/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Air pollution in the Mexico City... [FREE SOLUTION] | 91Ó°ÊÓ

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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 \((0.441 \mathrm{ppm})\). Mexico City sits at an altitude of 7400 feet, which means its atmospheric pressure is only \(0.67\) atm. Calculate the partial pressure of ozone at 441 ppb if the atmospheric pressure is 067 atm.

Short Answer

Expert verified
The partial pressure of ozone in Mexico City is approximately \(2.95 \times 10^{-7} \, \mathrm{atm}\).

Step by step solution

01

Write down given information and formula.

We are given the following information: - Concentration of ozone in Mexico City = 441 ppb = 0.441 ppm - Atmospheric pressure at Mexico City's altitude = 0.67 atm We will use the formula for partial pressure: Partial pressure of a gas = (Mole fraction of the gas) x (Total pressure) Here, we have to find the mole fraction of ozone (O3) first.
02

Convert the concentration of ozone from ppm to the mole fraction.

1 ppm is equal to \(1 \times 10^{-6}\) mole fraction. Since we have the concentration of ozone in ppm, we can convert it to mole fraction by multiplying by \(1 \times 10^{-6}\). Mole Fraction of O3 = 0.441 ppm x \(1 \times 10^{-6}\) Mole Fraction of O3 = \(4.41 \times 10^{-7}\)
03

Calculate the partial pressure of ozone.

Now we can use the mole fraction of ozone and the given atmospheric pressure (0.67 atm) to calculate the partial pressure of ozone using the formula: Partial pressure of ozone = (Mole fraction of ozone) x (Total pressure) Partial_pressure_of_ozone = \((4.41 \times 10^{-7}) \times (0.67 \, \mathrm{atm})\) Partial_pressure_of_ozone = \(2.9547 \times 10^{-7} \, \mathrm{atm}\) Therefore, the partial pressure of ozone in Mexico City is approximately \(2.95 \times 10^{-7} \, \mathrm{atm}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atmospheric pressure
Atmospheric pressure is the force exerted by the weight of the air above us. At sea level, this pressure is approximately 1 atm, which stands for atmosphere. However, this value changes with altitude. As you go higher, like in a city situated 7,400 feet above sea level, such as Mexico City, the atmospheric pressure decreases.

This is because there is less air, or fewer air molecules, pressing down from above when you are at higher altitudes. Moreover, the atmospheric pressure affects various things, like the temperature and how gases behave in that area.
  • Sea level pressure: ~1 atm
  • Mexico City’s pressure: 0.67 atm
  • Higher altitude = Lower atmospheric pressure
Understanding atmospheric pressure is crucial, especially in scientific calculations such as determining the partial pressure of gases, which in our example refers to ozone.
Ozone concentration
Ozone concentration in an area is a measure of how much ozone, often referred to as \(\text{O}_3\), is present in the air. It is usually reported in parts per billion (ppb) or parts per million (ppm). Ozone plays a significant role in our atmosphere, particularly in the stratosphere where it protects us from the sun's harmful ultraviolet rays.

In cities like Mexico City, at ground level, ozone in high concentrations acts as an air pollutant. The concentration of ozone in Mexico City has been measured to be 441 ppb, translating to 0.441 ppm. This shows how much of the air is made up of ozone compared to other gases, and it is a critical figure when evaluating air quality. High ozone levels often lead to health issues and can be harmful to both humans and the environment.
  • Ozone is crucial for blocking UV rays.
  • Measured in ppb/ppm — higher at ground levels can indicate pollution.
  • In Mexico City, measured concentration: 441 ppb (0.441 ppm).
Mole fraction
The mole fraction, denoted by an \( x_i \), is a concept used in chemistry to express the concentration of a component in a mixture, like air. It is the ratio of the number of moles of one component to the total number of moles of all the components in the mixture. This fraction helps in determining the partial pressure of gaseous components in a mixture under given conditions.

To find the mole fraction of a gas when its concentration is given in ppm, you can multiply the ppm value by \(1 \times 10^{-6}\). For instance, the ozone in Mexico City showed a concentration of \(0.441\, \mathrm{ppm}\); thus, its mole fraction becomes \(0.441 \times 10^{-6}\), equaling to \(4.41 \times 10^{-7}\). Understanding this process is key when calculating partial pressures, as these calculations often rely on using the mole fractions.
  • Mole fraction formula: \(\frac{\text{moles of component}}{\text{total moles}}\)
  • Used in calculating partial pressure.
  • Conversion from ppm: multiply by \(1 \times 10^{-6}\).
Air pollution in Mexico City
Air pollution in Mexico City is recognized as some of the worst in the world. The city’s unique geography contributes to this issue. Situated in a high-altitude valley surrounded by mountains, temperature inversions often trap pollutants, exacerbating air quality problems. This setting limits the movement of air and increases the concentration of pollutants.

One of the most concerning pollutants is ozone. Although beneficial higher in the atmosphere, at ground level, it becomes a harmful component of smog. Ozone in high concentrations can cause respiratory problems and other health concerns among the residents. Efforts have been introduced to reduce these pollutants, but the unique geographic and climatic conditions make it a persistent challenge.
  • Geographic location leads to pollutant trapping.
  • Ozone is a major pollutant contributing to smog.
  • Health impacts include respiratory issues.

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