Calculate the molality of each of the following aqueous solutions: (a) \(2.50 \mathrm{M} \mathrm{NaCl}\) solution (density of solution \(=1.08 \mathrm{~g} / \mathrm{mL}\) ), (b) 48.2 percent by mass KBr solution.

Understanding how to convert molarity (M) to molality (m) is essential for many chemistry calculations. Molarity is a concentration measure, defined as the number of moles of solute per liter of solution. Molality, on the other hand, is defined as the number of moles of solute per kilogram of solvent.

To convert molarity to molality, we need two key pieces of information: the density of the solution and the molar mass of the solute. The density allows us to find the mass of the solution, while the molar mass helps us find the mass of the solute.

The mass of the solution can be obtained by multiplying its volume (in liters, assuming we start with 1 L for simplicity) by its density. From there, we subtract the mass of the solute (calculated using molar mass and moles provided by molarity) to find the mass of the solvent. Dividing the number of moles of solute by the mass of the solvent (converted to kilograms) gives us molality.

Mass percent composition is a way to express the concentration of a solution or a mixture. It is the mass of a particular constituent divided by the total mass of the mixture or solution, multiplied by 100 to get a percentage.

For a solute in a solution, the mass percent tells us how many grams of the solute are present in every 100 grams of the solution. To find the molality from the mass percent, we first calculate the mass of the solute in grams by applying the mass percent to the total mass of the solution. We then calculate the moles of solute using its molar mass and divide by the mass of the solvent in kilograms.

As illustrated in the exercise, if you have a 48.2 percent by mass KBr solution, you know that 48.2 grams of KBr are in every 100 grams of the total solution. This information is pivotal and bridges the gap to calculating molality, which requires the knowledge of moles of solute and mass of solvent.

Molar mass is the mass of one mole of a substance and it is a bridge between the atomic or molecular scale and the everyday scale we measure in grams. It is expressed in grams per mole (g/mol).

The molar mass allows us to convert between the mass of a substance and the number of moles. For compounds like NaCl or KBr, the molar mass is found by adding the molar masses of the individual elements, which can be found on the periodic table.

In the context of the solutions at hand, knowing the molar mass of NaCl (58.44 g/mol) and KBr (119.0 g/mol) allows us to calculate the amount of moles present in a solution when we have the mass of the solute. These values are crucial for both molality and molarity calculations, as they enable chemists to quantify the amount of substances involved in a chemical solution.