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 correct answer is (a) \(10^{-2} \mathrm{~mL}\).

Step 1: Understand PPM

PPM stands for "parts per million," and it is a way to measure the concentration of one substance in a larger mixture. 10 PPM means there are 10 parts of \({\mathrm{SO}}_{2}\) in one million parts of air by volume.

Step 2: Calculate \\( {\mathrm{SO}}_{2} \\) Volume in 1 Liter of Air

Since 1 liter contains 1 million milliliters, 10 PPM of \({\mathrm{SO}}_{2}\) corresponds to \(\frac{10}{1,000,000} \, \text{liters} = 10^{-5} \, \text{liters}\). Convert liters to milliliters (1 liter = 1000 milliliters): \(10^{-5} \, \text{liters} \times 1000 \, (\frac{\text{milliliters}}{\text{liter}}) = 10^{-2} \, \text{milliliters}\).

Step 3: Choose the Correct Answer

Since the volume of \({\mathrm{SO}}_{2}\) per liter of air is calculated to be \(10^{-2} \, \text{mL}\), the correct answer is option (a) \(10^{-2} \, \text{mL}\).

Key Concepts

Understanding Parts per Million (PPM)

Parts per million, abbreviated as PPM, is a unit of measurement used to express the concentration of a solute in a solution. It is very similar to percentages but on a much smaller scale. Imagine that you have a large container with a million little parts in it; PPM tells you how many parts of the solute are in those million parts of the solution. For example, 10 PPM means that out of a million parts of air, 10 parts are sulfur dioxide (SO2). PPM is commonly used in environmental science to measure the concentration of pollutants, like gases in the air or contaminants in water. Because pollutants often occur in very low concentrations, PPM is a useful measure. It's helpful because it can express these small units in a way that's easy to understand.

Volume Conversion Simplified

Volume conversion is a handy tool when working with various units. Sometimes, problems will require us to change from one volume metric to another. To convert from liters to milliliters, remember:

• 1 liter (L) equals 1,000 milliliters (mL)

This conversion is essential in calculations involving PPM, especially since PPM often describes concentrations in terms of smaller units like milliliters. In our example problem, we had to convert from liters to milliliters to find the volume of SO2 in air correctly. Understanding this conversion is important, as it frequently pops up in chemistry and environmental science domains.

Measuring the Concentration of SO2

The concentration of sulfur dioxide, or SO2, in a given volume of air is an essential environment metric. It indicates how much of the gas is present, which is crucial for air quality assessments. To calculate the concentration, we take the PPM value and convert it into a practical volume measure. In terms of volume, this often means translating the PPM to how many milliliters it occupies per liter of air, just like in the exercise given. Here's how we can break it down: - If the air contains SO2 at a concentration of 10 PPM, that means there are 10 milliliters of SO2 for every million milliliters (essentially, 1 liter) of air. - Performing the calculation gives us 10 parts per 1,000,000 parts of air, simplifying our result to the exact volume representation we need. These measurements help determine if pollutant levels are within safe limits or if they require regulatory action or intervention.