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 10 \(\mathrm{m}\) above the ground) if ozone was at this concentration?

Short answer

There would be approximately 9,732.5 moles of ozone in the air above Los Angeles County if the ozone concentration is at the EPA standard of 84 ppb, considering a height of 10 meters above the ground.

Step-by-step solution

Convert ppb to moles per liter (M)

First, we have to convert the given ozone concentration in ppb to moles per liter. 1 ppb means one part ozone in 1 billion parts air. Since 1 mole of any gas occupies 22.4 L at standard conditions (1 atm, 0°C), we can use the formula: Molar concentration (M) = (ppb × 10^{-9}) / 22.4 M = (84 × 10^{-9}) / 22.4

Calculate the molar concentration

Now, we can find the molar concentration of ozone in the atmosphere by plugging in the values into the previously obtained equation: M = (84 × 10^{-9}) / 22.4 M ≈ 3.75 × 10^{-12} M So, the concentration of ozone in the atmosphere is approximately 3.75 × 10^{-12} moles per liter.

Convert square miles to square meters

Given the area of Los Angeles County as 4000 square miles, we need to convert it to square meters as we are considering the height in meters. We know: 1 square mile = 2.58999 × 10^6 square meters So, 4000 square miles = 4000 × (2.58999 × 10^6) square meters

Calculate the volume of the air

Now, we can find the volume of the air above Los Angeles County (considering a height of 10 meters above the ground). The volume is the product of the area and the height: Volume = Area × Height Volume ≈ 4000 × (2.58999 × 10^6) × 10 m³

Calculate the number of moles of ozone

Finally, using the molar concentration calculated in step 2, we can find the total number of moles of ozone in the atmosphere above Los Angeles County. Total moles of ozone = Molar concentration × Volume Total moles of ozone ≈ (3.75 × 10^{-12}) × (4000 × 2.58999 × 10^6 × 10) Calculating the total number of moles of ozone, we get: Total moles of ozone ≈ 9.7325 × 10^3 So, there would be approximately 9,732.5 moles of ozone in the air above Los Angeles County if the ozone concentration is at the EPA standard of 84 ppb.

Key concepts

Understanding Ozone Concentration

Ozone concentration refers to the amount of ozone present in a particular volume of air. It's commonly measured in 'parts per billion' (ppb), which indicates the number of ozone molecules in every billion air molecules. When monitoring air quality, especially in urban areas, it's critical to know the ozone concentration because of its effects on health and the environment. Ozone at ground level is an ingredient of smog, and high concentrations can lead to respiratory problems in humans and harm wildlife.

For practical applications and compliance with environmental standards, such as those set by the Environmental Protection Agency (EPA), it's often necessary to convert these concentration units into more scientifically useful numbers, such as moles, which denote the actual quantity of ozone molecules. This forms the basis for understanding the total impact of ozone on a region, which is significant in fields such as environmental science, public health, and policy-making.

PPB to Moles Conversion

Converting ppb (parts per billion) to moles is an essential step in quantifying the amount of a substance—in this case, ozone—in a given volume. This conversion allows us to relate a measurable concentration to a specific quantity of matter, which is represented in moles, a fundamental concept in chemistry known as the mole, symbolized by Avogadro's number (\(6.022 \times 10^{23}\) entities per mole).

The formula to convert ppb to molar concentration is:
\begin{align*}Molar\ concentration\ (M) &= \frac{ppb \times 10^{-9}}{22.4}\ \text{M} &= \frac{(\text{given ppb})\times 10^{-9}}{22.4}\end{align*}The number 22.4 in the formula represents the volume in liters that one mole of any ideal gas occupies at standard temperature and pressure (0°C, 1 atm). By performing this conversion, what was once an abstract measurement of concentration becomes a tangible quantity that we can work with across various calculations and comparisons.

Atmospheric Chemistry

Atmospheric chemistry is the branch of environmental chemistry dealing with chemical reactions, processes, and phenomena that take place in the Earth's atmosphere. Understanding the composition and reactivity of atmospheric gases like ozone is vital for evaluating environmental impact, predicting weather patterns, and assessing changes in climate.

Ozone, in particular, has a dual role in the atmosphere. In the stratosphere, it forms the ozone layer, which is critical for protecting life on Earth from harmful ultraviolet radiation. Conversely, at ground level, known as tropospheric ozone, it is a hazardous pollutant contributing to smog and respiratory issues.

In atmospheric chemistry, calculations often involve determining the amount of a particular gas within a volume of air, as seen in the exercise of calculating moles of ozone in Los Angeles County. This exercise combines the principles of ppb to moles conversion with understanding atmospheric layers and volumes, showcasing how theoretical calculations are applied to real-world scenarios to help inform environmental policies and health recommendations.