Conversion of SO₂ Concentration from mg/m³ to PPM

Conversion of SO₂ Concentration from mg/m³ to PPM at 25°C

Question

Convert 160 mg/m³ of SO₂ concentration into PPM at 25°C.

Given Data

Parameter	Value
SO₂ Concentration	160 mg/m³
Temperature	25°C
Molecular Weight of SO₂	64 g/mol
Molar Volume at STP	22.4 L/mol

Step 1: Volume of Gas at 25°C

At STP (0°C and 1 atm), one mole of gas occupies:

V₁ = 22.4 litres/mol

Using Charles' Law:

V₁/T₁ = V₂/T₂

Where:

T₁ = 273 K
T₂ = 273 + 25 = 298 K

Therefore:

V₂ = 22.4 × (298 / 273)

V₂ = 24.45 litres/mol

Step 2: General Conversion Formula

For converting concentration from mg/m³ to PPM:

PPM = (mg/m³ × Molar Volume at Temperature) / Molecular Weight

Step 3: Substitute Values

PPM = (160 × 24.45) / 64

PPM = 3912 / 64

PPM = 61.13

160 mg/m³ of SO₂ = 61.13 PPM

Shortcut Formula for Examinations

At 25°C and 1 atmosphere pressure:

PPM = (mg/m³ × 24.45) / Molecular Weight

For SO₂:

PPM = (mg/m³ × 24.45) / 64

Exam Tip: Remember the value 24.45 for gases at 25°C. It is frequently used in Environmental Engineering and Air Pollution numerical problems.

Final Answer

SO₂ Concentration = 61.13 PPM

Author: Mohan Dangi

Prepared for Environmental Engineering, Air Pollution Control, GATE, SSC JE, State Engineering Services and Civil Engineering Students.