Question

For a certain reaction, the rate constant changes from 2.5 M/s to 9.5 M/s when the temperature is increased from 25.4oC than at 36.1oC. What is the activation energy for this reaction in kJ? R = 8.314 J/molK K = oC+273.15 WATCH YOUR UNITS Arrhenius Equation ln(k2/k1) = -(Ea/R) (1/T2 - 1/T1) Report your answer with two significant figures.

Answer 1

The activation energy can be determined using the equation:
ln(k₂/k₁) = E_a/R x (1/T₁ - 1/T₂)
where
E_a = 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

We have to convert temperatures from degrees Celsius to Kelvin
T = degrees Celsius + 273.15
T₁ = 25.4 + 273.15
T₁ = 298.55 K
T₂ = 36.1+ 273.15
T₂ = 309.25 Kelvin=0.00335-0.00323

Also, as per question,

K₁ =2.5M/s

K₂=9.5 M/s

Putting all the values in the given equation, we get:

ln(k₂/k₁) = E_a/R x (1/T₁ - 1/T₂)
ln(9.5/2.5) = E_a/8.3145 J/K·mol x (1/298.55 K - 1/309.25 K)
ln(3.8) = E_a/8.3145 J/K·mol x 1.2 x 10^-4 K^-1
1.34 = E_a(1.44 x 10^-5 mol/J)
E_a = 93056 J/mol
or in kJ/mol, (divide by 1000)

E_a = 93.06 KJ/mol

Answer: The activation energy for this reaction is 93056 J/mol or 93.06 kJ/mol.