證明 ζi (ppb) * ρa (kg / m^3) * (Mi / Ma) = mi (μg / m+3)

1.證明 ζi (ppb) * ρa (kg / m^3) * (Mi / Ma) = mi (μg / m^3)

ζi(ppb)：污染物i混合比以ppb表示
ρa(kg/m^3)：空氣密度，以kg/m^3表示，20℃，1 atm時，ρa0 = 1.2 kg/m^3
ρa(kg/m^3)：空氣密度，任何溫度T(K)，壓力(atm)下，ρa = ρa0 * (293/T) * (P/1)
ρa(kg/m^3)：空氣密度，25℃，1 atm時，ρa = 1.18 kg/m^3
Mi：污染物i的分子量，g/mole
Ma：空氣分子量，28.97 g/mole
mi：污染物i的質量濃度，μg/m^3
Ci ：污染物i莫耳濃度，the molar concentration

解答：
課本公式(A) ζi = Ci / Ctotal
課本公式(B) Ctotal = N / V = P / RT
課本公式(C) ζi = Ci / (P / RT) = (Pi / RT) / (P/RT) = Pi / P

1. P = Ctotal * RT =Ca * RT

2. P = ﹝Ca (mole/m^+3) * Ma (g/mole) ﹞ * ﹝ RT / Ma (g/mole) ﹞
= ρa (g/m^3) * RT / Ma (g/mole) = ρa (kg/m^3 * 10^-3) * RT / Ma (g/mole)

3. Pi = ﹝mi(g/m^3) * RT ﹞ / Mi(g/mole)
= ﹝ mi(μg/m^3) * 10^6 ﹞ * RT / Mi (g/mole)

4. ζi (ppb) = Pi / P * 10^9

4. ζi (ppb) =
﹝mi(μg/m^3) * 10^6 * RT / Mi (g/mole) ﹞ / ﹝ρa (kg/m^3*10^-3) * RT / Ma (g/mole) ﹞

4. ζi (ppb) = ﹝ mi(μg/m^3) / Mi (g/mole) ﹞ / ﹝Ma (g/mole) /ρa (kg/m^3) ﹞ * 10^9

5. ζi (ppb) *ρa (kg/m^3) * ﹝Mi (g/mole) / Ma (g/mole) ﹞ = mi(μg/m&3)