Question

The "normal" lead content in human blood is about 0.40 part per million (i.e., \(0.40 \mathrm{~g}\) 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 ppm?

Short answer

0.00372 grams of lead are in 6.0 x 10³ grams of blood at 0.62 ppm.

Step-by-step solution

Understanding Parts Per Million (ppm)

Parts per million (ppm) is a unit of measurement used to denote the concentration of a substance in another. Specifically, 1 ppm means 1 gram of solute per 1,000,000 grams of solution. In this problem, it means the grams of lead per one million grams of blood.

Identify Given Values

We are told that the lead content in the blood is 0.62 ppm. This corresponds to 0.62 grams of lead per 1,000,000 grams of blood. The mass of blood in the problem is given as \(6.0 \times 10^3\) grams.

Set Up the Proportion

The given ppm tells us the ratio of lead to blood. If 0.62 grams of lead is mixed with 1,000,000 grams of blood, then we need to find \(x\) grams of lead in \(6.0 \times 10^3\) grams of blood. We set up the proportion as follows: \(\frac{0.62}{1,000,000} = \frac{x}{6.0 \times 10^3}\).

Solve the Proportion

Cross-multiply and solve for \(x\): \(0.62 \times 6.0 \times 10^3 = x \times 1,000,000\). Simplifying this, we find \(x = \frac{0.62 \times 6.0 \times 10^3}{1,000,000}\).

Calculate and Simplify

Calculating, \(x = \frac{3.72 \times 10^3}{1,000,000}\) which simplifies to \(0.00372\) grams of lead.

Key concepts

Parts per million (ppm)

The concept of parts per million (ppm) is essential in understanding the concentration of substances, such as lead in blood. PPM is a unit of measurement that describes the amount of one substance in a million parts of another. For example, 1 ppm of lead in blood means there's 1 gram of lead in 1,000,000 grams of blood. It's generally used when dealing with very dilute concentrations, which are common in environmental and biological contexts.

To visualize this, imagine a large swimming pool. If you add just 1 gram of a substance to the whole pool, that's 1 ppm. This unit allows us to discuss very tiny traces of chemicals and elements as if they are in larger, measurable quantities. This way of describing concentrations is particularly helpful when determining health risks or compliance with safety standards.

Concentration calculation

Calculating concentration using ppm may sound tricky, but it becomes simple with a basic understanding of ratios. In this given problem, we have the lead level at 0.62 ppm, meaning there are 0.62 grams of lead per 1,000,000 grams of blood.

To find out how much lead is in a specific amount of blood, say 6,000 grams, we first understand what 0.62 ppm represents: a fixed proportion of the substance in another. This requires setting up an equation or proportion that links the two quantities. Once we have the setup, solving it will give us the concentration of lead in that smaller blood sample. This process of scaling down the ppm to a smaller sample size is a cornerstone of chemical calculations.

Proportion setup in chemistry

Setting up a proportion in chemistry is a way to compare two ratios and solve for an unknown quantity. In terms of this exercise, we are comparing the known concentration in ppm with the desired concentration in 6,000 grams of blood.

The proportion is like this: if 0.62 grams of lead is in 1,000,000 grams of blood, then how much lead (let's call this \(x\)) is in 6,000 grams of blood? The equation becomes \(\frac{0.62}{1,000,000} = \frac{x}{6,000}\).

Solving this with cross-multiplication gets rid of the denominators, making it simpler to find \(x\). This method allows you to solve for any unknown in similar problems, making it a versatile tool in chemistry.

Toxicity levels in blood

Understanding toxicity levels in blood is vital for diagnosing and preventing lead poisoning. In the scenario we are discussing, a lead concentration of 0.80 ppm or higher is deemed dangerous, suggesting potential health risks.

Keeping the concentration below these levels is crucial because even small increases beyond the norm can greatly impact health. Lead is a toxic metal that can affect nearly every organ and system in your body. Children and unborn fetuses are particularly vulnerable, which is why careful monitoring of these levels is required.

• Health problems can include developmental issues in children.
• In adults, it can lead to decreased kidney function and reproductive problems.
• Chronic exposure can increase blood pressure and cause damage to the nervous system.

So, maintaining awareness of toxicity levels is not just about understanding math but about safeguarding health.