Convert the concentration of SO2 from 80 μg/m3 to units of parts per million. The gas has a temperature of 25˚C and a pressure of 101.325 kPa. (Problem 2-56)

0.0306 ppm

Explanation:

Parts per million is defined as the mass of a solute in milligram per 1 liter of solvent. It is also a unit of concentration of a solution.

From the definition,

1 mg/l = 1 ppm

Converting μg/m3 to mg/l,

1 μg = 10^-6 g

Therfore, 1 mg = 10^3 μg

= 80 μg/m3 * 1 mg/10^3 μg

= 0.08 mg/m3

Molecular weight of SO2 = 32 + (16*2)

= 64 g/mol

Concentration (in ppm) = (concentration (mg/m3) * 24.45) / molecular weight of SO2

24.45 = volume (liters) of a mole (gram molecular weight) of a gas when the pressure is at 1 atmosphere (760 torr or 760 mm Hg) and at 25°C. where R is the ideal gas constant; T is the temperature in kelvins (273.16 + T°C); and P is the pressure in mm Hg.

= (0.08 * 24.45) / 64

= 0.0306 ppm

0.031 parts per million

Explanation:

80 micrograms/m^3 = 80 micrograms/m^3 * 1m^3/1000L = 0.08 micrograms/L

Concentration in parts per million = concentration in micrograms/L * molar volume/MW

Concentration in micrograms/L = 0.08

Molar volume at 25°C and 101.325kPa (1 atm) is 24.45L

MW of SO2 = 64g/mole

Concentration in ppm = 0.08*24.45/64 = 0.031 ppm