### Calculate the Rate Constant for a ReactionTo determine the rate constant \( k \) for a reaction at a given temperature, we can use the Arrhenius equation. This equation relates the rate constant to the temperature, activation energy, and frequency factor of the reaction. **Problem Statement:**Calculate the rate constant, \( k \), for a reaction at 50.0 °C that has an activation energy of 87.9 kJ/mol and a frequency factor of \( 2.76 \times 10^{11} \) s\(^{-1}\).**Given Data:**- Temperature, \( T \) = 50.0 °C- Activation Energy, \( E_a \) = 87.9 kJ/mol- Frequency Factor, \( A \) = \( 2.76 \times 10^{11} \) s\(^{-1}\)### Step-by-Step Calculation1. **Convert Temperature to Kelvin:** \[ T = 50.0 + 273.15 = 323.15 \, \text{K} \]2. **Convert Activation Energy to Joules (J):** Since \( 1 \, \text{kJ} = 1000 \, \text{J} \), \[ E_a = 87.9 \times 1000 = 87900 \, \text{J/mol} \]3. **Use the Arrhenius Equation:** \[ k = A e^{-\frac{E_a}{RT}} \] where: - \( R \) is the gas constant, \( 8.314 \, \text{J/mol·K} \) - \( A \) is the frequency factor - \( E_a \) is the activation energy - \( T \) is the temperature in Kelvin Plugging in the values: \[ k = 2.76 \times 10^{11} \, \text{s}^{-1} \cdot \exp\left(-\frac{87900}{8.314 \times 323.15}\right) \]4. **Calculate the Exponential Term:** \[ k = 2.76 \times 10^{11} \, \text{s}^{-1} \cdot \exp\

Given data: The activation energy is E=87.9 kJ/mol. The temperature is T=50°C. The frequency factor…

Answered: Calculate the rate constant, k, for a…

Calculate the rate constant, k, for a reaction at 50.0 °C that has an activation energy of 87.9 kJ/mol and a frequency factor of 2.76 x 1011 s-. k =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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