Question

Assume there are \(2 \times 10^{20} \mathrm{CO}\) molecules per cubic meter in a sample of tropospheric air. Furthermore, assume there are \(1 \times 10^{19} \mathrm{O}_{3}\) molecules per cubic meter at the point of maximum concentration of the ozone layer in the stratosphere. a. Which cubic meter of air contains the larger number of molecules? b. What is the ratio of \(\mathrm{CO}\) to \(\mathrm{O}_{3}\) molecules in a cubic meter?

Short answer

a. The cubic meter with \(\mathrm{CO}\) molecules has more molecules. b. The ratio is 20:1.

Step-by-step solution

Compare the Number of Molecules

First, we need to compare the number of molecules per cubic meter in each sample. The tropospheric air sample contains \(2 \times 10^{20}\) \(\mathrm{CO}\) molecules, while the stratospheric ozone layer sample contains \(1 \times 10^{19}\) \(\mathrm{O}_{3}\) molecules. Since \(2 \times 10^{20} > 1 \times 10^{19}\), the air sample with \(\mathrm{CO}\) molecules contains more molecules per cubic meter.

Calculate the Ratio

Next, we calculate the ratio of \(\mathrm{CO}\) molecules to \(\mathrm{O}_{3}\) molecules in a cubic meter. This is done by dividing the number of \(\mathrm{CO}\) molecules by the number of \(\mathrm{O}_{3}\) molecules: \[ \text{Ratio} = \frac{2 \times 10^{20}}{1 \times 10^{19}} = 20 \] Thus, the ratio of \(\mathrm{CO}\) to \(\mathrm{O}_{3}\) is 20:1.

Key concepts

Carbon Monoxide (CO)

Carbon monoxide, often abbreviated as CO, is a colorless, odorless gas that can be extremely dangerous. It is produced by the incomplete combustion of carbon-containing fuels such as coal, wood, or oil, and thus can accumulate to high concentrations in enclosed spaces. However, in the atmosphere, CO is present at much lower and safer levels. While not harmful in the quantities commonly found outdoors, elevated levels indoors or in enclosed spaces can be deadly.
CO travels upwards in the atmosphere, where it can persist for about one to two months. This ability to stay in the air allows it to disperse widely across the globe. Because of this persistent nature, measuring and understanding CO levels can provide crucial information about air quality and atmospheric health.

• CO is a greenhouse gas contributing to climate change.
• High atmospheric CO levels can interfere with the amount of ozone produced in the atmosphere.

Ozone (O₃)

Ozone, or O₃, is a pale blue gas with a distinct sharp smell. It plays a dual role in Earth's atmosphere. Near the Earth's surface, it's a harmful pollutant and a key component of smog. However, in the upper atmosphere, the stratosphere, it forms the crucial ozone layer which protects living organisms by blocking harmful ultraviolet (UV) radiation from the sun.
Despite its benefits in the stratosphere, ground-level ozone can pose significant health risks, including respiratory issues and other health problems.

• Stratospheric ozone is beneficial and protects Earth from UV radiation.
• Tropospheric ozone is considered a pollutant and can affect human health.

Ozone formation and destruction are highly influenced by atmospheric conditions and pollutants, making atmospheric chemistry complex and dynamic.

Troposphere and Stratosphere

The Earth's atmosphere can be divided into several layers, each with unique characteristics. The troposphere is the lowest layer, extending about 8 to 15 kilometers above the Earth's surface. This is the layer where most weather conditions occur, and it's rich in greenhouse gases, including water vapor and carbon dioxide.
The stratosphere lies directly above the troposphere, extending up to about 50 kilometers high. Here, temperatures increase with altitude due to the absorption of UV radiation by ozone. The stratosphere is crucial for protecting the planet from the sun's UV radiation because of the high concentration of ozone which absorbs and scatter the solar radiation.

• Troposphere contains weather and most human-related air pollution.
• Stratosphere houses the ozone layer, crucial for UV protection.

Understanding these layers is essential for comprehending many atmospheric chemistry processes including those involving CO and O₃.

Molecular Ratio

A molecular ratio is a simple but powerful concept in atmospheric chemistry and many other scientific fields. It refers to the comparison of two quantities, expressed as a fraction or ratio. In our exercise, we calculated the molecular ratio of CO to O₃ by dividing their concentrations in given samples.
For example, if you have 20 molecules of CO for every 1 molecule of O₃, the ratio of CO to O₃ is 20:1. This numerical approach helps in understanding and quantifying the abundance of different species in the atmosphere. By analyzing these ratios, scientists can infer processes like pollutant emission sources, chemical reactions in the atmosphere, and the relative contribution of different gases to air pollution.

• Molecular ratios can help identify changes in atmospheric composition.
• They are crucial for modeling atmospheric processes and understanding pollution dynamics.

Atmospheric Chemistry

Atmospheric chemistry is the study of the chemical composition of the Earth's atmosphere and the reactions and interactions among atmospheric components. It plays a critical role in understanding climate change, pollution, and air quality.
Key ingredients in atmospheric chemistry include gases like carbon dioxide, ozone, and water vapor, as well as particulates like dust and soot. These elements interact in complex ways, driven by sunlight and other environmental factors. A focus on the troposphere and stratosphere is especially important because reactions in these layers significantly affect the environment and human health.

• Atmospheric chemistry monitors changes in air pollution and greenhouse gases.
• It helps forecast climate change impacts and guides environmental policies.

Engaging with atmospheric chemistry offers invaluable insights for tackling urgent environmental issues and for maintaining the delicate balance necessary for life on Earth.