**First-Order Reaction Kinetics**In this exercise, we are given a first-order chemical reaction where reactant A is converted into products. The rate constant (k) for this first-order reaction is 0.0700 s⁻¹ at 400 °C.\[ A \longrightarrow \text{products} \]We are asked to determine the time (t) after which only 16.2% of the reactant remains.To find the time t, we can use the integrated rate law for a first-order reaction, which is given by:\[ [A]_t = [A]_0 e^{-kt} \]Where:- \([A]_t\) is the concentration of reactant A at time t- \([A]_0\) is the initial concentration of reactant A- \(k\) is the first-order rate constant- \(t\) is the timeGiven that we know what percentage of the reactant remains, we can rearrange the equation as:\[ \frac{[A]_t}{[A]_0} = e^{-kt} \]By substituting \(\frac{[A]_t}{[A]_0} = 0.162\):\[ 0.162 = e^{-kt} \]Taking the natural logarithm (ln) of both sides:\[ \ln(0.162) = -kt \]We then solve for t:\[ t = \frac{\ln(0.162)}{-k} \]Finally, by plugging in the given rate constant \( k = 0.0700 \, \text{s}^{-1} \):\[ t = \frac{\ln(0.162)}{-0.0700\, \text{s}^{-1}} \]\[t = \boxed{\ \ \ \ \ \ \ }\]This calculated value represents the time in seconds at which 16.2% of the original amount of reactant A remains.

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Answered: The rate constant for this first-order…

The rate constant for this first-order reaction is 0.0700 s- at 400 °C. A products > After how many seconds will 16.2% of the reactant remain? t =

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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