\(\mathrm{AKNO}_{3}\) solution is made using \(88.4 \mathrm{~g}\) of \(\mathrm{KNO}_{3}\) and diluting to a total solution volume of \(1.50 \mathrm{~L}\). Calculate the molarity and mass percent of the solution. (Assume a density of \(1.05 \mathrm{~g} / \mathrm{mL}\) for the solution.)

Understanding mass percent is crucial for students studying chemistry, particularly when working with solutions. Mass percent, often expressed as weight/weight percentage, is a way of representing the concentration of a component in a mixture. It is the mass of the solute divided by the total mass of the solution (which includes both the solute and the solvent), multiplied by 100%.

Let's simplify the concept using an everyday example before returning to our exercise. Imagine you have a mixture of salt and water. If you have 20 grams of salt in 100 grams of water, the mass of the total solution is the sum of them, 120 grams. To find the mass percent of salt, we'd perform the following calculation: \( \frac{20g}{120g} \times 100\% = 16.67\% \).

In the exercise, the mass percent requires you to first determine the total mass of the solution. You do this by multiplying the density of the solution by its volume. If the solution's density is 1.05 g/mL and the volume is 1500 mL (1.50 L converted to mL), the total mass will be \(1.05 \frac{g}{mL} \times 1500 mL = 1575 g\). Then, knowing the mass of \(\mathrm{KNO}_{3}\) used (88.4 g), you would use the formula for mass percent: \( \frac{88.4g}{1575g} \times 100\% \). This would yield the mass percent of the solute in the solution, an essential value for many lab and industrial applications.

Solution concentration can be quantified in several ways, and one common method is molarity. Molarity is the number of moles of a solute per liter of solution, usually expressed as moles per liter (M). It is a measure of how 'concentrated' a solution is. The higher the molarity, the more particles of the solute are present in a given volume of solvent.

To get a clear grasp, consider molarity as a way to tell how strong your cup of coffee is; more coffee beans result in a stronger, or more 'molar', beverage.

In our exercise, calculating molarity involves several steps. The first step is to find the molar mass of \(\mathrm{KNO}_{3}\), then determine the number of moles of \(\mathrm{KNO}_{3}\) by dividing its mass by the molar mass. Once moles are found, you would divide them by the solution's volume in liters to obtain the molarity. If you have 0.59 moles of \(\mathrm{KNO}_{3}\) in 1.50 liters of solution, you divide \(0.59 \text{moles}\) by \(1.50 \text{liters}\) to get the molarity, which provides a vital quantitative description of the solution's concentration.

Molar mass is a property that connects the microscopic world of atoms and molecules to the macroscopic world we can measure. It is the mass of one mole of a substance (expressed in grams per mole), and it directly relates atomic mass units to grams, making it a bridge between atoms and the tangible amounts we work with in the lab.

For example, water \(\mathrm{H}_{2}\mathrm{O}\) has a molar mass approximately of 18 g/mol because each hydrogen (H) is about 1 g/mol and oxygen (O) is about 16 g/mol, adding up to 18 g/mol for one molecule of water.

In the exercise, the first step to calculate molarity is to find the molar mass of \(\mathrm{KNO}_{3}\). You do this by summing the atomic masses of potassium (K), nitrogen (N), and oxygen (O), which, according to the periodic table, are approximately 39, 14, and 16 g/mol, respectively. Since \(\mathrm{KNO}_{3}\) contains one atom of K and N each, and three atoms of O, its molar mass is \(39 + 14 + (3 \times 16) = 101 g/mol\). Knowing this allows you to relate the given mass of \(\mathrm{KNO}_{3}\) to the number of moles, providing the cornerstone for later calculations of both molarity and mass percent.