The "normal" lead content in human blood is about 0.40 part per million (that is, \(0.40 \mathrm{~g}\) of lead per million grams of blood). A value of 0.80 part per million (ppm) is considered to be dangerous. How many grams of lead are contained in \(6.0 \times 10^{3} \mathrm{~g}\) of blood (the amount in an average adult) if the lead content is \(0.62 \mathrm{ppm} ?\)

Understanding parts per million (ppm) is fundamental when dealing with concentrations in various scientific fields, including chemistry and environmental science. The term ppm is a way of denoting extremely dilute concentrations of substances. One ppm implies that in a mixture, one part of a substance is present per million parts of the mixture.

Let's break it down to simplify: if you had one million marbles and only one of those was blue while the rest were red, the blue marbles would represent one part per million of the entire collection. Translated into a scientific context, if we say there is 1 ppm of a substance in a solution, it means that in one million units of the solution, there is one unit of the substance. For instance, 1 ppm of lead in blood means that for every million grams of blood, there is one gram of lead.

When it comes to blood lead levels, these measurements are vital for assessing exposure to lead, a toxic metal that can lead to serious health problems. Blood lead levels are measured in ppm because the concentrations are usually quite low. The normal level of lead in human blood is about 0.40 ppm, meaning there are 0.40 grams of lead in one million grams of blood.

Exposure to higher concentrations, such as 0.80 ppm, is considered dangerous and can impair organ function, affect brain development, and lead to various other health issues. Therefore, knowing how to calculate the actual amount of lead in a given volume of blood is important for diagnosing and preventing lead poisoning.

In chemistry, understanding proportions is essential for a multitude of calculations, including those for concentrations. Proportions allow us to compare two ratios or fractions and find an unknown quantity when we have a set relationship. It operates on the principle that if two ratios are equal, their cross-products are also equal. This is very useful in ppm calculations where we need to find the amount of a substance in a certain weight or volume of solution based on a known concentration.

For instance, in our blood lead level problem, the known ratio is the ppm concentration (0.62 grams of lead in one million grams of blood), and we use it to find the amount of lead in a different quantity of blood (6000 grams in this case). Setting up a proportion helps us to directly scale the known concentration to the desired quantity of the solution or mixture.

When we solve for concentration, we are typically aiming to find out how much of a certain substance is present in a specific volume or mass of a mixture. The step-by-step solution provided makes it clear how to approach this using a proportion based on ppm.

The proportion in the example given reflects the relationship between the known lead content in ppm (0.62 grams of lead per million grams of blood) and the unknown quantity of lead in 6000 grams of blood. Cross-multiplication is the method used to solve this proportion. This involves multiplying the numerator of one fraction by the denominator of the other and setting these two products equal to each other to solve for the unknown quantity. Hence, we get our unknown 'x' to find out exactly how many grams of lead are in 6000 grams of blood based on the given concentration.