Problem 76 - Chemistry The Central Science

Question

(a) The EPA threshold for acceptable levels of lead ions in water is \(<15\) ppb. What is the molarity of an aqueous solution with a concentration of 15 ppb? (b) Concentrations of lead in the bloodstream are often quoted in units of \(\mu g / d L\) . Averaged over the entire country, the mean concentration of lead in the blood was measured to be 1.6 \(\mu g / d L\) in \(2008 .\) Express this concentration in ppb.

Step-by-Step Solution

Answer

(a) The molarity of an aqueous solution with a concentration of 15 ppb is approximately \(7.25 * 10^{-11}\) M. (b) The mean concentration of lead in the blood in 2008, given as 1.6 μg/dL, is equivalent to 16 ppb.

Step 1: Part (a) - Finding the molarity of a 15 ppb lead ion solution

Step 1: Convert ppb to μg/L 15 ppb = 15 μg/L Step 2: Convert μg to grams 15 μg = 15 * 10^(-6) g Step 3: Calculate the moles of lead ions Moles of lead ions = mass / molecular weight Moles of lead ions = (15 * 10^(-6) g) / (207.2 g/mol) Step 4: Calculate the molarity Molarity of lead ions = Moles of lead ions / Volume of the solution in liters Molarity of lead ions = (15 * 10^(-6) g) / (207.2 g/mol * 1 L) Molarity ≈ 7.25 * 10^(-11) M

Step 2: Part (b) - Converting the concentration of lead in the bloodstream to ppb

Step 1: Convert μg/dL to μg/L 1.6 μg/dL * (1 L / 10 dL) = 16 μg/L Step 2: Convert μg/L to ppb 16 μg/L = 16 ppb So, the concentration of lead in the bloodstream is 16 ppb.

Key Concepts

Molarity Calculation

The concept of molarity is essential for chemists and students alike, as it measures the concentration of a solute in a solution. Specifically, molarity is defined as the number of moles of solute per liter of solution. Calculating molarity is straightforward with the formula:
\[ M = \frac{n}{V} \] where \(M\) is the molarity, \(n\) is the number of moles of the solute, and \(V\) is the volume of the solution in liters. For lead ions in water, if we consider a mass of 15 µg in 1 L of water, and knowing that the atomic mass of lead is 207.2 g/mol, we can find the molarity using the steps provided in the example. It's crucial to convert all measurements to compatible units, such as converting micrograms to grams, to perform these calculations accurately.

ppb to Molarity Conversion

Parts per billion (ppb) is a concentration unit used to describe tiny amounts of a substance in another. It's commonly used for measuring pollutant levels in air, water, and body fluids. To convert from ppb to molarity, we first need to understand that 1 ppb is equivalent to 1 µg of solute per liter of solution. After this conversion, the path to molarity involves determining the mass of the substance in grams, then its amount in moles, and finally the molarity. For instance, with 15 ppb of lead, we convert this to micrograms per liter, then to grams, and divide by the molecular weight to find the moles of lead. Dividing this by the volume of the solution gives us the molarity.

Step-by-Step Conversion

• 15 ppb = 15 µg/L
• Convert the mass of lead from µg to g (since molar mass is in g/mol).
• Calculate the number of moles by dividing the mass in grams by the molar mass of lead.
• Finally, since the concentration is in a 1 L solution, the molarity is the number of moles per liter.

Blood Lead Concentration

The measurement of lead concentration in blood is a critical health metric, often expressed in micrograms per deciliter (µg/dL). Due to lead's toxic effects, even low levels in the bloodstream can be harmful. Converting this measure into ppb allows for comparing with standard limits, such as those set by environmental agencies, which are typically in ppb. The conversion is similar to the one we do for solutions: multiply the concentration in µg/dL by 10 to convert it to µg/L and then interpret this as ppb, since 1 µg/L is equivalent to 1 ppb. For example, a blood lead concentration of 1.6 µg/dL translates to 16 ppb, allowing for direct comparison with guidelines and demonstrating how concentrations in the bloodstream relate to regulatory standards.