The rate of most of the chemical reactions increases with an increase in temperature. The rate constant of a chemical process doubles for every 10 degrees Celsius rise in temperature.

Until 1889, there was no precise way to physically determine the temperature dependence of the rate of a chemical reaction. Svante Arrhenius improved on J.H. Van’t Hoff’s work in 1889 by providing an equation that quantitatively related temperature and a process’s rate constant. The proposed equation was given a name: Arrhenius Equation.

**Arrhenius Equation**

**The Arrhenius equation can quantitatively explain the temperature dependency of the rate of a chemical process.**

**k = Ae ^{-Ea/RT}**

**k**= rate constant of the reaction**A**= Arrhenius Constant**E _{a}**= Activation Energy for the reaction (in Joules mol

^{−1})

**R**= Universal Gas Constant

**T**= Temperature in absolute scale (in kelvins)

This equation shows the dependence of the rate of a chemical reaction on the temperature.

The Arrhenius factor, also known as the frequency factor or pre-exponential factor, is represented by A. E_{a} is the activation energy in joules/mole, and R is the gas constant.

**k = Ae ^{-Ea/RT}**

Taking both sides of the equation’s natural logarithm

ln k = -(E_{a}/RT) + ln A………… (a)

At temperature T_{1}, equation (a) can be written as;

ln k_{1} = E_{a}/RT_{1} + ln A…………. (i)

At temperature T_{2}, equation

ln k_{2} = E_{a}/RT_{2} + ln A………… (ii)

For a given reaction, A is constant.

The values of rate constants for temperatures T_{1 }and T_{2} are k_{1} and k_{2}, respectively.

Subtracting equation (i) from (ii)

ln k_{2} – ln k_{1} = (E_{a}/RT_{1}) – (E_{a}/RT_{2})

ln (k_{2}/k_{1}) = E_{a}/R ((1/T_{1}) -(1/T_{2}))

log k_{2}/k_{1} = (E_{a}/2.303R) × ((1/T_{1}) -(1/T_{2})) …… (iii)

**Graphical Representation**

**ln k = -(E _{a}/RT) + ln A** A straight line with slope is drawn when ln k vs 1/T is plotted = -(E

_{a}/R) and intercept = ln A

**Temperature and Average Kinetic Energy**

The average kinetic energy increases as the absolute temperature rises. As a result, the number of molecules with energy larger than the threshold energy grows (as illustrated by the Maxwell distribution curves below). The number of effective collisions between reactant molecules increases as a result. As a result, the rate of reaction often rises with increasing temperature.

**Solved Problems**

A reaction of the second order was observed. The reaction rate constant was 8.9 x 10^{-3} L/mol at three degrees Celsius and 7.1 x 10^{-2} L/mol at 35 degrees Celsius. What is the activation energy of this reaction?

**Solution**

The activation energy can be determined using the equation:

ln(k_{2}/k_{1}) = E_{a}/R x (1/T_{1} – 1/T_{2})

where

E_{a} = the activation energy of the reaction in J/mol

R = the ideal gas constant = 8.3145 J/K·mol

T_{1} and T_{2} = absolute temperatures (in Kelvin)

k_{1} and k_{2} = the reaction rate constants at T_{1} and T_{2}

**Step 1: Convert temperatures from degrees Celsius to Kelvin**

T = degrees Celsius + 273.15

T_{1} = 3 + 273.15

T_{1} = 276.15 K

T_{2} = 35 + 273.15

T_{2} = 308.15 Kelvin

**Step 2:**** Find Activation Energy E _{a}**ln(k

_{2}/k

_{1}) = E

_{a}/R x (1/T

_{1}– 1/T

_{2})

ln(7.1 x 10

^{-2}/8.9 x 10

^{-3}) = E

_{a}/8.3145 J/K·mol x (1/276.15 K – 1/308.15 K)

ln(7.98) = E

_{a}/8.3145 J/K·mol x 3.76 x 10

^{-4}K

^{-1}

2.077 = E

_{a}(4.52 x 10

^{-5}mol/J)

E

_{a}= 4.59 x 10

^{4}J/mol

**The activation energy for this reaction is 4.59 x 10 ^{4} J/mol.**

**References**

- https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_General_Chemistry_(Petrucci_et_al.)/14%3A_Chemical_Kinetics/14.09%3A_The_Effect_of_Temperature_on_Reaction_Rates
- https://byjus.com/chemistry/temperature-dependence-on-chemical-reaction/
- https://www.chemicals.co.uk/blog/how-does-temperature-affect-the-rate-of-a-reaction
- https://www.nagwa.com/en/explainers/158132862453/
- https://unacademy.com/content/jee/study-material/chemistry/effect-of-temperature-on-the-rate-of-reaction/
- Rate of Reaction of Sodium Thiosulfate and Hydrochloric Acid. Retrieved 5 September 2019, from https://www.flinnsci.com/api/library/Download/78da6c8204aa48a294bd9a51844543ad
- https://www.studysmarter.us/explanations/chemistry/physical-chemistry/rate-of-reaction-and-temperature/