Concentrated nitric acid used in the laboratory work is \(68 \%\) nitric acid by mass in aqueous solution. What should be the molarity of such a sample of the acid if the density of solution is \(1.504 \mathrm{~g} \mathrm{~mL}^{-1}\) ?

When we talk about mass percentage, we refer to the proportion of a particular substance within a mixture or solution, expressed as a percentage of the total mass. It represents how much mass of the solute is present compared to the total mass of the solution. In our case, the concentrated nitric acid is 68% nitric acid by mass, meaning that for every 100 grams of the solution, 68 grams are pure nitric acid, and the remaining 32 grams are water and any other substances present.

To convert this percentage into a usable quantity for further calculations, it is common to assume a convenient volume of the solution, such as 100 mL in this example. While the volume can be arbitrary, it is chosen to simplify the math — yet it does not change the resulting molarity because molarity is a ratio that would remain constant regardless of the total amount of solution.

Solution density is the mass of the solution per unit volume. It is a crucial value when determining the amount of solute in a given volume of solution. Knowing the density allows us to convert volume to mass, which is a necessary step in many chemical calculations, particularly in converting mass percentage to the actual mass needed to find molarity.

In the example, the density of the nitric acid solution is given as 1.504 g/mL. This means that each milliliter of the solution weighs 1.504 grams. By multiplying this density by the volume of the solution we are considering, we obtain the total mass of the solution, which is then used alongside the mass percentage to find the mass of nitric acid present.

The concept of moles and molar mass is the cornerstone of chemical quantification. In chemistry, the mole is a unit that measures the amount of substance, while molar mass is the mass of one mole of that substance. The molar mass serves as a conversion factor between grams and moles and is especially helpful in stoichiometry.

The molar mass of nitric acid is approximately 63.01 g/mol, which tells us that one mole of nitric acid weighs about 63.01 grams. To find the number of moles from the mass of nitric acid obtained in our calculations, we use the formula:
\[\text{moles of nitric acid} = \frac{\text{mass of nitric acid}}{\text{molar mass of nitric acid}}\].

This step is fundamental because it allows us to transition from the mass-based perspective to one based on the number of particles or entities, which is amenable to many chemical equations and concentration measures like molarity.

The concentration of solutions is a measure of how much solute exists within a certain amount of solvent. Molarity, one form of expressing concentration, is defined as the number of moles of a solute per liter of solution (mol/L). It is an essential concept for scientists and chemists as it allows for the standardization of solutions for use in experiments and calculations.

To calculate molarity, we use the formula:
\[Molarity (M) = \frac{\text{number of moles of solute}}{\text{volume of solution in liters}}\].

By dividing the number of moles of nitric acid by the volume of the solution in liters, we obtain the molarity. This step finalizes our quest to understand the strength and composition of the nitric acid solution. Remember, the volume must be in liters to ensure that the molarity is correctly expressed in mol/L. By providing this standardized unit of concentration, scientists can effectively communicate and replicate results in a universally understood manner.