A saturated solution of \(\mathrm{NaCl}\) contains 36 \(\mathrm{g}\) \(\mathrm{NaCl}\) in 114 \(\mathrm{mL}\) of solution. What is the molarity of the solution?

Understanding a saturated solution is crucial when dealing with chemical solutions. Imagine trying to dissolve sugar in a cup of tea; there's a point where no more sugar will dissolve, no matter how much you stir. This state is what we call a saturated solution. It's the maximum concentration of solute that a solvent can hold at a given temperature and pressure. Beyond this point, any added solute will remain undissolved, often forming crystals at the bottom of the container.

In the case of our textbook exercise, we speak of a saturated solution of sodium chloride (NaCl), also known as table salt, in water. Knowing that we have a saturated solution is important because it implies we are working at the solute's solubility limit. Different solutes have different solubility limits, which can be altered by changing the temperature or the solvent itself.

When chemists work with chemical reactions, they need a way to quantitatively describe the amounts of substances involved. That's where the concept of 'moles' comes into play. A mole is a unit that measures the amount of substance, or more specifically, the number of particles, such as atoms or molecules. One mole is defined as approximately 6.022 x 10²³ particles, known as Avogadro's number.

To convert grams to moles, as we see in our exercise, you'll need the molar mass of the compound you're working with. The molar mass is the weight of one mole of a substance and is usually expressed in grams per mole (g/mol). By dividing the mass of the substance by its molar mass, you get the number of moles, which is fundamental for calculating concentrations and reacting substances in stoichiometry.

The concentration of a solution tells us how much solute is dissolved in a specific amount of solvent. It's a measure of the 'strength' or 'intensity' of the solution. Molarity is one of the most common units used to express concentration, especially in chemistry. It's defined as the number of moles of solute per liter of solution (mol/L).

Why is this important? Knowing the concentration of solutions allows chemists to predict how substances will react with one another. It's crucial for creating solutions with the precise properties needed for specific chemical reactions, such as those in medical formulations or industrial processes. The exercise you are working on uses molarity as a way to quantify the concentration of the NaCl solution, which demonstrates its direct application in a real-world scenario.

The molar mass of a compound is its weight per mole. In our case, we're interested in the molar mass of sodium chloride (NaCl). Sodium chloride is made up of one sodium atom and one chloride atom. By adding the atomic weights of sodium (approximately 22.99 g/mol) and chlorine (approximately 35.45 g/mol), we find that the molar mass of NaCl is around 58.44 g/mol.

This value is vital for calculations in chemistry. For example, in the exercise, the molar mass of NaCl allows us to convert the mass of NaCl into moles, which is the first step in determining the molarity of the solution. Being precise with molar mass values is crucial because a small error in this value can significantly affect the outcome of mole conversion and, consequently, the accuracy of the entire solution's concentration.