Problem 6 - Chemistry: Principles and Reactions

Question

Lead is a poisonous metal that especially affects children because they retain a larger fraction of lead than adults do. Lead levels of \(0.250 \mathrm{ppm}\) in a child cause delayed cognitive development. How many moles of lead present in \(1.00 \mathrm{~g}\) of a child's blood would \(0.250 \mathrm{ppm}\) represent?

Step-by-Step Solution

Answer

Moles of lead = (1.00 g x (0.250/1000000))/207.2 g/mol = 1.2077 × 10^-6 mol Thus, there are 1.2077 × 10^-6 moles of lead present in 1.00 g of a child's blood with a concentration of 0.250 ppm.

Step 1: Convert ppm to mass fraction

Parts per million (ppm) is a unit of concentration that indicates 1 part in 1000000 parts. We will convert the given lead concentration (0.250 ppm) to mass fraction for further calculations. 1 ppm = 1 part in 1000000 parts = 1/1000000 So, 0.250 ppm = 0.250/1000000

Step 2: Find the mass of lead in 1.00 g of blood

Now that we have the mass fraction of lead in the blood, we will find the mass of lead in 1.00 g of blood. Mass of lead = Mass of blood x Mass fraction of lead Mass of lead = 1.00 g x (0.250/1000000)

Step 3: Convert mass to moles using the molar mass of lead

To find the moles of lead, we will divide the mass of lead by the molar mass of lead. The molar mass of lead (Pb) is 207.2 g/mol. Moles of lead = Mass of lead / Molar mass of lead Moles of lead = (1.00 g x (0.250/1000000))/207.2 g/mol Now, calculate the moles of lead.

Key Concepts

Cognitive Development

Lead toxicity has a significant impact on cognitive development, especially in children. Cognitive development refers to the growth and change in a child's ability to think, learn, and assess their environment. This includes critical processes such as memorization, problem-solving, and communication skills. Young children are particularly vulnerable to lead exposure because their bodies absorb and retain lead more easily than adults. This can lead to harmful effects on their developing brain.
Research shows that even low levels of lead exposure, such as 0.250 parts per million, can cause delayed cognitive development. These delays might manifest as learning disabilities, attention deficits, and behavioral issues. Affected children might have trouble with basic developmental milestones such as language skills, comprehension, and even physical coordination.
It is vital to monitor and minimize lead exposure to protect the delicate process of cognitive development in children. By doing so, we improve their potential for future academic and life success.

Parts Per Million

Understanding parts per million (ppm) is crucial when dealing with very granular measurements. Ppm is used to express dilute concentrations and is especially relevant in environmental and health sciences. It describes one unit of substance dispersed within a million units of another substance.
Essentially, 1 ppm means that for every million parts of a mixture, there is one part of the variable of interest. In the context of the exercise, this means that 0.250 ppm indicates 0.250 parts of lead per 1 million parts of blood.

• To convert ppm to a mass fraction, the calculation involves dividing by 1,000,000.
• In simpler terms, 0.250 ppm is expressed as 0.250/1,000,000.

This small fractional amount illustrates how even tiny concentrations of harmful substances like lead can be detected and quantified in medical and environmental tests. Accurate understanding and manipulation of ppm values are essential in scenarios where precise dosage and exposure limits are critical.

Molar Mass

The molar mass is an essential basic concept in chemistry that connects the microscopic world of atoms to the macroscopic world of grams and moles. Molar mass represents the mass of one mole of a given substance and is expressed in grams per mole (g/mol). This value is calculated by summing the masses of all the atoms in a molecule from their atomic weights on the periodic table.
For lead (Pb), the molar mass is 207.2 g/mol. Knowing this allows you to convert between the mass of a substance and the amount in moles, which is a more practical unit for stoichiometry and chemical reactions.

• In practice, to find the moles of lead present, you take the mass of lead and divide it by its molar mass.
• This calculation can reveal how many lead atoms are present in a sample, which is crucial for assessing exposure levels.

The precise use of molar mass is fundamental in laboratories, ensuring safety protocols are adhered to and calculations reflect the actual amounts of substances involved.