Problem 55 - Chemistry: The Central Science in SI Units, Global Edition

Question

Commercial aqueous nitric acid has a density of \(1.12 \mathrm{~g} / \mathrm{mL}\) and is 3.7 M. Calculate the percent \(\mathrm{HNO}_{3}\) by mass in the solution.

Step-by-Step Solution

Answer

The commercial aqueous nitric acid solution has approximately 20.8% HNO3 by mass.

Step 1: Calculate the mass of 1 L of the solution

To find the mass of 1 L of the solution, we will use the given density, which is \(1.12 \,\text{g}/\text{mL}\). Since there are 1000 mL in 1 L, we can calculate the mass as follows: Mass of 1 L of solution = Density × Volume = \(1.12\, \frac{\text{g}}{\text{mL}} × 1000\, \text{mL} = 1120\, \text{g}\)

Step 2: Calculate the number of moles of HNO3 in 1 L of the solution

We have the molarity of the solution (3.7 M), which gives us the number of moles of HNO3 per liter of the solution. So, in 1 L of the solution, there are: Number of moles of HNO3 = Molarity × Volume = \(3.7\, \text{M} × 1\, \text{L} = 3.7\, \text{moles}\)

Step 3: Calculate the mass of HNO3 in 1 L of the solution

Now, we need to find the molar mass of HNO3. The atomic masses of hydrogen (H), nitrogen (N), and oxygen (O) can be found in the periodic table, which are approximately 1, 14, and 16, respectively. So, the molar mass of HNO3 is: Molar mass of HNO3 = 1 (for H) + 14 (for N) + 16 × 3 (for three O atoms) = 63 \(\mathrm{g/mol}\) We can now use the molar mass and the number of moles of HNO3 to find the mass of HNO3 present in 1 L of the solution: Mass of HNO3 in 1 L of the solution = Number of moles × Molar mass = \(3.7\, \text{moles} × 63\, \frac{\text{g}}{\text{mol}} = 233.1\, \text{g}\)

Step 4: Calculate the percentage of HNO3 by mass

Finally, we can find the percentage of HNO3 by mass in the solution by dividing the mass of HNO3 by the mass of the solution and multiplying by 100: Percentage of HNO3 by mass = \(\frac{\text{Mass of HNO3}}{\text{Mass of 1 L of the solution}} × 100\% = \frac{233.1\, \text{g}}{1120\, \text{g}} × 100\% \approx 20.8\% \) Thus, the commercial aqueous nitric acid solution has approximately 20.8% HNO3 by mass.

Key Concepts

Density

Density is a key concept in chemistry that refers to how much mass is contained in a given volume. It is expressed as mass per unit volume, usually in units like grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). To determine the density of a solution, you divide its mass by its volume.
For example, if a solution has a density of 1.12 g/mL, this means that every milliliter of the solution weighs 1.12 grams. If you extend this to a larger volume, like 1 liter (1000 mL), it helps calculate the total mass of that volume.
This property allows chemists to relate different amounts of a substance, helping them convert between mass and volume, which is crucial for preparing solutions with precise concentrations.

Molarity

Molarity is a measure of the concentration of a solute in a solution, expressed as the number of moles of the solute present in one liter of the solution. It is denoted by the unit M (moles per liter).
For example, in the given problem, nitric acid (HNO3) has a molarity of 3.7 M, which means there are 3.7 moles of nitric acid in every liter of solution.
To find how many moles are in any volume, simply multiply the molarity by the volume in liters. Molarity provides a way to express the concentration of solutions, enabling scientists to replicate precise laboratory conditions.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It allows chemists to convert between the mass of a substance and the number of moles.
To calculate the molar mass, you sum up the atomic masses of all the atoms in a molecule. For nitric acid (HNO3), molar mass is calculated by adding the atomic masses of hydrogen (1 g/mol), nitrogen (14 g/mol), and oxygen (16 g/mol times 3 since there are three oxygen atoms).
This results in a molar mass of 63 g/mol for nitric acid, which is used to determine how much one mole of nitric acid weighs. Using molar mass is fundamental for stoichiometric calculations in chemistry, allowing the conversion between mass and moles in chemical reactions.

Solution Chemistry

Solution chemistry involves the study and practice of preparing and using solutions, which are homogeneous mixtures of substances. Solutions are characterized by solute (the dissolved substance) and solvent (the substance in which the solute is dissolved).
In solution chemistry, concentration is a critical concept—often measured by terms like molarity and percent composition by mass. The percent composition tells you the mass fraction of one component relative to the whole solution, which is crucial for determining how much of a substance is present relative to the mixture.
Understanding and manipulating solutions through concepts like solubility, dilution, and reaction extent allow chemists to create specific conditions for reactions to occur, quantify reaction outputs, and infer the properties of substances involved in reactions.