Question

Concentrated nitric acid is a \(70.0 \%\) solution of nitric acid, \(\mathrm{HNO}_{3},\) in water. The density of the solution is \(1.41 \mathrm{~g} / \mathrm{mL}\) at \(25^{\circ} \mathrm{C} .\) Calculate the molarity of nitric acid in this solution.

Short answer

The molarity of the nitric acid solution is approximately 15.66 M.

Step-by-step solution

Identify given data

First, extract the data given in the problem:- Nitric acid solution is 70.0% by mass.- Density of the solution is \(1.41 \, \text{g/mL}\).- We want to find the molarity of \(\text{HNO}_3\).

Assume a basis for calculation

Assume 100 g of the nitric acid solution to simplify calculations. This means 70 g is \(\text{HNO}_3\) (since it's 70% by mass), and the remaining 30 g is water.

Calculate the number of moles of \(\text{HNO}_3\)

The molar mass of \(\text{HNO}_3\) is \(1 (\text{H}) + 14 (\text{N}) + 48 (3 \times \text{O}) = 63 \, \text{g/mol}\). Calculate moles of \(\text{HNO}_3\) as follows: \[\text{moles of } \text{HNO}_3 = \frac{70 \, \text{g}}{63 \, \text{g/mol}} \approx 1.111 \, \text{moles}\]

Compute the volume of the solution

Use the density to find volume:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}} \Rightarrow \text{Volume} = \frac{100 \, \text{g}}{1.41 \, \text{g/mL}} \approx 70.92 \, \text{mL}\]Convert this to liters for molarity calculation: \[= 0.07092 \, \text{L}\]

Calculate molarity

Molarity \(M\) is given by the formula:\[M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]Substitute the values:\[M \approx \frac{1.111 \, \text{moles}}{0.07092 \, \text{L}} \approx 15.66 \, \text{M}\]

Key concepts

Concentration

Understanding concentration is key when dealing with solutions. Concentration tells us how much solute is present in a given amount of solvent or solution. It is a way to express how strong or weak a solution is. There are various ways to express concentration, such as:

• Mass percent, which is the mass of solute divided by the total mass of solution, multiplied by 100. In this exercise, it's given as 70% nitric acid, meaning 70 grams of nitric acid per 100 grams of solution.
• Molarity, another common way to express concentration, is the number of moles of solute per liter of solution. This exercise's goal is to find the molarity of nitric acid in the solution.

When calculating molarity, knowing either the volume or mass percent and the solution's density helps convert from one form of concentration to another.

Solution Density

Density of a solution is crucial because it connects mass with volume. Density is defined as the mass of the solution divided by its volume, often expressed in grams per milliliter (g/mL). In this problem, the density provided is 1.41 g/mL.

• Density helps us calculate volume. With the given mass percent, assume a mass (like 100 grams) to simplify calculations.
• Knowing the mass and density allows you to find the solution's volume, an important step in calculating molarity.

Thus, the relationship between mass and volume through density is a stepping stone to find the concentration of our solute in molarity units.

Nitric Acid

Nitric acid, ( ext{HNO}_3), is a highly corrosive mineral acid commonly used in laboratories. It has various applications, including:

• Diagenesis simulations - transforming sediment into rock in geology.
• Nitration processes - introducing ( ext{NO}_2) groups into organic compounds.
• Serve as a reagent in fertilizers and explosives production.

The molar mass of nitric acid is calculated by summing the atomic masses of its constituent elements: hydrogen (H) equals 1, nitrogen (N) is 14, and oxygen (O) is 16 multiplied by 3, totaling 63 g/mol. This information becomes crucial when calculating the number of moles required in molarity determination.

Mole Concept

The mole concept is a fundamental aspect of stoichiometry in chemistry, bridging the microscopic world of atoms with the macroscopic world we can observe.

• One mole of a substance contains Avogadro's number, ( ext{6.022} imes ext{10}^{23}), of particles (atoms, molecules, or ions).
• Moles connect mass to quantity. For instance, using nitric acid again, knowing its molar mass (63 g/mol) allows us to convert grams into moles, which is essential in calculating the molarity.

In this exercise, we take the grams of ( ext{HNO}_3) and convert it to moles. The concept helps us understand the proportionate relationship between the different components in a solution.