Question

Compare the amount of nitric oxide in air at a concentration of \(300 \mathrm{ppbv}\) with the amount of nitrate ion in a fog consisting of 10000 droplets \(\mathrm{cm}^{-3}\) having an average diameter of \(2 \mu \mathrm{m}\) and a concentration in the droplets of \(3 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-}\).

Short answer

Nitric oxide concentration in air is significantly higher than nitrate in fog.

Step-by-step solution

Calculate the Volume of Fog Droplets

To determine the total volume of the fog, first we calculate the volume of a single droplet using the formula for the volume of a sphere, \( V = \frac{4}{3}\pi r^3 \). The radius is half of the diameter, so here it will be \( r = 1 \mu \text{m} = 1 \times 10^{-6} \text{m} \). Therefore, the volume of one droplet is \[ V = \frac{4}{3} \pi (1 \times 10^{-6})^3 \approx 4.19 \times 10^{-18} \text{m}^3 \].

Total Volume of All Droplets

Multiply the volume of one droplet by the number of droplets per cubic centimeter to find the total volume of the droplets: \( V_{\text{total}} = 1 \times 10^4 \text{droplets/cm}^3 \times 4.19 \times 10^{-18} \text{m}^3/\text{droplet} \). Convert \( \text{m}^3 \) to \( \text{cm}^3 \) (1 \( \text{m}^3 = 10^6 \text{cm}^3 \)) to get \[ V_{\text{total}} \approx 4.19 \times 10^{-8} \text{cm}^3/\text{cm}^3 \].

Calculate Nitrate Ion Quantity in Fog

Using the concentration of nitrate ions, \( 3 \times 10^{-5} \text{mol/L} \), find the quantity of nitrate ions in the volume of fog. First, convert \( \text{mol/L} \) to \( \text{mol/cm}^3 \): \( 1 \text{L} = 10^3 \text{cm}^3 \), so the concentration is \( 3 \times 10^{-8} \text{mol/cm}^3 \). Multiply this concentration by the total volume from Step 2 to find the number of moles of nitrate ions: \[ n_{\text{nitrate}} = 3 \times 10^{-8} \text{mol/cm}^3 \times 4.19 \times 10^{-8} \text{cm}^3 \approx 1.26 \times 10^{-15} \text{mol} \].

Convert Nitric Oxide Concentration to Moles

Use the concentration of nitric oxide, given as \( 300 \text{ppbv} \), as parts per billion volume. Assuming standard conditions where 1 \( \text{mol} \) is represented in approximately 24.45 \( \text{L} \text{gas} \), find the number of moles in a cubic centimeter: \[ n_{\text{NO}} = \frac{300 \times 10^{-9} \text{mol}}{24.45 \text{L}} = \approx 1.23 \times 10^{-11} \text{mol/cm}^3 \].

Compare the Quantities

Compare the moles of nitric oxide (\( 1.23 \times 10^{-11} \text{mol/cm}^3 \)) with the moles of nitrate ions in the fog (\( 1.26 \times 10^{-15} \text{mol} \)). Clearly, the concentration of nitric oxide in the air is much higher than the amount of nitrate ions in the fog.

Key concepts

Nitric Oxide Concentration

Nitric oxide concentration in air is often measured in parts per billion by volume (ppbv). This full expression denotes the number of nitric oxide (NO) molecules in relation to a billion molecules of air. In environmental chemistry, understanding the concentration of gases like nitric oxide is crucial because it impacts air quality and the environment. For example, if you have 300 ppbv of nitric oxide, it means 300 parts of NO for every billion air parts. To express this concentration in moles per volume, you can use the fact that at standard conditions, one mole of any gas occupies approximately 24.45 liters. Therefore, 300 ppbv can be converted to moles per cubic centimeter using a conversion from billions of liters to moles, providing insight into the number of molecules present in a given volume of air.

Nitrate Ion in Fog

Fog contains suspended water droplets, and these droplets can contain dissolved ions like nitrate ions (NO₃⁻). The concentration is often expressed in moles per liter (mol/L), indicating how many moles of nitrate ions are present in one liter of fog droplets. When calculating the total amount of nitrate ions in fog, it's essential to consider both the concentration within the droplets and the total volume of the droplets themselves. This is because the ions are dispersed throughout this entire volume, affecting how we measure environmental chemistry changes and reactions within the fog. The concentration of nitrate ions in fog can hint at the potential for acid rain or other forms of atmospheric deposition when these ions might wash out and impact the surrounding environment.

Volumetric Calculations

Volumetric calculations are a fundamental part of determining the total content or concentration of substances in environmental chemistry. They employ the concept of volume to calculate quantities, which is particularly useful when dealing with gases and liquids in the atmosphere. In the case of fog droplets, the volume can be determined using the geometry of droplets—typically spherical in shape. The volume of a single droplet is calculated with the formula for the volume of a sphere: \( V = \frac{4}{3}\pi r^3 \). Multiplying this by the number of droplets gives the total volume of the droplets.This total volume can then be used in further calculations to find the total amount of a substance, such as nitrate ions, present in a surrounding environment. These calculations are crucial to evaluate air pollution levels and the potential impact on health and ecosystems.

Molar Concentration

Molar concentration, often referred to as molarity, is a measure of the concentration of a solute in a solution, in this case, nitrate ions in water droplets. It is expressed in terms of the number of moles of solute per liter of solution (mol/L). This measure helps in understanding how much of a chemical is present in a given volume. To convert from mol/L to mol/cm³, an essential step is involved, as 1 liter equals 1000 cubic centimeters. This conversion becomes necessary when dealing with micro-scale environments like fog, where volume calculations are often made in smaller units. Understanding molar concentration allows scientists and researchers to make judgments about chemical reactions' potential and intensity. It is pivotal in comparing concentrations across different phases or states of matter, such as gases and liquids.

Comparison of Chemical Quantities

To compare chemical quantities, such as the concentration of gases and dissolved ions, first convert everything to the same unit. In this exercise, that would be moles per cubic centimeter. This provides a common ground to evaluate and compare vastly different conditions in environmental chemistry. For example, comparing nitric oxide in air with nitrate ions in fog involves assessing which is more abundant in the environment. This comparison can illuminate the presence and behavior of chemicals in various environmental settings, leading to better understanding and management of pollution levels. Chemical quantity comparisons can disclose crucial information about the environmental impact that different substances could have, especially concerning health and global ecological balance.