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

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Question: 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?

Options:

  1. 20.8
  2. 40.8
  3. 60.8
  4. 80.8

Correct Answer: 40.8

Solution: 

Using the Arrhenius equation and the two-point form, Ea can be estimated as Ea ≈ 2.303RT²(Δlnk/Δ(1/T)). With R = 8.314 J/(mol·K), Ea ≈ 40.8 kJ/mol.

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

Practice Questions

Q1
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?
  1. 20.8
  2. 40.8
  3. 60.8
  4. 80.8

Questions & Step-by-Step Solutions

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.
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