Air pollution in the Mexico City metropolitan area is among the worst in the world. The concentration of ozone in Mexico City has been measured at 441 ppb (0.441 ppm). Mexico City sits at an altitude of 7400 feet, which means its atmospheric pressure is only 0.67 atm. (b) How many ozone molecules are in 1.0 L of air in Mexico City? Assume T = 25 °C.

Verified step by step guidance

1. Convert the concentration of ozone from ppm to a fraction: 0.441 ppm means 0.441 parts of ozone per million parts of air, which is 0.441/1,000,000.
2. Use the ideal gas law to find the number of moles of air in 1.0 L at the given conditions. The ideal gas law is PV = nRT, where P is pressure (0.67 atm), V is volume (1.0 L), R is the ideal gas constant (0.0821 L·atm/mol·K), and T is temperature in Kelvin (25 °C = 298 K).
3. Calculate the total moles of air using the rearranged ideal gas law: n = PV/RT.
4. Determine the moles of ozone by multiplying the total moles of air by the fraction of ozone (0.441/1,000,000).
5. Convert the moles of ozone to molecules using Avogadro's number (6.022 x 10^23 molecules/mol).

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the number of gas molecules in a given volume under specific conditions of temperature and pressure. In this case, it will help determine how many ozone molecules are present in 1.0 L of air in Mexico City.

Molar Volume of a Gas

At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 liters. However, since the conditions in Mexico City differ (lower pressure and a specific temperature), the molar volume will need to be adjusted accordingly. Understanding how to calculate the molar volume under non-STP conditions is crucial for determining the number of ozone molecules in the air.

Concentration Units (ppb and ppm)

Parts per billion (ppb) and parts per million (ppm) are units used to express the concentration of a substance in a solution or mixture. In this context, the concentration of ozone is given in ppb, which must be converted to a more usable form (like moles or molecules) to find the total number of ozone molecules in 1.0 L of air. Understanding these units is vital for accurate calculations.