Problem 23 - A Complete Resource Book in Chemistry for JEE Main

Question

The pollution of \(\mathrm{SO}_{2}\) in air is \(10 \mathrm{ppm}\) by volume. The volume of \(\mathrm{SO}_{2}\) per litre of air is (a) \(10^{-2} \mathrm{~mL}\) (b) \(10^{-3} \mathrm{~mL}\) (c) \(10^{-4} \mathrm{~mL}\) (d) \(10^{-6} \mathrm{~mL}\)

Step-by-Step Solution

Answer

The volume of SO2 per liter of air is 0.01 mL or 10^{-2} mL.

Step 1: Understanding PPM

PPM stands for parts per million. In this problem, it means that there are 10 parts of \( ext{SO}_2\) for every 1 million parts of air. Therefore, out of 1,000,000 mL of air, 10 mL is \( ext{SO}_2\).

Step 2: Set Up the Proportion

If 10 parts per million of air is \( ext{SO}_2\), then we can set up a proportion to find out how much \( ext{SO}_2\) is present per liter (1000 mL) of air. The proportion is: \[ \frac{10 \, ext{mL} \( ext{SO}_2\)}{1000000 \, ext{mL air}} = \frac{x \, ext{mL} \( ext{SO}_2\)}{1000 \, ext{mL air}} \]

Step 3: Solving the Proportion

Cross-multiply to find the value of \(x\) which represents the volume of \( ext{SO}_2\) in one liter of air:\[ 10 imes 1000 = 1000000 imes x \]\[ 10000 = 1000000x \]Solve for \(x\) by dividing both sides by 1000000:\[ x = \frac{10000}{1000000} = 0.01 \, ext{mL} \]

Step 4: Final Answer and Conclusion

The final calculation shows that in one liter of air, the volume of \( ext{SO}_2\) is 0.01 mL. This is equivalent to \\[ 10^{-2} \, ext{mL} \]

Key Concepts

Understanding Parts Per Million (PPM)

Parts per million (PPM) is a way to describe the concentration of something in air, water, or another medium. When we say that something is present at 10 PPM, it means there are 10 units of that substance within one million units of the total mixture.
For this exercise, the PPM describes sulfur dioxide (SO₂) in the air. With 10 PPM of SO₂, it means if you had a volume of 1,000,000 milliliters (mL) of air, 10 mL of that would be sulfur dioxide.
This method of measurement is crucial because it allows for precise communication of very small quantities, which is common in pollution measurements. PPM is particularly useful in environmental science and chemistry, where even tiny amounts of a substance can have significant effects.

Sulfur Dioxide (SO₂) in the Air

Sulfur dioxide (SO₂) is a chemical compound consisting of one sulfur atom and two oxygen atoms. It is a significant air pollutant, primarily produced by burning fossil fuels like coal and oil. It can also come from volcanic eruptions and various industrial processes.
When released into the atmosphere, SO₂ can contribute to acid rain, which harms ecosystems, buildings, and even human health. Breathing in sulfur dioxide can irritate the respiratory system and worsen conditions like asthma. This makes monitoring its levels crucial for environmental and public health.
In this exercise, SO₂'s concentration is given in terms of parts per million, allowing us to calculate how much SO₂ is present in a given volume of air. Because SO₂ is often found in small concentrations, using PPM is an effective way to measure and report its levels in the air.

Performing Volume Calculations for Concentrations

Calculating volumes in relation to concentration is an essential task in chemistry, especially when dealing with pollutants like SO₂ in the air. To determine how much of a substance is present in a specific volume, we set up a proportion based on known quantities.
In this example, we're given that the concentration of SO₂ is 10 PPM. That translates to 10 mL of SO₂ per 1,000,000 mL of air. Our task is to find out how much SO₂ exists in just 1 liter (or 1,000 mL) of air.
Here's how you set up the calculation: the proportion \( \frac{10 \, \text{mL of SO}_2}{1000000 \, \text{mL of air}} = \frac{x \, \text{mL of SO}_2}{1000 \, \text{mL of air}} \) allows us to solve for \( x \), the unknown volume of SO₂ in 1 liter of air. Solving this gives us 0.01 mL or \( 10^{-2} \) mL.
This approach shows how small concentrations can be calculated over different volumes, which helps in assessing pollution levels accurately.