### Determining the Rate Constant Using the Arrhenius Equation#### Problem Statement:The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy \( E_a = 31.0 \, \text{kJ/mol} \). If the rate constant of this reaction is \( 8.5 \times 10^5 \, M^{-1} \cdot s^{-1} \) at \( 254.0 \, ^\circ\text{C} \), what will the rate constant be at \( 336.0 \, ^\circ\text{C} \)?Round your answer to 2 significant digits.#### Solution Explanation:The Arrhenius equation is given by:\[ k = A e^{\left(-\frac{E_a}{RT}\right)} \]where:- \( k \) is the rate constant,- \( A \) is the pre-exponential factor,- \( E_a \) is the activation energy,- \( R \) is the universal gas constant (\( 8.314 \, \text{J/mol} \cdot \text{K} \)),- \( T \) is the temperature in Kelvin (K).Given data:- \( E_a = 31.0 \, \text{kJ/mol} = 31.0 \times 10^3 \, \text{J/mol} \) (conversion from kJ to J)- Initial Rate Constant \( k_1 = 8.5 \times 10^5 \, M^{-1} \cdot s^{-1} \) at \( T_1 = 254.0 \, ^\circ\text{C} = 527.15 \, \text{K} \) (conversion from Celsius to Kelvin)- Final temperature \( T_2 = 336.0 \, ^\circ\text{C} = 609.15 \, \text{K} \)The Arrhenius equation can be used in a ratio form to find the new rate constant \( k_2 \) at temperature \( T_2 \):\[ \ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \

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The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy E =31.0 kJ/mol. If the rate constant of this reaction is 8.5 × 10° M¯'s -1 at 254.0 °C, what will the rate constant be at 336.0 °C? Round your answer to 2 significant digits.

The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy E =31.0 kJ/mol. If the rate constant of this reaction is 8.5 × 10° M¯'s -1 at 254.0 °C, what will the rate constant be at 336.0 °C? Round your answer to 2 significant digits.

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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