A certain reaction has an activation energy of 70.0 kJ/mol and a frequency factor of A = 2.60 × 10^12 M⁻¹·s⁻¹. Using the Arrhenius equation, what is the rate constant, k, of this reaction at 30.0 °C?

• A. 1.02 × 10^11 s⁻¹
• B. 3.45 × 10^9 s⁻¹
• C. 4.56 × 10^10 s⁻¹
• D. 1.23 × 10^7 s⁻¹

Answer: (A)

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: T(K) = 30.0 + 273.15.
2. Use the Arrhenius equation: k = A * exp(-Ea / (R * T)), where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.
3. Convert the activation energy from kJ/mol to J/mol by multiplying by 1000: Ea = 70.0 kJ/mol * 1000.
4. Substitute the values into the Arrhenius equation: A = 2.60 × 10^12 M⁻¹·s⁻¹, Ea = 70000 J/mol, R = 8.314 J/mol·K, and T = 303.15 K.
5. Calculate the exponent: -Ea / (R * T) and then compute the rate constant k using the Arrhenius equation.