Question

The units of parts per million (ppm) and parts per billion (ppb) are commonly used by environmental chemists. In general, 1 ppm means 1 part of solute for every \(10^{6}\) parts of solution. Mathematically, by mass: $$ \mathrm{ppm}=\frac{\mu \mathrm{g} \text { solute }}{\mathrm{g} \text { solution }}=\frac{\mathrm{mg} \text { solute }}{\mathrm{kg} \text { solution }} $$ In the case of very dilute aqueous solutions, a concentration of 1.0 ppm is equal to \(1.0 \mu \mathrm{g}\) of solute per \(1.0 \mathrm{~mL}\), which equals 1.0 g solution. Parts per billion is defined in a similar fashion. Calculate the molarity of each of the following aqueous solutions. a. \(5.0 \mathrm{ppb} \mathrm{Hg}\) in \(\mathrm{H}_{2} \mathrm{O}\) b. \(1.0 \mathrm{ppb} \mathrm{CHCl}_{3}\) in \(\mathrm{H}_{2} \mathrm{O}\) c. \(10.0 \mathrm{ppm}\) As in \(\mathrm{H}_{2} \mathrm{O}\) d. \(0.10\) ppm DDT \(\left(\mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}\right)\) in \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

The molarities of the solutions are: a. Hg: \(2.49 \times 10^{-5} \,M\) b. CHCl₃: \(8.38 \times 10^{-6} \,M\) c. As: \(1.34 \times 10^{-4} \,M\) d. DDT: \(2.82 \times 10^{-7} \,M\)

Step-by-step solution

Convert ppb/ppm to mass of solute

We will use the given concentrations to find the mass of solute in micrograms (for ppb) or milligrams (for ppm). a. For 5.0 ppb Hg, the mass of solute (Hg) can be found as follows: \(5.0 \, ppb = \frac{5.0 \, \mu g \text{ Hg}}{1.0\, g \text{ solution}}\) b. For 1.0 ppb CHCl₃, the mass of solute (CHCl₃) can be found as follows: \(1.0 \, ppb = \frac{1.0 \, \mu g \text{ CHCl}_3}{1.0\, g \text{ solution}}\) c. For 10.0 ppm As, the mass of solute (As) can be found as follows: \(10.0 \, ppm = \frac{10.0 \, mg \text{ As}}{1.0\, kg \text{ solution}}\) d. For 0.10 ppm DDT, the mass of solute (C₁₄H₉Cl₅) can be found as follows: \(0.10 \, ppm = \frac{0.10 \, mg \text{ C}_{14}\text{H}_{9}\text{Cl}_{5}}{1.0\, kg \text{ solution}}\)

Calculate the moles of solute

Next, we will calculate the moles of solute in each solution by dividing the mass of solute by molar mass of the solute. a. Moles of Hg: \(\text{Moles of Hg} = \frac{5.0 \,\mu g \text{ Hg}}{200.59 \,g/mol} = 2.49 \times 10^{-8} \,mol\) b. Moles of CHCl₃: \(\text{Moles of CHCl}_3 = \frac{1.0 \,\mu g \text{ CHCl}_3}{119.38 \,g/mol} = 8.38 \times 10^{-9} \,mol\) c. Moles of As: \(\text{Moles of As} = \frac{10.0 \,mg \text{ As}}{74.92 \,g/mol} = 1.34 \times 10^{-4} \,mol\) d. Moles of DDT: \(\text{Moles of C}_{14}\text{H}_{9}\text{Cl}_{5} = \frac{0.10 \,mg \text{ C}_{14}\text{H}_{9}\text{Cl}_{5}}{354.48 \,g/mol} = 2.82 \times 10^{-7} \,mol\)

Find the molarities of the solutions

Finally, we will divide the moles of solute by the volume of the solution (in liters) to get the molarities. a. Molarity of Hg: \(\text{Molarity} = \frac{2.49 \times 10^{-8} \,mol}{0.001 \,L} = 2.49 \times 10^{-5} \,M\) b. Molarity of CHCl₃: \(\text{Molarity} = \frac{8.38 \times 10^{-9} \,mol}{0.001 \,L} = 8.38 \times 10^{-6} \,M\) c. Molarity of As: \(\text{Molarity} = \frac{1.34 \times 10^{-4} \,mol}{1 \,L} = 1.34 \times 10^{-4} \,M\) d. Molarity of DDT: \(\text{Molarity} = \frac{2.82 \times 10^{-7} \,mol}{1 \,L} = 2.82 \times 10^{-7} \,M\) In summary, the molarities of the solutions are: a. \(\mathrm{Hg} = 2.49 \times 10^{-5} \,M\) b. \(\mathrm{CHCl}_3 = 8.38 \times 10^{-6} \,M\) c. \(\mathrm{As} = 1.34 \times 10^{-4} \,M\) d. \(\mathrm{DDT} = 2.82 \times 10^{-7} \,M\)

Key concepts

Environmental Chemistry

Environmental chemistry is a crucial field focusing on the study of chemical processes occurring in the environment, which can be natural or influenced by humans. It encompasses the monitoring and understanding of how chemicals move through ecosystems, their effects on human health, and their overall environmental impact.

When it comes to analyzing pollutants such as heavy metals, pesticides, or organic chemicals, environmental chemists often use units like parts per million (ppm) and parts per billion (ppb). These units help in communicating how much of a given substance is present in a particular environment, such as water, soil, or air, relative to other substances. These measurements are especially important at low concentrations, where the substances may still have significant biological effects despite being present in very small amounts.

In practice, environmental chemists track the levels of these substances to assess pollution, ensure compliance with environmental regulations, and work on remediation strategies to reduce the presence of harmful chemicals in the environment.

Concentration Calculation

Concentration calculation is a fundamental concept in chemistry that involves determining the amount of a substance within a specific volume of solution. The concentration can be expressed in various units, with ppm and ppb being particularly useful for very dilute solutions often encountered in environmental chemistry.

Understanding how to convert between units such as ppm, ppb, milligrams, micrograms, and kilograms is vital. As demonstrated in the example, conversion allows us to move from a mass-based concentration to a mole-based concentration, which is crucial for more accurate chemical analyses and reactions calculations. The understanding of these conversions also aids in risk assessment and regulatory processes, helping to keep pollutant levels within safe limits for both humans and ecosystems.

Educating on the significance of these units and how to convert between them helps in appreciating the precision needed to monitor and control the presence of contaminants at extremely low concentrations in the environment.

Solution Molarity

Solution molarity is a term used to express the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution (M or mol/L). It's a standard unit of concentration in chemistry that provides a direct measure of particle number, which is crucial for stoichiometric calculations in chemical reactions.

In the context of environmental chemistry, calculating the molarity from units of ppm or ppb involves first finding the mass of the solute in micrograms or milligrams as explained in the exercise. Following this, one would convert the mass to moles by using the molar mass of the compound, and then finally, divide by the volume of the solution in liters to find the molarity.

This calculation helps us to understand the amount of a substance on a molecular level, which is particularly important when dealing with chemical reactions, such as the neutralization of contaminants or calculating the dosages needed for water treatment processes. The use of molarity in environmental studies ensures that scientists and engineers have a precise and standardized way to describe chemical concentrations, which is essential for research, monitoring, and environmental management.