Problem 18 - Chemistry: An Atoms-Focused Approach

Question

Zinc, copper, lead, and mercury ions are toxic to Atlantic salmon at concentrations of \(6.42 \times 10^{2} \mathrm{m} M, 7.16 \times\) \(10^{-3} \mathrm{m} M, 0.965 \mathrm{m} M,\) and \(5.00 \times 10^{-2} \mathrm{m} M,\) respectively. What are the corresponding concentrations in milligrams per liter?

Step-by-Step Solution

Answer

Question: Convert the given concentrations of toxic ions in millimolar (mM) to milligrams per liter (mg/L): Zn = 6.42 x 10^2 mM, Cu = 7.16 x 10^-3 mM, Pb = 0.965 mM, Hg = 5.00 x 10^-2 mM. Answer: The corresponding concentrations in milligrams per liter are: Zn = 41943.96 mg/L, Cu = 0.455074 mg/L, Pb = 199.944 mg/L, Hg = 10.0295 mg/L.

Step 1: Calculate molar mass

We need to find the molar mass of each ion in grams per mole (g/mol). Molar masses of each ion can be found in the periodic table or in a reference table. The molar masses are: Zn = 65.38 g/mol Cu = 63.55 g/mol Pb = 207.2 g/mol Hg = 200.59 g/mol

Step 2: Convert mM to M

1 mM is equal to 0.001 M. We will convert the given concentrations in mM to M: Zn: \((6.42 \times 10^{2} \mathrm{mM}) \times 0.001 = 0.642 \mathrm{M}\) Cu: \((7.16 \times 10^{-3} \mathrm{mM}) \times 0.001 = 7.16 \times 10^{-6} \mathrm{M}\) Pb: \((0.965 \mathrm{mM}) \times 0.001 = 9.65 \times 10^{-4} \mathrm{M}\) Hg: \((5.00 \times 10^{-2} \mathrm{mM}) \times 0.001 = 5.00 \times 10^{-5} \mathrm{M}\)

Step 3: Convert M to mg/L

For each ion, we will use its molar mass to convert M to mg/L by these formulas: mg/L = M × Molar mass × 1000 Zn: \(0.642 \mathrm{M} \times 65.38 \frac{\mathrm{g}}{\mathrm{mol}} \times 1000 = 41943.96 \, \mathrm{mg/L}\) Cu: \(7.16 \times 10^{-6} \mathrm{M} \times 63.55 \frac{\mathrm{g}}{\mathrm{mol}} \times 1000 = 0.455074 \, \mathrm{mg/L}\) Pb: \(9.65 \times 10^{-4} \mathrm{M} \times 207.2 \frac{\mathrm{g}}{\mathrm{mol}} \times 1000 = 199.944 \, \mathrm{mg/L}\) Hg: \(5.00 \times 10^{-5} \mathrm{M} \times 200.59 \frac{\mathrm{g}}{\mathrm{mol}} \times 1000 = 10.0295 \, \mathrm{mg/L}\) So, the corresponding concentrations in milligrams per liter are: Zn: \(41943.96 \, \mathrm{mg/L}\) Cu: \(0.455074 \, \mathrm{mg/L}\) Pb: \(199.944 \, \mathrm{mg/L}\) Hg: \(10.0295 \, \mathrm{mg/L}\)

Key Concepts

Toxic Ions

Toxic ions are atoms or molecules that carry a charge due to the loss or gain of electrons and are harmful to living organisms. In the context of this exercise, we focus on zinc (Zn), copper (Cu), lead (Pb), and mercury (Hg) ions. These metals can be particularly harmful to aquatic life, such as Atlantic salmon, when present in water at specific concentrations. When these ions are present at elevated levels, they can disrupt biological processes in organisms, leading to toxic effects.

• Zinc (Zn): While important for biological processes in trace amounts, high concentrations can cause harmful effects like enzyme inhibition and disruption of metabolic pathways in aquatic organisms.
• Copper (Cu): Essential for life, but as little as 0.01 mg/L can be toxic to fish, affecting their gills and resulting in respiratory problems.
• Lead (Pb): Known for its neurotoxicity, it can accumulate in biological systems harming both animals and humans over time.
• Mercury (Hg): Even in small quantities, mercury is highly toxic and can affect the central nervous system of aquatic organisms.

Understanding how these ions function and behave in the environment is crucial for assessing their risk and managing their concentrations in aquatic environments.

Environmental Chemistry

Environmental chemistry involves the study of chemical processes occurring in the environment; it includes natural processes and the effects of human activities. The exercise on toxic ions allows us to explore how chemicals interact within natural ecosystems, and why monitoring these levels is vital for protecting wildlife.
One of the primary concerns is the industrial and agricultural release of heavy metals into water systems. These toxins, once in the environment, can persist for a long time and enter the food chain. They can become concentrated in organisms through a process known as biomagnification, posing significant risks to humans consuming the affected organisms.

• Pollution Sources: These include mining activities, industrial discharge, and improper waste disposal. They can introduce toxic ions into aquatic environments.
• Impact on Aquatic Life: Elevated levels of metals like zinc, copper, lead, and mercury can lead to increased mortality rates, reduced growth, and reproductive harm in aquatic species.
• Remediation Efforts: Technologies like phytoremediation and ion exchange are being developed to reduce the concentrations of these metal ions in the environment.

Understanding environmental chemistry helps us develop better strategies for pollution control and environmental protection.

Unit Conversion

Unit conversion is a fundamental skill in chemistry that allows us to turn specific measurements into a different unit, facilitating better understanding and comparison of data. In this exercise, we convert molarity in millimoles (mM) to molarity in moles per liter (M), and then to milligrams per liter (mg/L), which is a more intuitive unit for expressing concentration levels in environmental samples.
Here's a step-by-step breakdown of vital unit conversion steps found in the exercise:

• Millimoles to Moles: To convert from millimoles to moles, you multiply by the conversion factor of 0.001 because 1 mM = 0.001 M.
• Moles to Milligrams/Liter (mg/L): Once the concentration is in moles (M), it's converted to mg/L by using the formula: \[\text{mg/L} = \text{M} \times \text{Molar mass} \times 1000\]Here, the molar mass of each ion (in g/mol) is used. This conversion lets us understand the concentration in practical terms.

Performing these conversions accurately is essential for making reliable, real-world assessments of chemical concentrations.

Concentration Calculations

Concentration calculations allow us to quantify the amount of a substance within a specific volume and are crucial for assessing the presence and potential impact of toxic ions in water.
The given exercise requires converting concentrations initially provided in millimoles per liter (mM) into milligrams per liter (mg/L), a more intuitive unit for environmental contexts, using each ion's molar mass.

• Identify the Initial Concentration: Start with the concentration value in mM for each ion. For example, mercury is given as \(5.00 \times 10^{-2}\) mM.
• Convert mM to M: As 1 mM is 0.001 M, convert the given values using this factor, giving mercury's molarity as \(5.00 \times 10^{-5}\) M.
• Convert M to mg/L: Multiply the molarity by the molar mass and by 1000 to convert to mg/L. For mercury, \(5.00 \times 10^{-5} \times 200.59 \times 1000 = 10.0295\) mg/L.

These calculations are pivotal for understanding the toxicity levels of different ions in real-world environments, ensuring pollutant levels are monitored and managed effectively.