A particular first-order reaction has a rate constant of 1.35 × 10² s⁻¹ at 25.0°C. Using the Arrhenius equation, what is the rate constant (k) at 95.0°C if the activation energy (Ea) is 55.5 kJ/mol?

• A. 1.35 × 10² s⁻¹
• B. 5.40 × 10² s⁻¹
• C. 2.68 × 10³ s⁻¹
• D. 8.90 × 10² s⁻¹

Answer: (C)

Verified step by step guidance

1. Start by understanding the Arrhenius equation, which is used to calculate the rate constant (k) at different temperatures. The equation is: $k=A{e}^{-}$, where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
2. Convert the temperatures from Celsius to Kelvin. The temperature at 25.0°C is $298.15$ K and at 95.0°C is $368.15$ K.
3. Use the Arrhenius equation in its logarithmic form to find the new rate constant at 95.0°C: $\ln \frac{k}{\mathrm{k\_0}}=\frac{\mathrm{E\_a}}{R}(\frac{1}{\mathrm{T\_0}}-\frac{1}{T})$, where k₀ is the rate constant at the initial temperature, and k is the rate constant at the new temperature.
4. Substitute the known values into the equation: $\ln \frac{k}{1.35}=\frac{55500}{8.314}(\frac{1}{298.15}-\frac{1}{368.15})$. Note that the activation energy is converted from kJ/mol to J/mol.
5. Solve for the new rate constant k by calculating the right side of the equation and then exponentiating both sides to find k. This will give you the rate constant at 95.0°C.