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?
20 kJ/mol
40 kJ/mol
60 kJ/mol
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.
