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 4000 square miles; consider a height of 100 \(\mathrm{m}\) above the ground) if ozone was at this concentration?

Short answer

If the ozone concentration in the air above Los Angeles County were at the EPA standard of 84 ppb, there would be approximately 3566055.456 moles of ozone in the 100-meter-high volume, considering an area of 4000 square miles.

Step-by-step solution

Convert area and concentration units

First, we need to convert the given area (4000 square miles) to square meters. 1 square mile = 2589988.1103 square meters So, 4000 square miles = 4000 * 2589988.1103 \(m^2\) = 10359952281 \(m^2\) Next, we need to convert the ozone concentration (84 ppb) to parts per million (ppm). 1 ppb = 0.001 ppm So, 84 ppb = 84 * 0.001 ppm = 0.084 ppm

Determine the volume of air above Los Angeles County

We are given the height to consider as 100 meters. So, the volume of air above the county can be found by multiplying the area by the height. Volume = Area x Height = 10359952281 \(m^2\) x 100 m = 1035995228100 \(m^3\)

Calculate the number of moles of ozone in the volume

Since ozone concentration is given in parts per million (ppm), it can be interpreted as the ratio of moles of ozone to total moles of air: Mole fraction of ozone = 0.084 ppm Now, we need to find the total moles of air in the volume. We can do so by using the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. We will assume that the atmospheric pressure is 1 atm and the temperature is 298 K (approximately room temperature). Then, we can rearrange the formula to solve for n: n = PV/RT Assuming an ideal gas mixture, ozone and other gases have the same pressure. So, we can use the total pressure (1 atm) in the equation and get the total moles of air in the volume. We also have the value of R in appropriate units: R = 0.0821 L atm / K mol We need to convert the volume from \(m^3\) to liters because the gas constant is given in L atm / K mol: 1 \(m^3\) = 1000 L So, 1035995228100 \(m^3\) = 1035995228100 * 1000 L = 1035995228100000 L Now, we can plug in the values: n_total (moles of air) = (1 atm * 1035995228100000 L) / (0.0821 L atm / K mol * 298 K) = 42443497138.5 moles Now, we can use the mole fraction of ozone to find the number of moles of ozone: n_ozone = Mole fraction of ozone * n_total = 0.084 ppm * 42443497138.5 moles We have to take into account that the mole fraction is given in parts per million, so we divide the result by 1,000,000: n_ozone = (0.084 / 1,000,000) * 42443497138.5 moles = 3566055.456 moles So, there would be 3566055.456 moles of ozone in the air above Los Angeles County if the ozone concentration was at the EPA standard of 84 ppb.

Key concepts

Ozone Concentration

The concentration of ozone in the atmosphere is often measured in parts per billion (ppb), which means one part of ozone per billion parts of air. It is essential to understand ozone concentration because ozone plays a significant role in absorbing harmful ultraviolet radiation from the sun. However, at ground level, high concentrations can be detrimental to health and the environment.
In urban areas, like Los Angeles County, monitoring ozone levels is crucial due to the dense population and industrial activities that can contribute to pollution. Environmental Protection Agency (EPA) standards currently cap the allowable ozone concentration in these urban settings at 84 ppb. This guideline helps ensure air quality does not pose a risk to public health.
Ozone concentration at this level serves as a critical measure for gauging air quality and implementing appropriate environmental policies to protect citizens.

Ideal Gas Law

The ideal gas law is a fundamental equation used to relate the pressure, volume, temperature, and number of moles of a gas. It is mathematically represented as \( PV = nRT \), where:

• \( P \) stands for pressure in atmosphere (atm),
• \( V \) is volume in liters (L),
• \( n \) represents the number of moles of gas,
• \( R \) is the gas constant (0.0821 L atm / K mol),
• \( T \) is temperature in Kelvin (K).

The ideal gas law assumes that gas particles are in constant random motion and interact through elastic collisions, with no attractions or repulsions.
In the context of atmospheric chemistry, this law helps determine the number of moles of a specific gas like ozone when considering its volume and the atmospheric conditions such as pressure and temperature. Converting volumes to liters and measuring pressure in atmospheres aligns with the units of the gas constant for consistency in calculations.

Mole Calculations

Mole calculations are crucial in determining the amount of substance present in a given volume, especially when using the ideal gas law. The concept of a mole refers to Avogadro's number \( (6.022 \times 10^{23}) \) of molecules or atoms. In gas calculations, knowing the number of moles can help in exploring concentrations and reactions in the atmosphere.
To find the number of moles of air, the ideal gas law is rearranged to \( n = \frac{PV}{RT} \). This method allows us to derive the total moles of air in an extensive volume entered by the large area of Los Angeles County (given in the exercise).
Once the total moles of air are calculated, knowing the mole fraction of ozone (in ppm) enables us to determine the exact moles of ozone in that volume. It highlights the practicality of moles in quantifying substances in chemistry, especially within calculated environmental scenarios.

Environmental Standards

Environmental standards are regulations that help maintain certain levels of pollutants, ensuring the protection of both human health and the environment. The EPA sets specific guidelines for pollutants like ozone to safeguard the wider public and avert potential health hazards.
For example, ozone at the ground level can cause respiratory problems and other health issues, thus the EPA standard of limiting ozone concentration to 84 ppb acts as a preventative measure.
These standards have evolved through scientific research and public health assessments, underlining the importance of scientifically backed limits in preserving air quality. They allow communities and policymakers to develop strategies for pollution reduction, improve air quality, and encourage industries to adhere to safe operational practices.