At \(20^{\circ} \mathrm{C}\), an aqueous solution of \(\mathrm{HNO}_{3}\) that is \(35.0 \% \mathrm{HNO}_{3}\) by mass has a density of \(1.21 \mathrm{~g} / \mathrm{mL}\). (a) How many grams of \(\mathrm{HNO}_{3}\) are present in \(1.00 \mathrm{~L}\) of this solution? (b) What volume of this solution will contain \(500 . \mathrm{g} \mathrm{HNO}_{3}\) ?

The percent by mass (also known as mass percent or weight percent) is a way of expressing the concentration of a component in a mixture or a solution. It is calculated by dividing the mass of the solute, which is the substance dissolved in the mixture, by the total mass of the solution and then multiplying by 100 to get a percentage. For example, in the given exercise, a solution with a concentration of 35.0% HNO3 by mass means that for every 100 g of solution, there are 35 g of nitric acid (HNO3).

Understanding percent by mass is especially important when preparing lab solutions or when studying chemistry concepts such as stoichiometry and molarity, as it provides a basis for more complex calculations like determining the amount of solute in a given volume of solution.

Density is defined as mass per unit volume and is expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³) for SI units. In the context of solution concentration calculations, knowing the density of a solution allows you to convert between mass and volume, enabling you to find out how much solute is present in a particular volume of solution or how much volume is needed for a certain mass of solute. In the given exercise, the density of the HNO3 solution is 1.21 g/mL, which means each milliliter of the solution has a mass of 1.21 g. To find the mass of a liter (1000 mL) of this solution, you would multiply the density by the volume (in mL), illustrating the relationship between these properties.

Stoichiometry is the aspect of chemistry that deals with the quantitative relationships that the substances undergoing a chemical reaction follow based on the balanced chemical equations. It involves calculations of the masses, volumes, and moles of reactants and products. While stoichiometry was not directly applied in the given exercise, understanding it is crucial when proceeding with chemical reactions where HNO3 would be a reactant or product. It allows us to predict how much of each substance is needed or produced in a reaction. For instance, if a certain chemical process required 500 g of HNO3, stoichiometry would help us calculate the mass of other reactants needed for the reaction to occur completely.

Molarity is a measure of concentration that expresses the number of moles of a solute per liter of solution. It is denoted by the unit moles per liter (M). To calculate molarity, you need to know the amount of solute (in moles) and the volume of the solution (in liters). Molarity is frequently used in chemistry labs and calculations since it directly relates to the number of solute particles in a given volume of solution, which is essential for predicting the behavior of solutions in chemical reactions. Although our exercise does not specifically require calculating molarity, understanding how to convert mass percent into molarity can be crucial for applications in which volume-based concentration is more relevant than mass-based concentration.