Problem 24 - Chemistry The Science in Context

Question

Pesticides in the Environment Pesticide concentrations in the Rhine River between Germany and France between 1969 and 1975 averaged \(0.55 \mathrm{mg} / \mathrm{L}\) of hexachlorobenzene \(\left(\mathrm{C}_{6} \mathrm{Cl}_{6}\right), 0.06 \mathrm{mg} / \mathrm{L}\) of dieldrin \(\left(\mathrm{C}_{12} \mathrm{H}_{8} \mathrm{Cl}_{6} \mathrm{O}\right),\) and \(1.02 \mathrm{mg} / \mathrm{L}\) of hexachlorocyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{Cl}_{6}\right) .\) Express these concentrations in \(\mathrm{ppb}\) and in millimoles per liter.

Step-by-Step Solution

Answer

Answer: The concentrations of the pesticides in the Rhine River are as follows: - Hexachlorobenzene: \(550\, \mathrm{ppb}\) and \(1.93\, \mathrm{mmol/L}\) - Dieldrin: \(60\, \mathrm{ppb}\) and \(0.16\, \mathrm{mmol/L}\) - Hexachlorocyclohexane: \(1020\, \mathrm{ppb}\) and \(3.50\, \mathrm{mmol/L}\)

Step 1: Determine molecular weights of given compounds

Calculate the molecular weights of Hexachlorobenzene (C6Cl6), Dieldrin (C12H8Cl6O), and Hexachlorocyclohexane (C6H6Cl6) using the periodic table. Hexachlorobenzene: \(C_6Cl_6 = 6(12.01) + 6(35.45) = 72.06+212.7 = 284.76 \,\text{g/mol}\) Dieldrin: \(C_{12}H_8Cl_6O = 12(12.01) + 8(1.01) + 6(35.45) + 16.00\) \(= 144.12 + 8.08 + 212.7 + 16.00 = 380.9\, \text{g/mol}\) Hexachlorocyclohexane: \(C_6H_6Cl_6 = 6(12.01) + 6(1.01) + 6(35.45)\) = \(72.06 + 6.06 + 212.7 = 290.82\, \text{g/mol}\)

Step 2: Convert to ppb

parts per billion (ppb) is a unit of concentration defined as \(1 \mathrm{g}/10^9 \mathrm{g}\). To convert the given concentrations in mg/L, we will use the conversion factor \(1\, \mathrm{mg/L} = 10^3\, \mathrm{ppb}\). Hexachlorobenzene: \((0.55 \mathrm{mg/L})(10^3\, \mathrm{ppb}/1\, \mathrm{mg/L})=550\, \mathrm{ppb}\) Dieldrin: \((0.06\, \mathrm{mg/L})(10^3\, \mathrm{ppb}/1\, \mathrm{mg/L})=60\, \mathrm{ppb}\) Hexachlorocyclohexane: \((1.02\, \mathrm{mg/L})(10^3\, \mathrm{ppb}/1\, \mathrm{mg/L})=1020\, \mathrm{ppb}\)

Step 3: Convert to millimole per liter

To convert the given concentrations in mg/L to millimoles per liter (mmol/L), we first divide by the molecular weight of each compound and then multiply by \(10^3\) to change units from mol/L to mmol/L. Hexachlorobenzene: \((0.55\, \mathrm{mg/L}) (\frac{1\, \mathrm{mol}}{284.76\, \mathrm{mg}})(10^3\, \mathrm{mmol}/1\, \mathrm{mol}) = 1.93\, \mathrm{mmol/L}\) Dieldrin: \((0.06\, \mathrm{mg/L}) (\frac{1\, \mathrm{mol}}{380.9\, \mathrm{mg}})(10^3\, \mathrm{mmol}/1\, \mathrm{mol}) = 0.16\, \mathrm{mmol/L}\) Hexachlorocyclohexane: \((1.02\, \mathrm{mg/L}) (\frac{1\, \mathrm{mol}}{290.82\, \mathrm{mg}})(10^3\, \mathrm{mmol}/1\, \mathrm{mol}) = 3.50\, \mathrm{mmol/L}\) The concentration of pesticides in the Rhine River is: - Hexachlorobenzene: \(550\, \mathrm{ppb}\) and \(1.93\, \mathrm{mmol/L}\) - Dieldrin: \(60\, \mathrm{ppb}\) and \(0.16\, \mathrm{mmol/L}\) - Hexachlorocyclohexane: \(1020\, \mathrm{ppb}\) and \(3.50\, \mathrm{mmol/L}\)

