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

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

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

Step 1: Understand that the rate constant (k) of a reaction increases with temperature.
Step 2: Know that the Arrhenius equation relates the rate constant to temperature and activation energy: k = A * e^(-Ea/(RT)), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
Step 3: Recognize that if the rate constant doubles (k2 = 2 * k1) when the temperature increases by 10°C, we can use this information to find the activation energy.
Step 4: Use the fact that a doubling of the rate constant can be approximated using the equation: ln(k2/k1) = (Ea/R) * (1/T1 - 1/T2). Since T2 is T1 + 10°C, convert this to Kelvin (10°C = 10 + 273.15 = 283.15 K).
Step 5: Simplify the equation for a small temperature change (10°C) to find that Ea is approximately 40 kJ/mol.
Step 6: Conclude that the activation energy (Ea) of the reaction is approximately 40 kJ/mol.

Arrhenius Equation – The Arrhenius equation relates the rate constant of a reaction to temperature and activation energy, showing how changes in temperature affect reaction rates.
Activation Energy (Ea) – The minimum energy required for a reaction to occur, which can be estimated from the temperature dependence of the rate constant.
Temperature Dependence of Reaction Rates – Understanding how reaction rates change with temperature, particularly the concept that a small increase in temperature can significantly affect the rate constant.