Problem 77 - Chemistry The Central Science In Si Units

Question

As of the writing of this text, EPA standards limit atmospheric ozone levels in urban environments to 84 ppb. How many moles of ozone would there be in the air above Los Angeles County (area about 10,000 square kilometers; consider a height of \(100 \mathrm{~m}\) above the ground) if ozone was at this concentration?

Step-by-Step Solution

Answer

3,746,880 moles of ozone.

Step 1: Determine Volume of Air

First, calculate the volume of air above Los Angeles County by using the given area and height. The area is given as 10,000 square kilometers, which is equivalent to 10,000,000,000 square meters (since 1 km² = 1,000,000 m²). The height is given as 100 meters. Therefore, the volume of air is calculated as:\[ V = ext{Area} \times ext{Height} = 10,000,000,000 \, \text{m}^2 \times 100 \, \text{m} = 1,000,000,000,000 \, \text{m}^3 \]

Step 2: Convert Ozone Concentration from ppb to moles/m³

At a concentration of 84 parts per billion (ppb), there are 84 ozone molecules per billion molecules of air. To convert this to moles, use the molar volume of an ideal gas at standard temperature and pressure (STP) which is approximately 22.4 liters per mole. Note that 1 m³ = 1,000 liters, so 1 m³ of air holds about 44.64 moles of air (since 22.4 liters per mole means there are 1000/22.4 moles per m³). Since ozone concentration is 84 ppb, the moles of ozone per m³:\[ \text{Moles of O}_3 / \text{m}^3 = \frac{84}{1,000,000,000} \times 44.64 \, \text{moles/m}^3 = 3.74688 \times 10^{-6} \, \text{moles/m}^3 \]

Step 3: Calculate Total Moles of Ozone

Finally, calculate the total moles of ozone in the air using the volume of air and the moles of ozone per cubic meter calculated in Step 2. Multiply this per-cubic-meter value by the total volume to find the total moles:\[ \text{Total Moles of O}_3 = 3.74688 \times 10^{-6} \, \text{moles/m}^3 \times 1,000,000,000,000 \, \text{m}^3 = 3,746,880 \text{ moles} \]

Key Concepts

Understanding Ozone Concentration

Ozone concentration is a measure of how much ozone gas is present in a specific volume of air. It is commonly measured in parts per billion (ppb). For instance, when we say that the ozone level is 84 ppb, it means that in every billion molecules in the air, 84 of them are ozone molecules.
This is important for environmental science because ozone at ground level is a significant pollutant that can affect human health and vegetation.

• Measurements like ppb help to monitor and regulate ozone to maintain air quality standards.
• The Environmental Protection Agency (EPA) sets limits to protect public health, which currently stands at 84 ppb for urban environments.

By understanding ozone concentration, scientists and policymakers can better gauge how much ozone is in the air and create regulations to limit this pollution.

The Ideal Gas Law Explained

The Ideal Gas Law is a fundamental principle in chemistry, represented by the equation \( PV = nRT \). This equation links together the pressure \( P \), volume \( V \), number of moles \( n \), the gas constant \( R \), and temperature \( T \).
Here's a basic rundown:

• \( P \) stands for the pressure of the gas.
• \( V \) is the volume the gas occupies.
• \( n \) represents the amount of substance in moles.
• \( R \) is the ideal gas constant \(0.0821 \text{ L atm mol}^{-1} \text{K}^{-1}\).
• \( T \) is the temperature, measured in Kelvin.

This law can be used to determine any one of these variables if the others are known. For atmospheric sciences, it helps us determine the behavior of gases like ozone in the atmosphere under different environmental conditions.

What is Molar Volume?

Molar volume is an essential concept in chemistry referring to the volume occupied by one mole of a substance, ideally a gas, under standard conditions. Typically, this is 22.4 liters per mole at standard temperature and pressure (STP), which is 0°C (273.15 K) and 1 atmosphere of pressure.
In our calculations, molar volume helps convert concentrations in parts per billion to moles per cubic meter.

• Since 1 cubic meter equals 1,000 liters, and knowing that 1 mole occupies 22.4 liters under STP, we find that 1 m³ of air holds about 44.64 moles of air.

This conversion is crucial for finding how many moles of ozone are present in a given volume of air, which in turn, assists in evaluating compliance with environmental standards.

Environmental Science and Ozone

Ozone in the atmosphere plays a dual role.
While stratospheric ozone protects life on Earth by blocking harmful ultraviolet radiation from the sun, ground-level ozone is a different story.
It forms when pollutants emitted by cars, power plants, and other industrial sources react in the presence of sunlight.
In environmental science, managing ozone concentration is crucial. High ozone levels at ground level can:

• Cause respiratory problems and other health concerns.
• Harm sensitive vegetation and ecosystems.
• Reduce agricultural crop yields.

Efforts to understand and control ozone levels are a significant part of environmental policies aimed at improving air quality and protecting both human health and the environment.