How many million molecules is that? Now work out parts per million of SO2 that 3

Question

How many million molecules is that?

Now work out parts per million of SO2 that 30 micrograms represents in that air sample.

Often we need to convert micrograms of a contaminant in an air sample into ppm of that contaminant in air. The next few questions will walk you through those steps in converting micrograms of a contaminant into ppm. Since ppm means parts per million, and with air samples, that means molecules per million molecules, you will need to know how many molecules of contaminant you have and how many million molecules of air you have. The million molecules of air you have is dependent upon temperature,pressure, and volume of air. Let's calculate how many molecules of air are in a cubic meter of air sample at 1.0 atm and 25 C. How would you do that?

Explanation / Answer

applying Ideal gas equation

PV = nRT

Pressure = 1 atm

V= 1m^3 = 1000dm^3 = 1000 L

T= 298 K

R = 0.0821 L atm / mol K

n = PV / RT = 1 X 1000 / 0.0821 X 298 = 40.87 moles

the number of molecules in 1 mole = 6.023 X 10^23 molecules

Number of molecules in 40.87 moles = 2.46 X 10^25 molecules = 2.46 X 10^19 millions of molecules

b) the amount of SO2 in 1m3 of air = 30mg = 30 X 10^-3 grams

molecular weight of SO2 = 64 g / mole

moles of SO2 = 30 X 10^-3 / 64 = 4.69 X 10^-4 mole

ppm of SO2 = 30 mg of SO2/ per million of air molecule

                      = 30 / 2.46 X 10^19 millions of molecules

                       = 12.19 X 10^-19 ppm

Number of SO2 molecules = 6.023 X 10^23 X 4.69 X 10^-4 = 2.824 X 10^20 molecules

So SO2 molecules / 1m^3 = 2.824 X 10^20 molecules

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