1.Various pesticides and solvents often find their way into open dumps. Based on

Question

1.Various pesticides and solvents often find their way into open dumps. Based on airborne concentrations of a certain solvent vapor near a dump, you have calculated that the concentrations in Jonesville, an hour’s travel time downwind, should be 2 ng/m3. Instead, you measure only 0.2 ng/m3. What would be the required pseudo-first-order rate constant if this difference were due to attack by some atmospheric species whose concentration can be assumed to be approximately constant at 3 * 105 molecules per cubic centimeter?

Explanation / Answer

A pseudo first order reaction is a second order reaction with the concentration of one reactant being very high so that it remains approximately constant throughout the reaction.

Let the reaction be represented by-

S(solvent) +atmospheric reactant(A)--->products

If the reaction is pseudo first order as [A]=constant=3 * 105 molecules/cm3

So, the rate law is Rate=k[S][A]=k''[S] k''=k[A]=constant

integrated rate equation,

[A]=[A]o exp(-k"t)=[A]o exp(-k[A]t)

or,

[A]/[A]o=exp(-k[A]t)

[A]=0.2 ng/m3 after time=t=1 hr

[A]o=2ng/m3

0.2/2=exp(-k*3 * 105 molecules/cm3)*1hr

ln 0.1=-k*3 * 105 molecules/cm3)*1hr

or,-2.302=-k*3 * 105 molecules/cm3)*1hr

k=2.302/3*10^5=7.673*10^-6 cm3/molecules hr

k=7.673*10^-6 cm3/molecules hr

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