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If the rate constant of a reaction doubles when the temperature increases by 10°

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Question: If the rate constant of a reaction doubles when the temperature increases by 10°C, what is the approximate activation energy?

Options:

  1. 20 kJ/mol
  2. 40 kJ/mol
  3. 60 kJ/mol
  4. 80 kJ/mol

Correct Answer: 40 kJ/mol

Solution: 

Using the Arrhenius equation and the rule of thumb that a 10°C increase roughly doubles the rate constant, we can estimate the activation energy to be around 40 kJ/mol.

If the rate constant of a reaction doubles when the temperature increases by 10°

Practice Questions

Q1
If the rate constant of a reaction doubles when the temperature increases by 10°C, what is the approximate activation energy?
  1. 20 kJ/mol
  2. 40 kJ/mol
  3. 60 kJ/mol
  4. 80 kJ/mol

Questions & Step-by-Step Solutions

If the rate constant of a reaction doubles when the temperature increases by 10°C, what is the approximate activation energy?
  • Step 1: Understand the Arrhenius equation, which relates the rate constant (k) to temperature (T) and activation energy (Ea). The equation is k = A * e^(-Ea/(RT)), where A is the pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin.
  • Step 2: Recognize that a 10°C increase in temperature approximately doubles the rate constant (k). This is a common rule of thumb in chemistry.
  • Step 3: Use the relationship between the rate constant and temperature to estimate the activation energy. If doubling k occurs with a 10°C increase, we can use this information to find Ea.
  • Step 4: The rule of thumb suggests that the activation energy can be estimated using the formula Ea ≈ 10 * R * ln(2), where ln(2) is the natural logarithm of 2 (approximately 0.693).
  • Step 5: Calculate the gas constant R, which is approximately 8.314 J/(mol·K).
  • Step 6: Plug in the values: Ea ≈ 10 * 8.314 J/(mol·K) * 0.693. This gives Ea ≈ 57.6 J/mol per 10°C increase.
  • Step 7: Convert the activation energy from J/mol to kJ/mol by dividing by 1000. This gives Ea ≈ 0.0576 kJ/mol per 10°C increase.
  • Step 8: Since we are looking for the activation energy for a 10°C increase that doubles the rate constant, we can estimate Ea to be around 40 kJ/mol.
  • Arrhenius Equation – The Arrhenius equation relates the rate constant of a reaction to temperature and activation energy, showing how temperature affects reaction rates.
  • Activation Energy – The minimum energy required for a chemical reaction to occur, which can be estimated using changes in rate constants with temperature.
  • Temperature Dependence of Reaction Rates – Understanding how reaction rates change with temperature, particularly the rule of thumb that a 10°C increase can double the rate constant.
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