A certain first-order reaction is 57% complete in 55 s. What are the values of the rate constant and the half-life for this process?a.\[ k = \] ______ \[ \text{s}^{-1} \]b.\[ t_{1/2} = \] ______ sExplanation: This problem involves determining the rate constant ($ k $) and the half-life ($ t_{1/2} $) for a first-order reaction. The completion rate and time are provided, and you would typically use formulas specific to first-order kinetics to solve for the unknowns. A first-order reaction has rate constants of $ 4.6 \times 10^{-2} \, \text{s}^{-1} $ and $ 8.9 \times 10^{-2} \, \text{s}^{-1} $ at 0°C and 20°C, respectively. What is the value of the activation energy?Activation energy = [____] kJ/mol

Answered: A certain first-order reaction is 57%…

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

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A certain first-order reaction is 57% complete in 55 s. What are the values of the rate constant and the half-life for this process?

a.
\[ k = \] ______ \[ \text{s}^{-1} \]

b.
\[ t_{1/2} = \] ______ s

Explanation: This problem involves determining the rate constant ($ k $) and the half-life ($ t_{1/2} $) for a first-order reaction. The completion rate and time are provided, and you would typically use formulas specific to first-order kinetics to solve for the unknowns.

A first-order reaction has rate constants of $ 4.6 \times 10^{-2} \, \text{s}^{-1} $ and $ 8.9 \times 10^{-2} \, \text{s}^{-1} $ at 0°C and 20°C, respectively. What is the value of the activation energy?

Activation energy = [____] kJ/mol

Expert Solution

Step 1: First-order reaction:

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The rate of the first-order reaction depends only on one reactant. According to the first-order kinetics the rate constant of the first-order reaction is given by:

$straight k space equals space 1 over straight t space ln space fraction numerator straight a over denominator straight a minus straight x end fraction$

Where k = rate constant =?

t = time = 55 s

a = initial concentration of the reactant = 100

a-x = remaining concentration of the reactant after t time = 100-57 = 43

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