A. 1 ppm of O₃
B. 1 ppm of SO₂
C. 4 ppm of NH₃
D. 1 ppm of CO
E. 1ppm of CO₂
Choose the correct answer from the options given below:
Converting Gas Concentrations: ppm to µg/m³
This question requires us to convert gas concentrations from parts per million (ppm) to micrograms per cubic meter (µg/m³) at 25°C, assuming ideal gas behavior. We then need to arrange these converted concentrations in increasing order.
Understanding the ppm to µg/m³ Conversion Formula
The conversion from ppm (volume) to µg/m³ (mass/volume) for gases relies on the ideal gas law ($PV = nRT$). At standard ambient temperature and pressure (25°C and 1 atm), the molar volume of an ideal gas is approximately 24.465 L/mol or 0.024465 m³/mol. This leads to the conversion formula:
$$ \text{Concentration } (\mu g/m^3) = \text{ppm} \times \text{MW} (\text{g/mol}) \times \left( \frac{1 \text{ mol}}{0.024465 \text{ m}^3} \right) \times \frac{10^6 \mu g}{1 \text{ g}} $$Simplifying this, we get a conversion factor:
$$ \text{Concentration } (\mu g/m^3) \approx \text{ppm} \times \text{MW} (\text{g/mol}) \times 40.875 $$This means that 1 ppm of a gas is equivalent to approximately 40.875 times its molecular weight in µg/m³ at 25°C and 1 atm.
Calculating Molecular Weights and Concentrations
First, let's determine the molecular weights (MW) for each gas involved:
- O₃ (Ozone): MW = $16.00 \times 3 = 48.00$ g/mol
- SO₂ (Sulfur Dioxide): MW = $32.07 + (16.00 \times 2) = 64.07$ g/mol
- NH₃ (Ammonia): MW = $14.01 + (1.01 \times 3) = 17.04$ g/mol
- CO (Carbon Monoxide): MW = $12.01 + 16.00 = 28.01$ g/mol
- CO₂ (Carbon Dioxide): MW = $12.01 + (16.00 \times 2) = 44.01$ g/mol
Next, we apply the conversion formula to find the concentration of each gas in µg/m³:
| Gas (Label) | Concentration (ppm) | Molecular Weight (g/mol) | Calculated Concentration (µg/m³) |
|---|---|---|---|
| O₃ (A) | 1 | 48.00 | $1 \times 48.00 \times 40.875 \approx 1962.0$ |
| SO₂ (B) | 1 | 64.07 | $1 \times 64.07 \times 40.875 \approx 2616.0$ |
| NH₃ (C) | 4 | 17.04 | $4 \times 17.04 \times 40.875 \approx 2779.5$ |
| CO (D) | 1 | 28.01 | $1 \times 28.01 \times 40.875 \approx 1144.5$ |
| CO₂ (E) | 1 | 44.01 | $1 \times 44.01 \times 40.875 \approx 1798.5$ |
Ordering Concentrations in Increasing Sequence
Now, we list the calculated concentrations in ascending order:
- CO (D): 1144.5 µg/m³
- CO₂ (E): 1798.5 µg/m³
- O₃ (A): 1962.0 µg/m³
- SO₂ (B): 2616.0 µg/m³
- NH₃ (C): 2779.5 µg/m³
Therefore, the correct increasing order of concentrations is D, E, A, B, C.
Important Questions from Conversion
Choose the American English word for 'Pavement'
In American English the word 'POST' means
Match the following:
(a) Autumn 1. Faucet (b) Nappy 2. Fall (c) Tap 3. Diaper (d) Pavement 4. Side walk Match the following :
(a) Petrol 1. Elevator (b) Lorry 2. Apartment (c) Flat 3. Gasoline (d) Lift 4. Truck In the idiom 'a storm in a teacup', which of the following is used as a replacement for the word 'storm' in American English?
