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 300 K if R = 8.314 J/(mol·K)? (2022)

For a reaction with an activation energy of 50 kJ/mol, what is the rate constant at 300 K if R = 8.314 J/(mol·K)? (2022)

Step 1: Identify the values given in the problem. We have the activation energy (Ea) = 50 kJ/mol, the temperature (T) = 300 K, and the gas constant (R) = 8.314 J/(mol·K).
Step 2: Convert the activation energy from kJ/mol to J/mol. Since 1 kJ = 1000 J, we have Ea = 50 kJ/mol * 1000 J/kJ = 50000 J/mol.
Step 3: Write down the Arrhenius equation: k = Ae^(-Ea/RT). Here, A is the pre-exponential factor, but we will focus on calculating k without it for now.
Step 4: Substitute the values into the equation. We need to calculate the exponent first: -Ea/(RT).
Step 5: Calculate RT: R = 8.314 J/(mol·K) and T = 300 K, so RT = 8.314 * 300 = 2494.2 J/mol.
Step 6: Now calculate -Ea/RT: -50000 J/mol / 2494.2 J/mol = -20.05.
Step 7: Calculate e^(-20.05). Use a calculator to find this value, which is approximately 1.84e-9.
Step 8: Since we don't have the value of A, we can express k as k = A * 1.84e-9. Without A, we cannot find the exact value of k, but we have the form of the equation.

Arrhenius Equation – The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature.
Activation Energy – The minimum energy required for a chemical reaction to occur.
Gas Constant – The universal gas constant (R) is used in calculations involving gases and thermodynamics.