The temperature at which a reaction is running is increase from 11.052 celsius to 102.567 celsius. If the rate constant increases by a factor of 5.608, what is the activation energy of the reaction in kJ/mol?
Use the Arrhenius equation.
I AM STILL LOST
The Arrhenius equation is
ln(k2/k1)=(Ea/R)*[(1/T1) - (1/T2)]
You have T1 and T2. You have k1 and that times 5.608 will give you k2. R is 8.314 J/mol*K. Solve for Ea. Plug and chug.
Is the answer 16.733 kJ/mol.
I obtained 16.726 kJ/mol. I used 273.15 to convert to K. Using 8.314 (4 significant figures) would round to 16.73 kJ/mol for both answers.
To solve this problem, you can use the Arrhenius equation:
ln(k2/k1) = (Eₐ/R) * [(1/T1) - (1/T2)]
Where:
k1 and k2 are the rate constants at temperatures T1 and T2 respectively,
Eₐ is the activation energy,
R is the gas constant (8.314 J/mol*K),
T1 and T2 are the temperatures in Kelvin.
You are given that T1 = 11.052 °C and T2 = 102.567 °C, and that the rate constant increases by a factor of 5.608.
First, convert T1 and T2 to Kelvin:
T1 = 11.052 + 273.15 = 284.202 K
T2 = 102.567 + 273.15 = 375.717 K
Next, rewrite the equation using the given values:
ln(5.608) = (Eₐ/8.314) * [(1/284.202) - (1/375.717)]
Solving for Eₐ:
Eₐ/8.314 = ln(5.608) / [(1/284.202) - (1/375.717)]
Eₐ/8.314 = ln(5.608) / [(375.717 - 284.202) / (284.202 * 375.717)]
Eₐ = 8.314 * ln(5.608) * (284.202 * 375.717) / (375.717 - 284.202)
Calculating this expression:
Eₐ = 8.314 * ln(5.608) * (284.202 * 375.717) / (375.717 - 284.202)
Using a calculator, the value is approximately 16.726 kJ/mol.
Rounding to four significant figures would give you 16.73 kJ/mol, which is the same as your answer (16.733 kJ/mol) with the given significant figures.