Benzene is a carcinogenic (cancer-causing) compound. A benzene-contaminated water sample contains \(0.000037 \%\) benzene by mass. What volume of the water in liters contains \(175 \mathrm{mg}\) of benzene? (Assume that the density of the solution is \(1.0 \mathrm{~g} / \mathrm{mL}\).)

When dealing with chemical concentrations, it's common to see percentages used to indicate the amount of substance present in a solution. However, to perform calculations involving concentrations, converting percentages to decimals is often necessary. This conversion is quite simple: divide the percentage by 100. For instance, if you have a sample containing 0.000037% benzene, you would divide 0.000037 by 100, yielding a decimal value of 0.00000037. This conversion is crucial in calculations because it allows you to use the proportion of the solute (benzene in our example) in further mathematical operations.

Converting mass to volume is a common task in chemistry, especially when dealing with solutions. The density of a substance is the key to this conversion. Density is defined as the mass per unit volume and is usually expressed in grams per milliliter (g/mL) or kilograms per liter (kg/L). To convert mass to volume, you simply divide the mass by the density. In the context of the exercise, once you know the mass of water needed to contain 175 mg of benzene, you use the density of water, which is 1.0 g/mL, to find its volume. Since the density is 1 g/mL, the mass in grams is numerically equivalent to the volume in milliliters. Remember, for water solutions, the density is often close to 1 g/mL, making the conversion between mass and volume particularly straightforward.

Preparing a chemical solution with a desired concentration involves measuring the solute and solvent accurately and mixing them thoroughly. In the given problem, we calculate the volume of water needed to dissolve a specific mass of benzene to prepare a contaminated water sample. The concentration of benzene is already given, which guides us in determining the proportion of water required according to the concentration. This step is essential in solution preparation in a laboratory setting, where precise concentrations are critical for experiments and for industrial applications where specific dosages are needed for the desired effect.

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. In this exercise, stoichiometry principles are applied in a slightly different manner—no reaction is happening, but we’re looking at the proportional relationship between benzene and water in the solution. By using the concept of stoichiometry, you can determine how much mass of a substance corresponds to a certain volume by knowing its concentration. Stoichiometry is not only limited to reactions but is also a powerful tool for solving problems involving the preparation and dilution of solutions.