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
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?
Identify the word pair which is different in pronunciation in British English and American English usage:
British English
American English
(A)
cheque
-
check
(B)
metre
-
meter
(C)
schedule
-
schedule
(D)
licence
-
license
American English equivalent for 'puncture' is _______
'Window shade' in American English is _______ in British English.