Key Concepts

Molecular Weight Calculation

To find the molecular weight of a compound, you need to sum up the atomic weights of all the atoms in its chemical formula. For instance, Hexachlorobenzene, with the formula \(C_6Cl_6\), consists of six carbon atoms and six chlorine atoms. Using the periodic table, carbon (C) has an atomic weight of approximately 12.01 g/mol and chlorine (Cl) has an atomic weight of roughly 35.45 g/mol. Thus, the molecular weight is calculated as follows: \[6 \times 12.01 + 6 \times 35.45 = 284.76 \, \text{g/mol}\] Similarly, for Dieldrin \(C_{12}H_8Cl_6O\), you'll calculate the weight collectively of 12 carbons, 8 hydrogens, 6 chlorines, and one oxygen. Each element's atomic weight from the periodic table helps you add for a total like this:- Carbons: \(12 \times 12.01 = 144.12 \, \text{g/mol}\)- Hydrogens: \(8 \times 1.01 = 8.08 \, \text{g/mol}\)- Chlorines: \(6 \times 35.45 = 212.70 \, \text{g/mol}\)- Oxygen: \(1 \times 16.00 = 16.00 \, \text{g/mol}\) Add these all together to yield the molecular weight:\[144.12 + 8.08 + 212.70 + 16.00 = 380.90 \, \text{g/mol}\]Using these steps, you can find the molecular weight for any compound by using their chemical formula and the periodic table.

Parts Per Billion Conversion

The parts per billion (ppb) unit expresses very dilute concentrations of substances. It's incredibly useful in environmental studies where pollutant levels need to be identified in minute amounts. Essentially, 1 ppb equals 1 part of a substance in 1 billion parts of the solution. To translate a concentration from milligrams per liter (mg/L) into ppb, you apply a simple conversion factor because they both measure concentration by ratio of mass per volume of solution. For instance, if the concentration is 0.55 mg/L, to get the same concentration in ppb, you multiply by 1000 (since \(1 \, \text{mg/L} = 1000 \, \text{ppb}\)). Here’s what this looks like with Hexachlorobenzene: - \(0.55 \, \text{mg/L} \times 1000 = 550 \, \text{ppb}\)This conversion is straightforward, making it efficient for scientists to report and compare small concentrations across different substances or studies.

Pesticide Concentration

Pesticide concentration is an important measure in understanding environmental impacts. When pesticides are present in environments like rivers, their concentration might initially be reported in mg/L. However, to understand how many molecules are present, conversion to the number of moles, and then millimoles per liter (mmol/L), is quite critical:- First, use the calculated molecular weight.- Convert the mg/L concentration to moles by dividing the concentration by the molecular weight.For example, if Hexachlorobenzene is \(0.55 \mathrm{mg/L}\), divide by its molecular weight (284.76 g/mol): \[\left(0.55 \, \mathrm{mg/L}\right) \times \left(\frac{1 \, \mathrm{mol}}{284.76 \, \mathrm{mg}}\right) = 1.932 \, \mathrm{mmol/L}\]This millimolar concentration helps quantify the number of molecules present, which is significant for chemical assessments. Converting mg/L to mmol/L provides a more detailed understanding of the substance's presence in a solution and potential impacts on the ecosystem.