Question

Polychlorinated biphenyls (PCBs) are absorbed by our bodies from some of the foods we eat. If a \(65-\mathrm{kg}\) male is determined to have a PCB level of \(190 \mathrm{ppb}\), what is the mass (in grams) of PCBs in his body?

Short answer

The mass of PCBs in the man's body is approximately 0.01235 grams.

Step-by-step solution

Understanding Units

Determine the conversion factor from ppb to micrograms per kilogram. 1 ppb equates to 1 µg/kg.

Calculate micrograms

Using the conversion factor and the given PPB level, find out the amount of PCBs in micrograms. As we know, PCB level is \(190 \mathrm{ppb}\) or \(190 \mathrm{µg/kg}\). Therefore, for a \(65-\mathrm{kg}\) male, the total amount of PCBs will be \(190 \mathrm{µg/kg} \times 65 \mathrm{kg} = 12350 \mathrm{µg}\)

Convert to grams

Now that we have the total amount of PCBs in micrograms, the last step is to convert this to grams. As we know that \(1 \mathrm{g} = 1000000 \mathrm{µg}\) , so the mass of PCBs in the body is \(\frac{12350 \mathrm{µg}}{1000000} = 0.01235 \mathrm{g}\)

Key concepts

Polychlorinated Biphenyls

Polychlorinated biphenyls, commonly abbreviated as PCBs, are synthetic chemicals comprised of carbon, hydrogen, and chlorine atoms. These compounds were once widely utilized in various industrial applications due to their chemical stability and insulating properties. However, PCBs are now known to be highly toxic environmental pollutants. When they enter the body, they tend to accumulate in fatty tissues.
PCBs can infiltrate the human body through ingestion, inhalation, or dermal contact with contaminated environmental sources. Over time, they can lead to serious health concerns, including cancer and adverse effects on the immune, reproductive, nervous, and endocrine systems.
Understanding the characteristics and potential risks associated with PCBs is crucial for maintaining public health and implementing proper safety regulations.

Unit Conversion

In chemistry calculations, precise unit conversion is essential for obtaining accurate results. This exercise involves converting PCB concentration from parts per billion (ppb) to micrograms per kilogram (µg/kg).

• 1 ppb is equivalent to 1 µg/kg. That means if a concentration is given in ppb, you can directly say the same number in µg/kg.

Conversion skills allow one to translate measurements into more convenient or required units while maintaining the integrity of the data used in chemical and biological processes. This ensures clarity and uniformity in scientific analyses and communications.

Mass Calculation

Calculating mass requires a clear understanding of both the concentration and the total volume or mass of the subject involved. In this exercise involving PCBs, we start by determining the PCB concentration in a 65-kg human.
Given a PCB level of 190 ppb, this translates directly to 190 µg/kg due to a unit conversion (Step 1). Using this information:

• Multiply 190 µg/kg by 65 kg to obtain the total mass in micrograms: 12350 µg.
• To convert micrograms to grams, use the conversion where 1 gram equals 1,000,000 micrograms. Thus, 12350 µg becomes 0.01235 g when divided by 1,000,000.

Through careful calculations, we find that the mass of PCBs in the person's body is approximately 0.01235 grams. Such mass calculations are fundamental in dose assessments, environmental modeling, and biomedical research.