The secondary NAAQS for SO2 is 0.5 ppm (for a 3-hour average). Calculate the equivalent concentration in ug/m3 at standard temperature and pressure (STP, T = 25 C, P = 1 atm)

To calculate the equivalent concentration of sulfur dioxide (SO₂) in micrograms per cubic meter (µg/m³) from a given concentration in parts per million (ppm), we use the Ideal Gas Law. The relationship between ppm and µg/m³ is as follows:

\[
\text{Concentration in } \mu g/m^3 = \text{Concentration in ppm} \times \frac{\text{Molar mass of SO}_2 \times P}{R \times T}
\]

Where:
- **Concentration in ppm** is given as 0.5 ppm.
- **Molar mass of SO₂** = 64.066 g/mol.
- **P** is the pressure at standard temperature and pressure (STP), which is 1 atm.
- **R** is the ideal gas constant = 0.0821 L·atm/(mol·K).
- **T** is the temperature in Kelvin. Since STP is defined at 25°C, this converts to \( T = 25 + 273.15 = 298.15 \) K.

### Step-by-step calculation:

1. Convert the temperature to Kelvin:  
   \( T = 25 + 273.15 = 298.15 \) K.

2. Use the formula to calculate the concentration:

\[
\text{Concentration in } \mu g/m^3 = 0.5 \times \frac{64.066 \times 1}{0.0821 \times 298.15}
\]

Let's calculate that.The equivalent concentration of sulfur dioxide (SO₂) at 0.5 ppm is approximately **1.31 µg/m³** at standard temperature and pressure (STP: 25°C, 1 atm).

Would you like further clarification or details on any part of this calculation?

Here are 5 related questions for deeper exploration:
1. How does temperature affect the concentration in µg/m³ for gases?
2. What is the significance of secondary National Ambient Air Quality Standards (NAAQS)?
3. How is the molar mass of a gas determined?
4. Can you convert µg/m³ to ppm for other gases?
5. What would the SO₂ concentration in µg/m³ be at higher altitudes with lower atmospheric pressure?

**Tip:** The Ideal Gas Law provides a direct relationship between gas concentration in ppm and µg/m³, making it easier to interconvert the two under different conditions.

The secondary NAAQS for SO2 is 0.5 ppm (for a 3-hour average). Calculate the equivalent concentration in ug/m3 at standard temperature and pressure (STP, T = 25 C, P = 1 atm).

Learn how to calculate the equivalent concentration of SO₂ in µg/m³ from a given ppm value using the Ideal Gas Law. This guide covers the key formula and step-by-step calculations at standard temperature and pressure (25°C, 1 atm). Suitable for Grades 10-12.

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