Question

In the spring of \(1984,\) concern arose over the presence of ethylene dibromide, or EDB, in grains and cereals. EDB has the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Br}_{2}\) and until 1984 was commonly used as a plant fumigant. The federal limit for \(\mathrm{EDB}\) in finished cereal products is 30.0 parts per billion (ppb), where \(1.0 \mathrm{ppb}=\) \(1.0 \times 10^{-9} \mathrm{g}\) of \(\mathrm{EDB}\) for every 1.0 \(\mathrm{g}\) of sample. How many molecules of EDB are in 1.0 lb of flour if 30.0 ppb of EDB is present?

Short answer

There are approximately \(6.4 \times 10^{15}\) EDB molecules in 1.0 lb of flour when 30.0 ppb of EDB is present.

Step-by-step solution

Convert the weight of flour from lb to grams

1 lb is equal to 454 grams. So, 1.0 lb of flour is equivalent to 454.0 grams.

Calculate the weight of EDB in 1.0 g of flour

30.0 ppb means there are \(1.0 \times 10^{-9}\) g of EDB per 1.0 g of sample. Therefore, for 1.0 g of flour, there are \(30.0 \times (1.0 \times 10^{-9})\) g of EDB.

Determine the total weight of EDB in the entire sample of flour

Now we need to find out the total weight of EDB in the given flour sample. Since we have 454.0 grams of flour, the total weight of EDB will be: \(EDB_{total} = 454.0 \times 30.0 \times (1.0 \times 10^{-9})\) g

Find the number of EDB moles using its molecular weight

The molecular formula of EDB is \(C_2H_4Br_2\). Using the molecular weights of carbon (C), hydrogen (H), and bromine (Br), we can calculate the molecular weight of EDB: Molecular weight of EDB = \((2 \times 12.01) + (4 \times 1.007) + (2 \times 79.90)\) g/mol Now, we can calculate the number of moles of EDB present in the flour sample using the formula: Moles of EDB = \(\frac{EDB_{total}}{Molecular\:weight\:of\:EDB}\)

Calculate the number of EDB molecules using Avogadro's number

Avogadro's number (N) is approximately \(6.022 \times 10^{23}\). We can calculate the number of EDB molecules using the formula: Number of EDB molecules = Moles of EDB × Avogadro's number After performing all the calculations, you will get the number of EDB molecules in the given sample of flour.

Key concepts

Avogadro's Number

Avogadro's number, a fundamental constant in chemistry, is the key to relating mass in grams to the number of molecules or atoms in a substance. It is approximately equal to \(6.022 \times 10^{23}\), which means that one mole of any substance contains this many entities, be they atoms, molecules, or formula units.
For example, in the case of EDB molecules in flour, once you determine how many moles of EDB you have, you multiply those moles by Avogadro's number to find out the total number of individual EDB molecules. This transformation from a macro to micro perspective is critical for understanding molecular amounts in chemical calculations.

Molecular Weight

Molecular weight, also known as molecular mass, is the sum of the atomic weights of all atoms in a molecule. It is measured in atomic mass units (amu) or grams per mole (g/mol). To determine the molecular weight of ethylene dibromide (EDB), which has a chemical formula of \(C_2H_4Br_2\), you must add together the atomic weights of each element in the compound:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.007 g/mol
• Bromine (Br): 79.90 g/mol

In EDB, you have 2 carbon atoms, 4 hydrogen atoms, and 2 bromine atoms. Calculating the molecular weight involves adding \((2 \times 12.01) + (4 \times 1.007) + (2 \times 79.90)\). This value is crucial for converting grams of EDB to moles, facilitating further calculations.

Parts Per Billion (ppb)

Parts per billion (ppb) is a unit of measurement used to express extremely dilute concentrations of substances. It is defined as one part of a substance in a billion parts of a solution or mixture.
In the context of the exercise, if EDB is present at 30.0 ppb, it means there are \(30.0 \times 10^{-9}\) grams of EDB per gram of flour. This conversion makes it simpler to calculate the total mass of EDB in a larger sample, such as 454 grams of flour, by multiplying the ppb level with the sample's mass.

Chemical Contamination

Chemical contamination refers to the unintended presence of chemicals in places where they do not naturally occur. In the case of the EDB issue in 1984, EDB was used as a plant fumigant and ended up contaminating cereal grains. Chemical contamination is particularly concerning when substances are toxic or hazardous to health.
The exercise's calculation of EDB molecules in flour is not just about the numbers. It reflects real-world concerns over food safety and compliance with federal limits on chemical residues, emphasizing the importance of monitoring and controlling chemical exposure in consumable goods.

Unit Conversion

Unit conversion is a fundamental skill in chemistry, allowing you to translate between different measurement systems or scales. In the given exercise, there are several unit conversions:

• Converting pounds to grams: 1.0 lb equals 454 grams.
• Translating ppb to a total mass of contamination: 30.0 ppb is translated into parts per gram of the flour, then applied over the entire 454 grams.

Each conversion step ensures that calculations are consistent, precise, and dimensionally accurate, which is crucial in any kind of quantitative chemical analysis.