The breakdown of a certain pollutant $ X $ in sunlight is known to follow first-order kinetics. An atmospheric scientist studying the process fills a 40.0 L reaction flask with a sample of urban air and finds that the partial pressure of $ X $ in the flask decreases from 0.66 atm to 0.14 atm over 13. hours.Calculate the initial rate of decomposition of $ X $, that is, the rate at which $ X $ was disappearing at the start of the experiment. Round your answer to 2 significant digits.The diagram on the lower left shows a unit of measurement, “atm/s,” suggesting the answer should be given in atmospheres per second. On the lower right, there is an input box with a check option for “x10,” likely indicating the option to express the answer in scientific notation. There are also buttons for submitting the answer or clearing the response.

Answered: The breakdown of a certain pollutant 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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The breakdown of a certain pollutant $ X $ in sunlight is known to follow first-order kinetics. An atmospheric scientist studying the process fills a 40.0 L reaction flask with a sample of urban air and finds that the partial pressure of $ X $ in the flask decreases from 0.66 atm to 0.14 atm over 13. hours.

Calculate the initial rate of decomposition of $ X $, that is, the rate at which $ X $ was disappearing at the start of the experiment. Round your answer to 2 significant digits.

The diagram on the lower left shows a unit of measurement, “atm/s,” suggesting the answer should be given in atmospheres per second. On the lower right, there is an input box with a check option for “x10,” likely indicating the option to express the answer in scientific notation. There are also buttons for submitting the answer or clearing the response.

Expert Solution

Step 1: Formula of first order reaction

The decomposition of the pollutant X follows the first-order kinetics.

The pressure of the pollutant X before decomposition is P₀ = 0.66 atm,

The pressure of the pollutant X after 13 hours of decomposition is P_t = 0.14 atm,

The time in seconds is t = 13 hours = $open parentheses 13 cross times 60 cross times 60 close parentheses space s$ = 46800 s.

Formula: The formula of the rate of a first-order reaction at time t sec is Rate = KP_t, where K is the rate constant, and Pt is the pressure of the gas at time t s.

The rate constant for a first-order reaction is $K space equals space 1 over t ln P subscript 0 over P subscript t$ .

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