Question

You can purchase nitric acid in a concentrated form that is \(70.3 \% \mathrm{HNO}_{3}\) by mass and has a density of \(1.41 \mathrm{~g} / \mathrm{mL}\). Describe exactly how you would prepare \(1.15 \mathrm{~L}\) of \(0.100 \mathrm{M} \mathrm{HNO}_{3}\) from the concentrated solution.

Short answer

To prepare 1.15 L of 0.100 M HNO3, measure out 7.31 mL of the concentrated acid and dilute it with distilled water in a volumetric flask until the total volume is 1.15 L.

Step-by-step solution

Calculate the amount of solute needed

First, determine the amount of nitric acid (HNO3) needed in moles. This is found using the molarity equation: Molarity (M) = moles of solute / volume of solution (L). For a 0.100 M solution and a volume of 1.15 L, the moles of HNO3 required are: Moles = Molarity × Volume = 0.100 M × 1.15 L = 0.115 mol.

Determine mass of HNO3 needed

The molecular weight of HNO3 is 1(1.008) + 1(14.01) + 3(16.00) = 63.01 g/mol approximately. Using the number of moles calculated, the mass (g) of HNO3 needed is calculated as follows: Mass = moles × molar mass = 0.115 mol × 63.01 g/mol ≈ 7.25 g.

Calculate volume of concentrated HNO3 needed

With the mass of HNO3 determined and knowing the concentration of the solution by mass (70.3%), calculate the mass of the concentrated solution required. Total mass = (Mass of HNO3) / (Mass percent of HNO3) = 7.25 g / 0.703 ≈ 10.31 g. Next, convert this mass of solution to volume using the density of the concentrate: Volume = Mass / Density = 10.31 g / 1.41 g/mL ≈ 7.31 mL.

Dilute the concentrated HNO3 to the desired concentration

Add about 800 mL of distilled water to a 1.15 L volumetric flask. Then, carefully add the 7.31 mL of concentrated HNO3 to the flask. After that, fill the flask with distilled water until the bottom of the meniscus is at the 1.15 L mark. Mix thoroughly to ensure the acid is well-diluted.

Key concepts

Molarity Calculation

Understanding molarity calculation is crucial when preparing solutions in chemistry. Molarity, represented by the letter M, is defined as the number of moles of solute dissolved in one liter of solution. It is expressed as moles per liter (mol/L). To calculate molarity, use the formula:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution (L)}} \]
For example, to prepare a particular volume of diluted nitric acid with a specified molarity, first calculate the moles of nitric acid needed. If preparing 1.15 L of a 0.100 M solution, you would need \(0.100 \text{ mol/L} \times 1.15 \text{ L} = 0.115 \text{ mol} \) of nitric acid.

Solution Dilution

The process of solution dilution involves reducing the concentration of a solute in a solution, typically by adding solvent. To dilute a concentrated solution, you need to know the desired concentration and volume of the final solution. The Volume of the concentrated solution needed can be calculated by rearranging the molarity equation to solve for the Volume of stock solution. Remember to always add the concentrated solution to water, never the other way around, to prevent exothermic reactions that can cause splattering. After adding the calculated volume of concentrated acid, water is added until the total volume reaches the desired amount, which for our example is 1.15 L.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule. For example, nitric acid (\( \mathrm{HNO}_3 \)) has a molar mass of 1(1.008 g/mol for hydrogen) + 1(14.01 g/mol for nitrogen) + 3(16.00 g/mol for oxygen) = 63.01 g/mol. Knowing the molar mass allows us to convert between the moles of a substance and its mass, which is a step that's critical when preparing a solution from a concentrated acid.

Concentration by Mass

Concentration by mass, also known as mass percent, is a way of expressing the concentration of a solution by showing the mass of solute divided by the total mass of the solution, then multiplied by 100 to obtain a percentage. For a nitric acid solution that is 70.3% by mass, this means there are 70.3 grams of nitric acid in every 100 grams of solution. This measurement is important for calculating the actual amount of the concentrated acid needed to prepare a dilute solution. Based on the mass percent and the mass of the solute calculated from molarity, you can determine the mass of the concentrated solution required to get the necessary amount of solute.

Density of Solution

The density of a solution is the mass per unit volume, typically expressed in grams per milliliter (g/mL). It can be used to convert between the mass of a solution and its volume. When you're given that a nitric acid solution has a density of 1.41 g/mL, it means each milliliter of the solution weighs 1.41 grams. This property is utilised when we determine the volume of concentrated acid needed to prepare a diluted solution. After finding the required mass of the concentrated solution using the concentration by mass, the volume of the solution can be found by dividing the mass of the solution by its density. For instance, a solution with a mass of 10.31 grams and a density of 1.41 g/mL will have a volume of approximately 7.31 mL.