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?

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

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 \(m^3\)

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.