A particular first-order reaction has a rate constant of 1.35 x 10^0 s^-1 at 25°C. What is the magnitude of the rate constant k at 75.0°C if the activation energy Ea is 55.3 kJ/mol?

• A. 2.68 x 10^1 s^-1
• B. 3.12 x 10^1 s^-1
• C. 1.35 x 10^1 s^-1
• D. 4.57 x 10^1 s^-1

Answer: (D)

Verified step by step guidance

1. Identify that the problem involves calculating the rate constant at a different temperature using the Arrhenius equation: k = A * e^(-Ea/(RT)).
2. Recognize that the Arrhenius equation can be rearranged to compare rate constants at two different temperatures: ln(k2/k1) = (Ea/R) * (1/T1 - 1/T2).
3. Substitute the given values into the equation: k1 = 1.35 s^-1, Ea = 55.3 kJ/mol (convert to J/mol by multiplying by 1000), T1 = 25°C (convert to Kelvin by adding 273.15), and T2 = 75°C (convert to Kelvin by adding 273.15).
4. Use the gas constant R = 8.314 J/(mol*K) in the equation and solve for ln(k2/k1).
5. Exponentiate both sides to solve for k2, the rate constant at 75.0°C, using the relationship k2 = k1 * e^(ln(k2/k1)).