The density of an aqueous solution containing 10.0 percent ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) by mass is \(0.984 \mathrm{~g} / \mathrm{mL}\). (a) Calculate the molality of this solution. (b) Calculate its molarity. (c) What volume of the solution would contain 0.125 mole of ethanol?

In chemistry, molality is a measure of the concentration of a solute in a solution, which is defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality does not change with temperature because it's based on the mass of the solvent, rather than the volume of the solution.

To exemplify the calculation of molality, consider a solution containing ethanol. If you have 10 grams of ethanol in 90 grams of water, you first need to convert the mass of ethanol to moles by using its molar mass. After that, you'll also need to convert the mass of the solvent (water) to kilograms, as molality is measured in moles per kilogram.

Molarity is another central concept when it comes to describing solution concentration. It is defined as the number of moles of a solute per liter of solution. This unit of concentration varies with temperature because it involves volume, which can expand or contract with temperature changes.

When you're asked to calculate the molarity of an ethanol solution, you'll need to know both the number of moles of ethanol and the volume of the solution in liters. To find the volume, use the density of the solution. Once you have the required volume, you can divide the number of moles of ethanol by the volume to get the molarity.

The density of a chemical solution is a physical property that represents the mass of the solution per unit volume (typically grams per milliliter or kilograms per liter). Knowing the density is essential for translating between volumes and masses, which is often required in stoichiometry. Density plays a crucial role in calculating molarity, as seen in the previous example, where it helped determine the volume of the ethanol solution from its mass.

For substances that dissolve completely, their density can give insight into the concentration of the solution. The solution's density can help scientists determine how much solute is present compared to the solvent, shaping the solution's overall characteristics and behavior.

Stoichiometry is the section of chemistry that deals with the amounts of substances involved in reactions. It allows chemists to predict the quantities of reactants needed or products formed in a chemical reaction. When working with solutions, stoichiometry helps calculate how much of a solution is needed to react with a certain amount of another reactant or how much of a product will form.

For example, to find out the volume of an ethanol solution that contains a specific amount of ethanol, we apply stoichiometric principles. Knowing the molarity of the solution and the desired amount of ethanol in moles, we can easily calculate the volume of solution needed to obtain that amount of ethanol, demonstrating the practical utility of stoichiometry in solution-related calculations.