CO Concentration Conversion: ppm to mg/m³

This section provides a step-by-step method to convert Carbon Monoxide (CO) concentration from parts per million (ppm) to milligrams per cubic meter ($\text{mg/m}^3$) under specific conditions.

Key Data for Calculation

• Given CO concentration: $13.0 \text{ ppm}$
• Standard Temperature: $T = 298 \text{ K}$
• Standard Pressure: $P = 1 \text{ atm}$
• Molar Mass of CO ($M_{CO}$): Approximately $28.01 \text{ g/mol}$

Conversion Formula Application

To convert ppm (volume/volume) to $\text{mg/m}^3$ for a gas at a given temperature ($T$) and pressure ($P$), we use the ideal gas law principles. The molar volume ($V_m$) of an ideal gas at $298 \text{ K}$ and $1 \text{ atm}$ is approximately $24.45 \text{ L/mol}$ or $0.02445 \text{ m}^3/\text{mol}$.

The conversion formula is:

$ \text{Concentration (mg/m}^3\text{)} = \text{Concentration (ppm)} \times \frac{M_{CO}}{V_m} $

Using $V_m \approx 24.45 \text{ L/mol}$ for $298 \text{ K}$ and $1 \text{ atm}$:

Calculating CO in mg/m³

Substitute the known values into the formula:

$ \text{CO (mg/m}^3\text{)} = 13.0 \times \frac{28.01 \text{ g/mol}}{24.45 \text{ L/mol}} $

Perform the calculation:

$ \text{CO (mg/m}^3\text{)} \approx 13.0 \times 1.1456 $

$ \text{CO (mg/m}^3\text{)} \approx 14.89 $

Final Result Interpretation

The calculated concentration of CO is approximately $14.89 \text{ mg/m}^3$. Comparing this value with the given options, it is closest to $15 \text{ mg/m}^3$.