For a reaction with an activation energy of 50 kJ/mol, what is the rate constant

For a reaction with an activation energy of 50 kJ/mol, what is the rate constant at 350 K if the rate constant at 300 K is 0.1 s^-1?

For a reaction with an activation energy of 50 kJ/mol, what is the rate constant at 350 K if the rate constant at 300 K is 0.1 s^-1?

Step 1: Identify the given values: Activation energy (Ea) = 50 kJ/mol, Rate constant at 300 K (k1) = 0.1 s^-1, Temperature 1 (T1) = 300 K, Temperature 2 (T2) = 350 K.
Step 2: Convert the activation energy from kJ/mol to J/mol for consistency: 50 kJ/mol = 50000 J/mol.
Step 3: Use the Arrhenius equation: k2 = k1 * e^[-Ea/R(1/T2 - 1/T1].
Step 4: Identify the gas constant (R): R = 8.314 J/(mol·K).
Step 5: Calculate the term (1/T2 - 1/T1): 1/T2 = 1/350 K and 1/T1 = 1/300 K.
Step 6: Calculate 1/T2 - 1/T1: 1/350 - 1/300 = -0.00081667 K^-1.
Step 7: Substitute the values into the Arrhenius equation: k2 = 0.1 * e^[-50000/(8.314)(-0.00081667)].
Step 8: Calculate the exponent: -50000/(8.314)(-0.00081667) = 7.25.
Step 9: Calculate e^7.25, which is approximately 1432.3.
Step 10: Finally, calculate k2: k2 = 0.1 * 1432.3 = 0.4 s^-1.

Arrhenius Equation – The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy, allowing for the calculation of rate constants at different temperatures.
Temperature Dependence of Reaction Rates – Understanding how temperature affects the rate of chemical reactions and the significance of activation energy in this context.