Effect of Temperature on Rate of Reaction

Effect of Temperature on Rate of Reaction
Effect of Temperature on Rate of Reaction

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
Ea= 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. Ea 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 = -(Ea/RT) + ln A………… (a)

At temperature T1, equation (a) can be written as;

ln k1 = Ea/RT1 + ln A…………. (i)

At temperature T2, equation

ln k2 = Ea/RT2 + ln A………… (ii)

For a given reaction, A is constant.

The values of rate constants for temperatures Tand T2 are k1 and k2, respectively.

Subtracting equation (i) from (ii) 

ln k2 – ln k1 = (Ea/RT1) – (Ea/RT2)

ln (k2/k1) = Ea/R ((1/T1) -(1/T2))

log k2/k1 = (Ea/2.303R) × ((1/T1) -(1/T2)) …… (iii)

Graphical Representation

ln k = -(Ea/RT) + ln A A straight line with slope is drawn when ln k vs 1/T is plotted = -(Ea/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(k2/k1) = Ea/R x (1/T1 – 1/T2)
where
Ea = the activation energy of the reaction in J/mol
R = the ideal gas constant = 8.3145 J/K·mol
T1 and T2 = absolute temperatures (in Kelvin)
k1 and k2 = the reaction rate constants at T1 and T2

Step 1: Convert temperatures from degrees Celsius to Kelvin
T = degrees Celsius + 273.15
T1 = 3 + 273.15
T1 = 276.15 K
T2 = 35 + 273.15
T2 = 308.15 Kelvin

Step 2: Find Activation Energy Ea
ln(k2/k1) = Ea/R x (1/T1 – 1/T2)
ln(7.1 x 10-2/8.9 x 10-3) = Ea/8.3145 J/K·mol x (1/276.15 K – 1/308.15 K)
ln(7.98) = Ea/8.3145 J/K·mol x 3.76 x 10-4 K-1
2.077 = Ea(4.52 x 10-5 mol/J)
Ea = 4.59 x 104 J/mol

The activation energy for this reaction is 4.59 x 104 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/

About Author

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Jyoti Bashyal

Jyoti Bashyal, a graduate of the Central Department of Chemistry, is an avid explorer of the molecular realm. Fueled by her fascination with chemical reactions and natural compounds, she navigates her field's complexities with precision and passion. Outside the lab, Jyoti is dedicated to making science accessible to all. She aspires to deepen audiences' understanding of the wonders of various scientific subjects and their impact on the world by sharing them with a wide range of readers through her writing.

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