Question

Commercial aqueous nitric acid has a density of \(1.42 \mathrm{~g} / \mathrm{mL}\) and is 16 M. Calculate the percent \(\mathrm{HNO}_{3}\) by mass in the solution.

Short answer

The percent HNO3 by mass in the commercial aqueous nitric acid solution is approximately 71%.

Step-by-step solution

Calculate the mass of the solution

To do this, we first need the density of the solution, which is given as 1.42 g/mL. Since there are 1000 mL in 1 L, we can determine the mass of the solution by multiplying the density by 1000 mL. \(Mass_{solution} = Density * Volume\) \(Mass_{solution} = 1.42 \frac{g}{mL} * 1000 mL\) \(Mass_{solution} = 1420 g\) So, the mass of 1L of the solution is 1420 g. #Step 2: Calculate the mass of HNO3 in 1L of the solution#

Calculate the mass of HNO3

We are given the molarity of HNO3 as 16 M. This means there are 16 moles of HNO3 in 1L of the solution. To calculate the mass of HNO3, we need the molar mass of HNO3, which is approximately 63 g/mol. \(Mass_{HNO3} = Molarity * Molar \,mass * Volume\) \(Mass_{HNO3} = 16 mol/L * 63 \frac{g}{mol} * 1L\) \(Mass_{HNO3} = 1008 g\) So, there are 1008 g of HNO3 in 1L of the solution. #Step 3: Calculate the percent HNO3 by mass in the solution#

Calculate the percent HNO3 by mass

Now that we have the mass of HNO3 and the mass of the solution, we can determine the percent HNO3 by mass in the solution. Percent HNO3 by mass = \(\frac{Mass_{HNO3}}{Mass_{solution}} * 100\%\) Percent HNO3 by mass = \(\frac{1008 g}{1420 g} * 100\%\) Percent HNO3 by mass ≈ 71% Therefore, the percent HNO3 by mass in the commercial aqueous nitric acid solution is approximately 71%.

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution. In chemistry, it is typically used to express the number of moles of a solute per liter of solution. It is denoted by the letter 'M' and is calculated using the formula:

\[ Molarity = \frac{moles\ of\ solute}{liters\ of\ solution} \]
In the context of the exercise, molarity plays a crucial role in determining the amount of substance present in the solution. As shown in the step-by-step solution, the commercial aqueous nitric acid has a molarity of 16 M, meaning it contains 16 moles of nitric acid per liter. Understanding molarity allows students to calculate the mass of a solute in a solution when they know its molar mass, thus making it an essential concept in quantitative analysis and chemical preparation.

Molar Mass

Molar mass is the mass of one mole of a substance, usually measured in grams per mole (g/mol). It is a fundamental concept in chemistry because it acts as a conversion factor between grams and moles, allowing chemists to count entities (atoms, molecules, ions) by weighing. Each element's molar mass is found on the periodic table, while the molar mass of a compound is the sum of the molar masses of its constituent elements.

For example, in the given exercise, the molar mass of nitric acid (\(HNO_3\)) is approximately 63 g/mol. This value is critical in determining the mass of nitric acid in a given volume of solution when its molarity is known.

Aqueous Solution Chemistry

Aqueous solution chemistry involves studying substances dissolved in water — the solvent that constitutes the 'aqueous' aspect. Solutions form when solute molecules or ions disperse throughout the solvent. The physical properties, such as density, boiling point, and freezing point, can change compared to the pure solvent.

Density, particularly, is important as it relates mass to volume. In our exercise, the solution has a density of 1.42 g/mL. With density information and knowing the volume of the solution, we can calculate its mass, which is essential for finding the concentration of solutes in terms of mass percentage.

Stoichiometry

Stoichiometry is the aspect of chemistry that relates to the calculation of reactants and products in chemical reactions. It is also used in determining the relationships between different compounds in a reaction. The basic principles of stoichiometry apply to the quantities of substances, often described by mole ratios as determined by the balanced chemical equations, but also extended to include mass, volume, and concentrations.

In the exercise given, stoichiometry helps to connect the molar mass of nitric acid and its molarity to determine the mass percentage of the same acid in solution. This multidisciplinary approach demonstrates the interconnectedness of chemical concepts, showing that a good grasp of stoichiometry is vital for understanding and solving various problems in chemistry.