Question

The maximum allowable concentration of lead in drinking water is 9.0 ppb. (a) Calculate the molarity of lead in a 9.0- ppb solution. (b) How many grams of lead are in a swimming pool containing 9.0 ppb lead in 60 \(\mathrm{m}^{3}\) of water?

Short answer

The molarity of lead in a 9.0 ppb lead solution is \(4.35 \times 10^{-12} M\). There are \(5.40 \times 10^{-3} g\) of lead in a swimming pool containing 9.0 ppb lead in 60 m³ of water.

Step-by-step solution

Understanding ppb and Molarity

ppb (parts per billion) is a unit used to express the concentration of a substance in a solution. 1 ppb means 1 part of solute per billion (10⁹) parts of solution. Molarity (M) is the concentration of a substance in a given volume of solution, expressed as moles of solute per liter of solution. To find molarity, we need to divide the moles of solute by the volume of the solution in liters.

Convert the concentration of lead from ppb to molarity

Given, the concentration of lead in drinking water is 9.0 ppb. To convert ppb to molarity we can use the formula: Molarity (M) = (ppb × 10⁻⁹) / (Molar mass of solute × Volume of solution in L) We are given the concentration of lead in ppb and need the molarity of lead (Pb). The molar mass of lead (Pb) is 207.2 g/mol. Since the volume of the solution is not provided, we assume 1 L of the solution. Hence, the molarity of lead in a 9.0 ppb solution can be calculated as: Molarity (M) = (9.0 × 10⁻⁹) / (207.2 × 1)

Calculate the molarity of lead in a 9.0 ppb solution

Molarity (M) = (9.0 × 10⁻⁹) / 207.2 = 4.35 × 10⁻¹² M The molarity of lead in a 9.0 ppb lead solution is 4.35 × 10⁻¹² M.

Calculate the grams of lead in the swimming pool

We are given the volume of water in the swimming pool as 60 m³, which is equivalent to 60,000 L (since 1 m³ = 1,000 L). Now, to find the number of moles of lead in 60,000 L of water, we can use the molarity formula: Moles of lead = Molarity × Volume of solution in L Moles of lead = (4.35 × 10⁻¹² M) × (60,000 L) Next, to find the grams of lead in 60,000 L of water, we can use the formula: grams of lead = moles of lead × molar mass of lead grams of lead = (4.35 × 10⁻¹² M × 60,000 L) × 207.2 g/mol

Find the grams of lead in the swimming pool

grams of lead = (4.35 × 10⁻¹² M × 60,000 L) × 207.2 g/mol = 5.40 × 10⁻³ g There are 5.40 × 10⁻³ grams of lead in the swimming pool containing 9.0 ppb lead in 60 m³ of water.

Key concepts

Parts per billion (ppb)

Parts per billion (ppb) is a measurement used to describe the concentration of one part of a substance in one billion parts of a solution. This unit is particularly useful when dealing with very small quantities of a solute. In the context of water quality, ppb helps us understand how much of a certain substance, like lead, is present in a large volume of water.
For instance, if you have a solution where there is 1 ppb of a solute, it means that in one billion parts of that solution, there is one part solute. This concept is relevant in scenarios where small concentrations matter a lot, such as when regulating toxins or pollutants in drinking water. Using ppb allows for easy expression and comprehension of extremely low but crucial concentrations.
When converting ppb to molarity, which is a more common unit in chemistry, it requires considering the molar mass of the solute and the volume of the solution. This conversion helps chemists understand how these trace amounts relate to moles per liter, a standard measure of concentration.

Lead concentration

Lead concentration in water is usually viewed in parts per billion due to its toxic nature at very low levels. Exposure to even small amounts of lead can be harmful, particularly to children, potentially causing developmental issues and other health impacts. Thus, the maximum allowable concentration of lead in drinking water is typically set at very low levels, often in the ppb range, to protect public health.
In our exercise, we focus specifically on a level of 9.0 ppb. From a practical point of view, knowing how to calculate the molarity from such a small concentration is vital. By converting ppb to molarity, it provides a way to use the concentration in chemical equations and for further calculations, such as determining the mass of lead in a given volume of water.
To convert lead concentration from ppb to molarity, the formula \[M = \frac{\text{ppb} \times 10^{-9}}{\text{Molar mass of lead} \times \text{Volume of solution in L}}\]is used, with lead having a molar mass of 207.2 g/mol, providing results in moles per liter (M).

Solution chemistry

Solution chemistry involves understanding the properties and interactions of components in a solution—like how solutes dissolve, react, and are measured. It is a fundamental area in chemistry that aids in processes ranging from industrial applications to environmental monitoring.
In solution chemistry, determining the concentration of a solute, such as lead, is crucial to understanding the solution's properties. Concentrations are key to predicting how substances will interact in a solution, calculated in terms of molarity or ppb depending on the quantities involved.
Knowing molarity, which is moles per liter, allows chemists to carry out calculations for reactions and ensure accurate component mixing. For example, understanding how many grams of lead are present in a specific amount of water helps in adhering to safety guidelines and regulations for environmental health.
In the exercise, converting 9.0 ppb of lead in water to molarity and then finding out how many grams of lead are dissolved in a large body of water (like a swimming pool) is a typical application of solution chemistry. This ensures both safety and compliance with standards or regulations regarding substances in water.