If the rate of a reaction doubles when the temperature increases from 300 K to 3

If the rate of a reaction doubles when the temperature increases from 300 K to 310 K, what is the approximate activation energy (Ea) in kJ/mol?

If the rate of a reaction doubles when the temperature increases from 300 K to 310 K, what is the approximate activation energy (Ea) in kJ/mol?

Step 1: Understand that the rate of a reaction increases with temperature due to more molecules having enough energy to react.
Step 2: Recognize that the Arrhenius equation relates the rate of a reaction to temperature and activation energy (Ea).
Step 3: Note that the problem states the rate doubles when the temperature increases from 300 K to 310 K.
Step 4: Use the two-point form of the Arrhenius equation: Ea ≈ 2.303RT²(Δlnk/Δ(1/T)).
Step 5: Identify the values needed: R = 8.314 J/(mol·K), T1 = 300 K, T2 = 310 K.
Step 6: Calculate Δ(1/T) for the two temperatures: Δ(1/T) = (1/300) - (1/310).
Step 7: Calculate Δlnk, knowing that the rate doubles means ln(k2/k1) = ln(2).
Step 8: Substitute the values into the equation to find Ea.
Step 9: Convert the result from J/mol to kJ/mol by dividing by 1000.

Arrhenius Equation – The Arrhenius equation relates the rate of a chemical reaction to temperature and activation energy.
Temperature Dependence of Reaction Rates – Understanding how reaction rates change with temperature is crucial for calculating activation energy.
Two-Point Form of the Arrhenius Equation – This form allows for the estimation of activation energy using two different temperatures and their corresponding rate constants.