Problem 62 - Chemistry The Central Science In Si Units

Question

The indoor concentration of ozone above \(300 \mu \mathrm{g} / \mathrm{m}^{3}\) is considered to be unhealthy. What mass of ozone in grams is present in a room measuring \(3.2 \mathrm{~m} \times 2.8 \mathrm{~m} \times 4.1 \mathrm{~m}\) ?

Step-by-Step Solution

Answer

The mass of ozone is approximately 0.011 grams.

Step 1: Calculate the Volume of the Room

To determine the mass of ozone, we first need to calculate the volume of the room. Volume can be calculated by multiplying the dimensions of the room: length, width, and height.\[ V = 3.2 \, \text{m} \times 2.8 \, \text{m} \times 4.1 \, \text{m} \]\[ V = 36.736 \, \text{m}^3 \]

Step 2: Convert Concentration to Grams per Cubic Meter

The given concentration of ozone is above \(300 \, \mu \text{g/m}^3\). We'll use this value to find the mass of the ozone. First, convert \(300 \, \mu \text{g/m}^3\) to grams per cubic meter.\[ 300 \, \mu\text{g/m}^3 = \frac{300}{1,000,000} \, \text{g/m}^3 = 0.0003 \, \text{g/m}^3 \]

Step 3: Calculate the Total Mass of Ozone

Multiply the volume of the room by the concentration in grams per cubic meter to find the total mass of ozone in grams:\[ \text{Mass of Ozone} = 36.736 \, \text{m}^3 \times 0.0003 \, \text{g/m}^3 \]\[ \text{Mass of Ozone} = 0.0110208 \, \text{g} \]

Key Concepts

Understanding Molecular Chemistry and Ozone

Molecular chemistry is the branch of chemistry that deals with the composition, structure, and behavior of molecules. It's essential in understanding how different molecules, such as ozone ( O ₃ ), behave. Ozone is composed of three oxygen atoms. While it plays a protective role in the Earth's stratosphere by blocking harmful ultraviolet sunlight, at ground level, ozone can be detrimental to human health. It is considered a pollutant when present in high concentrations in the air we breathe. Understanding molecular chemistry helps us to comprehend the dual nature of ozone, aiding in efforts to monitor and regulate its presence in our environment.

Mastering Unit Conversion for Accurate Measurements

Unit conversion is a fundamental skill in chemistry that allows scientists and students to convert quantities from one unit to another. It's crucial for maintaining consistency and accuracy in experiments and calculations. For example, when dealing with ozone concentration, one might encounter micrograms per cubic meter (\(\mu \text{g/m}^{3}\)). This unit expresses the mass of a substance distributed in a given volume.

To convert a quantity in micrograms (\(\mu \text{g}\)) to grams (g), divide by 1,000,000 (since there are 1,000,000 micrograms in a gram).

This way, the concentration of 300 \(\mu \text{g/m}^{3}\) becomes 0.0003 g/m\(^{3}\).

Mastering these conversions is pivotal for determining the exact mass of pollutants, like ozone, in a specific volume or setting.

Environmental Chemistry and Indoor Air Quality

Environmental chemistry focuses on chemical processes occurring in the environment and the effects of human activity on these processes. Indoor air quality is a significant concern in this field, as various pollutants can build up to harmful levels without proper ventilation.
Ozone is one such pollutant. Inside enclosed spaces, elevated concentrations of ozone can cause respiratory problems and other health issues. In the given exercise, an ozone concentration of 300 \(\mu \text{g/m}^{3}\) was measured indoors, above the level considered safe. By calculating the room's ozone mass, we ensure the air remains safe to breathe. This is crucial, as maintaining low ozone levels indoors minimizes health risks and enhances the quality of life.