Question

The breakdown of a certain pollutant X in sunlight is known to follow first-order kinetics. An atmospheric scientist studying the process fills a 20.0Lreaction flask with a sample of urban air and finds that the partial pressure of X in the flask decreases from 0.473atm to 0.376atm over 5.6hours.

Calculate the initial rate of decomposition of X, that is, the rate at which Xwas disappearing at the start of the experiment.


Round your answer to 2 significant digits.

Answer 1

0.019 atm / hr

Step-by-step explanation:

Initial Concentration (Pressure) [A]o = 0.473 atm

Final Concentration (Pressure) [A] = 0.376 atm

Time = 5.6 hours

The breakdown follows first order kinetics.

The integrated rate law for a first order reaction is given as;

ln[A] = ln[A]o - kt

ln(0.376) = ln(0.473) - k (5.6)

ln(0.376) - ln(0.473) = - 5.6 k

5.6 k = 0.23

k = 0.0411 hr⁻¹

The rate of decomposition is given as;

Rate = k [X]

Where [X] represents Concentration (Pressure) = 0.473 atm

Rate = 0.0411 * 0.473 = 0.019 atm / hr