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

Explanation:

Change in the concentration of reactant that is consumed in per unit time is known as rate of reaction.

The given chemical reaction will be written as follows.

            $X \overset{sunlight}{\rightarrow} Pdt$

Hence, rate law for the given reaction will be as follows.

                   Rate = k$P_{x}$

where,           k = rate constant

                $P_{x}$ = initial pressure of the pollutant X

It is given that, $P_{i}$ =  initial partial pressure of X = 0.473 atm

                        $P_{f}$ =  final partial pressure of X = 0.376 atm

                         Time = 5.6 hours

Hence, formula for rate constant of first order reaction is as follows.

                k = $\frac{1}{t} ln(\frac{P_{i}}{P_{f}}$

                   = $\frac{1}{5.6} ln(\frac{0.473}{0.376})$

                   = 0.041 per hour

Therefore, rate of decomposition will be calculated as follows.

              Rate = $\frac{dP}{dt}$ = k$P_{i}$

                       = $0.041 hr^{-1} \times 0.473 atm$

                       = $0.019 atm hr^{-1}$

Thus, we can conclude that initial rate of decomposition of X is $0.019 atm hr^{-1}$.