Question

A. On a day with a temperature of 15 ∘C and a pressure of 785.0 torr , how many grams of peroxyacyl nitrates are found in the air above Los Angeles (1500. km3) if the concentration is 30.0 ppb by moles? The molar mass of the major peroxyacyl nitrate, peroxyacetyl nitrate, is 118.03 g/mol. Express your answer to three significant figures and include the appropriate units.

B.

Peroxyacyl nitrates contain two relatively weak bonds that can be broken by low-energy photons. The weakest is the N−O bond in the nitrate functional group of the molecule with a standard bond-dissociation energy of 201 kJ/mol. What is the longest wavelength of a photon, in nanometers, that has enough energy to cause the photodissociation of the weakest bond. Assume all energy of the photon is efficiently used for the photodissociation.

Express your answer to three significant figures and include the appropriate units.

Answer 1

A. PV = nRT
n = PV / RT = (787.0 torr) × (1.5 × 10^15 L) / ((62.36367 L Torr/K mol) ×
(15 + 273 K)) = 6.573 × 10^13 mol total

(6.573 × 10^13 mol) × (30.0 / 10^9) = 1.972 × 10^6 mol peroxyacetyl nitrate

(1.972 × 10^6 mol) × (118.03 g/mol) = 2.33 × 10^8 g peroxyacetyl nitrate


("15 C" is awfully cool for a sunny day in L.A.)

B. E = hc/λ

where E = 201 kj/mole
for 1 mole or 6.022 X 10^23 molecules ,E = 201 X 10^3 j
so for 1 molecule it will be 201 X 10^3 / 6.022 X 10^23 = 3.338 X 10^-19 J

h = 6.626 X 10^-34 J-s
c = velocity of light = 3 X 10^8 m/s
λ = ?

putting the values....
3.338 X 10^-19 = 6.626 X 10^-34 X 3 X 10^8 / λ

3.338 X 10^-19 = 1.988 X 10^-25 / λ

λ = 1.988 X 10^-25 / 3.338 X 10^-19 = 5.956 X 10^-7 m or 595.6 X 10^-9 m or 595.6 nm
hope this is correct.