Arrhenius Equation with Example and Activation Energy Graph
Arrhenius equation is used to calculate the rate of a reaction. It is an important part of chemical kinetics. It helps in understanding the effect of temperature on the rate of a reaction. This equation was proposed in 1889 by Svante Arrhenius.
Where k = Rate constant A= Frequency factor Ea= activation energy
R = gas constant T = Kelvin temperature
The basis of the Arrhenius equation is collision theory. According to this theory, a reaction is a collision between two molecules (of the same substance or of two different substances) to form an intermediate. This intermediate so formed is unstable, which exist for a short period of time. The intermediate breaks to give two molecules of the product. The energy used in forming the intermediate is known as the activation energy.
Now, if we take to log on both sides of the Arrhenius equation, the reaction changes to
Ln is natural logarithm, the values can be taken from the logarithmic table. For graphical representation,
If we compare this equation with the equation of a straight line, we get y = ln k x = 1/T m = -Ea / R c = ln A
This gives a straight-line graph but with a negative slope. Plotting k v/s (1/T)
EFFECT OF TEMPERATURE
From the graph, we conclude that temperature and rate if reactions are proportional. As the temperature increase, the rate of reaction also increases. Kinetic energy increases with temperature. So, when we increase the temperature the number of molecules with kinetic energy greater than the activation energy increases. This increases the rate of the overall reaction by decreases the activation energy.
For a 10 K change in temperature, the rate almost doubles.
Let’s take Arrhenius equations at time T1 and T2 where the rates of the reaction are K1 and K2 respectively. ln k1 = -Ea/RT1+ ln A -----(1) ln k2 = -Ea/RT2 + ln A -----(2)