Lead is a toxic metal that affects the central nervous system. \(\mathrm{APb}\)-contaminated water sample contains \(0.0011 \% \mathrm{~Pb}\) by mass. What volume of the water in milliliters contains \(115 \mathrm{mg}\) of \(\mathrm{Pb}\) ? (Assume that the density of the solution is \(1.0 \mathrm{~g} / \mathrm{mL}\).)

Molar concentration, also known as molarity, is a way of expressing the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters. Molarity is usually denoted by the symbol 'M' and has units of moles per liter ((mol/L)).

To understand this concept using the context of the exercise, consider that the mass of lead can be converted to moles. Since the molar mass of lead ((Pb)) is approximately 207.2 grams per mole, you can calculate the number of moles of lead in the sample and then express that as a molarity given the volume in which these moles are dissolved. Remember that in order to use molarity in calculations, you often need to know the volume of the solution, which brings us to the next concept, solution concentration.

Mass percent, also known as mass/mass percentage, is a concentration term describing the mass of solute as a percentage of the total mass of the solution. It is calculated by dividing the mass of the solute by the total mass of the solution and then multiplying by 100 to get a percentage.

In our exercise, the mass percent of lead in the water sample is given as 0.0011%. This information allows us to establish a direct relationship between the mass of the water sample and the mass of the dissolved lead. As demonstrated in the step-by-step solution, this ratio is crucial to setting up a proportion that can be used to find the volume of water containing a specific mass of lead.

Chemical calculations are an essential part of stoichiometry, which involves the quantitative aspects of chemical reactions and compounds. This includes calculations involving molar mass, solution concentration, conversions between mass and moles, and using balanced chemical equations to predict the amounts of reactants or products.

In the textbook exercise, you must use a series of chemical calculations to find the volume that contains a certain mass of lead. This requires converting mass percent to a usable amount (milligrams in this case), then using proportions to relate the mass of lead to the volume of water. These types of calculations are foundational for both laboratory work and understanding chemical properties in a variety of contexts.

The concentration of a solution indicates the amount of solute present in a given quantity of solvent or solution. There are various ways to express this, including molarity, molality, mass percent, and parts per million (ppm). Each unit of concentration serves a different situation and provides particular insights about the solution.

Returning to our water sample from the exercise, knowing the mass percent of lead helps to illustrate how dilute the toxic metal is within the solution. To find the exact volume of water containing 115 mg of lead, we used the given mass percent, demonstrating a practical application of understanding solution concentration. This knowledge is paramount in areas like environmental chemistry, where the concentration of pollutants must be measured and managed to ensure safety.