One of the highest concentrations of peroxyacyl nitrates has been found in the Los Angeles (LA) basin at 30 ppb , reaching its peak at mid-afternoon. Most of the pollution in the LA basin is created in an area of only 3000 `km^2` and the pollution depth below the inversion layer is normally about 500 m . This concentration was therefore found in 1500 `km^3` of air above Los Angeles.
a.) On a day with a temperature of 15 `^o` Celsius and a pressure of 775.0 torr , how many grams of peroxyacyl nitrates are found in the air above Los Angeles (1500 `km^3` ` ` ) if the concentration is 30.0 ppb by moles? The molar mass of the major peroxyacyl nitrate, peroxyacetyl nitrate, is 118.03 `(g)/(mol)` .
In order to solve the amount of peroxyacetyl nitrate (PAN) above Los Angeles, the knowledge of conversion of concentration is necessary. We know that ppb = parts per billion which means that one part of a substance is rational to 10^9 of the whole. Since it is represented as 30ppb per moles, it is also equivalent to 30 nanomoles of PAN per mole of air.
Next, we have to get the total number of moles in the volume of 15km^3. We can solve that by treating the air sample ideal thus using the ideal gas law.
`PV = n_(air)RT`
`n_(air) = (PV)/(RT)`
P = 775/760 = 1.0197 atm
V = 15km^3 * (1L)/(1.0x10^-12 km^3) =1.5x10^13 L
r = 0.08206 atm-L/mol-K
T = 15 + 273.15 = 288.15 K
`n_(air) = (1.0197 * 1.5x10^13)/(0.08206*288.15)`
`n_(air) ` = 6.46888x10^11 moles air
Let us go back to the 30 ppb:
`30 (nmol of PAN)/(mol es air) * 6.46888x10^11 mol es air`
= 1.94066x10^13 nmol PAN
Then we convert nanomoles to moles…
`1.94066x10^13 nmol PAN * (1x10^-9 mol)/(1 nmol)`
= 19,406.6 moles PAN
Finally, convert the number of moles to mass of PAN using the molar mass 118.03 g/mol**
`19,406.6 mol es PAN * (118.03 grams PAN)/(1 mol e PAN)`
= 2.291 x10^6 grams PAN
**the true molecular weight of PAN is 121.05