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. (a) Calculate the partial pressure of ozone at 441 ppb if the atmospheric pressure is 0.67 atm.

Verified step by step guidance

1. Understand that ppb (parts per billion) is a way to express very dilute concentrations of substances. In this context, 441 ppb means 441 parts of ozone per billion parts of air.
2. Convert the concentration from ppb to a fraction. Since 1 ppb is equivalent to 1 part in 1,000,000,000 parts, 441 ppb is equivalent to 441/1,000,000,000.
3. Calculate the partial pressure of ozone using the formula: \( P_{\text{ozone}} = \text{fraction of ozone} \times P_{\text{total}} \), where \( P_{\text{total}} \) is the total atmospheric pressure.
4. Substitute the given values into the formula: \( P_{\text{ozone}} = \frac{441}{1,000,000,000} \times 0.67 \text{ atm} \).
5. Perform the multiplication to find the partial pressure of ozone in atm.

Key Concepts

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture. It can be calculated using Dalton's Law, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of its individual gases. In this context, the partial pressure of ozone can be determined by multiplying the total atmospheric pressure by the mole fraction of ozone in the mixture.

Concentration Units

Concentration can be expressed in various units, including parts per billion (ppb) and parts per million (ppm). In this question, the concentration of ozone is given as 441 ppb, which can be converted to ppm by dividing by 1000. Understanding these units is crucial for accurately calculating the partial pressure of ozone in the atmosphere.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature, volume, and pressure. The ideal gas law (PV=nRT) is particularly relevant here, as it relates pressure (P), volume (V), and temperature (T) to the number of moles (n) of gas. Although this question primarily focuses on partial pressure, familiarity with gas laws helps in understanding the relationships between different gas properties.