APCH 211 TUT 7 (REVIEW TUT) 2011 Converting Gas Units Central to conversion between different gas concentrations is PV = nRT 2ppm of a gas means: 
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
there are 2 gas molecules for every 1 million molecules of air there are 2 moles of gas for every 1 million moles of gas 2 x 10‐6 atm partial pressure of gas for 1 atm total air pressure Example: Assuming a temperature of 25 °C, and a pressure of 1 atm; Convert 2 ppm to molecules/cm3 Since molecules of air = 1000, 000, can convert this to a volume using PV = nRT Using Avogadro’s number can determine moles of air 1
6.023
1000, 000
1.66
10
10
Rearrange the ideal gas equation to solve for the volume 1.66
10
0.0821
1.0
298
4.06
10
Convert from L to cm3: 4.06 x10‐14 cm3 Thus there are 2 molecules in 4.06 x10‐14 cm3 Or 4.92 x1013 molecules/cm3 (divide by 4.06 x10‐14 cm3) Follow up  Convert 2 ppm to Molarity Since 2 ppm means there are 2 molecules of gas for every 1000, 000 molecules of air (volume calculated above), and simply convert 2 molecules to moles using Avogadro ’s number 2
1
6.023
Thus the concentration = 8.2 x10‐8 M (
3.32
10
.
10
) .
Another common unit used with gases is g/m3 Example: Convert 320 g/m3 SO2 to ppb at 1 atm & 27 C 
Convert your grams to moles 320
10
1
64.1
4.99
10
APCH 211 TUT 7 (REVIEW TUT) 2011 
Convert to molecules SO2 6.023 10
3.01 10
1
Then find molecules of air (recall ppm, ppb, or any parts per, is dimensionless, so need same units on top & bottom) Using PV = nRT, moles of air = 40.7 mol Then molecules of air = 2.45 x1025 molecules (use Avogadro’s number) Note a billion is 109 So 2.45 x1016 molecule billion molecules of air Last ppb step 4.99
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10
3.01 10
2.45 10
123
QUESTION Convert a concentration of 32 ppb for any pollutant to its value on a) ppm scale, b) molecules/cm3 scale c) molarity scale Converting Water Units Unlike gases, the part per scale with water based solution refers to mass of solute to the mass of solution. Thus when looking at water, 1000mL or 1.0 L of natural water sample is very close to 1.0 kg, so if you have mg of solute per L, it is ~ to mg per kg, which works out to ppm. In general for water based solutions 
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
mg/L = ppm g/L = ppb ng/L = ppt Problem: Convert: a) 0.04 g/L to ppm & ppb b) 3 ppb to g/L APCH 211 TUT 7 (REVIEW TUT) 2011 QUESTION •
Convert a concentration of 32 ppb for any pollutant to its value on a) ppm scale (Answer = 0.032 ppm) b) molecules/cm3 scale (Answer = 7.9 x1011 molecules/cm3) c) molarity scale (Answer 1.3 x10‐9 M) Problem: Convert: a) 0.04 mg/L to ppm & ppb 4.0 x 10‐5 ppm; 0.040 ppb a) 3 ppb to mg/L 3.0 mg/L