have kinetic energy greater than activation energy.**ILLUSTRATIVE EXAMPLE (1):**The activation energy for the reaction is 209.5 k J per mole at 581 K.

Calculate
the faction of molecule of reactant s having energy equal to or greater than
activation energy.

**SOLUTION:**We known that

**fraction of molecule that have kinetic energy greater than activation energy is given by**

**Important cases of Arrhenius equation:**

**Case (1):**If T approaches to infinite

It means the
entire reactant molecule will be active; and crossing over the energy barrier. It will be possible when either

**Ea**is Zero or temperature**(T)**is infinite. These are practically not possible.
The maximum
value of K is

**A**when temperature tends to infinity.
Graph
indicate larger the activation energy, smaller is the value of rate constant
(K)

**Note:**

**For free radical combination reaction (Ea=0 ) thus K=A ,that means for free radical reaction rate constant equal to Arrhenius factor and becomes independence of temperature .**

**Case (2):**We know that (Ea) activation energy is always positive, thus K always increasing with increasing temperature whether reaction is exothermic or endothermic

**Mathematical prove:**since activation energy is always positive it can be never negative this is proven as:

**Case (3):**However in many complex reactions it is observed that rate constant found to be decreases with increasing temperature.

**For example**

**Mechanism:**

By equation
(1) and (2)

Since the
overall reaction is exothermic and

**Kc**decreases with increasing temperature as well as the decrease in**Kc**out weight the increase in**K**with temperature, thus**K obs**show a decrease with increase in temperature.**Case (4):**larger

**the activation energy greater the effect of temperature on rate constant.**

**Case (5):**At lower temperature, increase in temperature causes more changes in value of rate constant

**Case (6):**

“It means if
Ea=RT then rate constant become about 37% of the Arrhenius constant.

**ILLUSTRATIVE EXAMPLE (2):**Consider the following reaction

The
activation energy of backward reaction exceeds that of the forward reaction by
2RT (in J per mole). If the pre-exponential factor of forward reaction is 4
times of the reverse reaction. The absolute value of (G) Gibbs energy at STP
(in j per mole) for the reaction at 300 K is

(Given ln2= 0.7, RT= 2500 J per Mole at 300 K
and G is the Gibbs energy)

**(JEE Advanced 2018)****SOLUTION:**

**Given condition**

**ILLUSTRATIVE EXAMPLE (3):**Plots showing the variation of rate constant (K) with temperature (T) are given below. The plot that follow Arrhenius equation is

**(JEE Advanced 2010)**

**SOLUTION:**

**Hence on increasing temperature rate constant (K) increases exponentially.**

So option

**(A)**is correct**Calculation Activation Energy:**

**Take both side natural logarithm and obtained as**

**Note:**

**(1):**The above equation is the straight line with negative slope

**(2):**The slope of above equation gives Activation energy and intercept gives frequency factor

**(3)**Dependence of rate constant on temperature for two reactions is given as:

Slope of
reaction (2) is greater than (1) hence reaction (2) has higher activation
energy so reaction (2) is more sensitive to temperature.

**Calculation Activation Energy at two different temperatures (T**

_{1}and T_{2}):**ILLUSTRATIVE EXAMPLE (4):**In Arrhenius equation for a certain reaction, the value of A and Ea (activation energy) are 4 × 1013 sec–1 and 98.6 kJ mol–1 respectively. At what temperature, the reaction will have specific rate constant 1.1 × 10–3 sec–1?

**SOLUTION:**

**According to Arrhenius equation**

**ILLUSTRATIVE EXAMPPLE (5):**The energy of activation for a reaction is 100 kJ mol–1. Presence of a catalyst lowers the energy of activation by 75%.What will be effect on rate of reaction at 20ºC, other things being equal?

**SOLUTION:**

**The Arrhenius equation is**