The specific reaction rate of a chemical reaction at 300K is 0.001min-...
Calculation of Energy of Activation of a Chemical Reaction
Introduction
The energy of activation of a chemical reaction is the minimum amount of energy required to start the reaction. It is the energy required to break the bonds of the reactants and form new bonds to give the products.
Given Data
Specific reaction rate at 300K = 0.001 min⁻¹
Specific reaction rate at 310K = 0.002 min⁻¹
Formula
The formula for calculating the energy of activation is as follows:
ln(k₂/k₁) = (-Ea/R) x (1/T₂ - 1/T₁)
where k₁ and k₂ are the specific reaction rates at temperatures T₁ and T₂ respectively, Ea is the energy of activation, R is the gas constant (8.314 J/K mol), and ln is the natural logarithm.
Solution
Substituting the given data in the formula:
ln(0.002/0.001) = (-Ea/8.314) x (1/310 - 1/300)
ln(2) = (-Ea/8.314) x (0.00333)
Ea = -ln(2) x 8.314 x (1/0.00333)
Ea = 49.5 kJ/mol
Conclusion
Therefore, the energy of activation of the given chemical reaction is 49.5 kJ/mol.