**Title: Calculating the Rate Constant of a Reaction Using the Arrhenius Equation****Introduction:**The rate constant \((k)\) of a chemical reaction is a crucial factor in predicting how fast a reaction occurs. Understanding its dependence on temperature and activation energy allows chemists to control reaction rates effectively.**Problem Statement:**The rate constant of a certain reaction is known to obey the Arrhenius equation and has an activation energy \(E_a = 50.0\) kJ/mol. If the rate constant of this reaction is \(4.6 \times 10^2\) M\(^{-1}\)s\(^{-1}\) at \(83.0\)°C, what will the rate constant be at \(42.0\)°C?**Solution Steps:**1. **Restate Given Data:** - Activation Energy (\(E_a\)): 50.0 kJ/mol - Initial Rate Constant (\(k_1\)): \(4.6 \times 10^2\) M\(^{-1}\)s\(^{-1}\) - Initial Temperature (\(T_1\)): 83.0°C - Final Temperature (\(T_2\)): 42.0°C2. **Convert Temperatures to Kelvin:** \[ T_1 = 83.0 + 273.15 = 356.15 \text{ K} \] \[ T_2 = 42.0 + 273.15 = 315.15 \text{ K} \]3. **Apply the Arrhenius Equation:** The Arrhenius equation links the rate constant \(k\) with temperature \(T\) and activation energy \(E_a\): \[ k = A \exp\left(-\frac{E_a}{RT}\right) \] Where: - \(A\) is the pre-exponential factor - \(R\) is the universal gas constant (8.314 J/mol·K) - \(E_a\) is the activation energy (J/mol)4. **Use the Two-Point Form of the Arrhenius Equation:** Relate the rate constants at two temperatures: \[ \ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R}\left(

Answered: Image /qna-images/answer/3601d88a-3c17-4a27-aa4b-9c5ee10f8d96.jpg

The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy E = 50.0 kJ/mol. If the rate constant reaction is 4.6 × 10² M-¹-1 "S at 83.0 °C, what will the rate constant be at 42.0 °C? Round your answer to 2 significant digits. -1 -1 k = MS S X

The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy E = 50.0 kJ/mol. If the rate constant reaction is 4.6 × 10² M-¹-1 "S at 83.0 °C, what will the rate constant be at 42.0 °C? Round your answer to 2 significant digits. -1 -1 k = MS S X

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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