Question

A solution was prepared by mixing 50.00 \(\mathrm{mL}\) of 0.100 \(\mathrm{M}\) \(\mathrm{HNO}_{3}\) and 100.00 \(\mathrm{mL}\) of 0.200 \(\mathrm{M} \mathrm{HNO}_{3}\) . Calculate the molarity of the final solution of nitric acid.

Short answer

The molarity of the final solution of nitric acid is \(0.167 \ \mathrm{M}\).

Step-by-step solution

Calculate moles of Nitric Acid from both solutions

First, we will calculate the moles of nitric acid in each solution using the given volumes and molarities. From Solution 1 (50.00 mL of 0.100 M HNO3): Moles of \(\mathrm{HNO}_{3}\) = Molarity * Volume Moles of \(\mathrm{HNO}_{3}\) = 0.100 M * 0.050 L (Note: We converted mL to L by dividing by 1000) Moles of \(\mathrm{HNO}_{3}\) (1) = 0.005 mol From Solution 2 (100.00 mL of 0.200 M HNO3): Moles of \(\mathrm{HNO}_{3}\) = Molarity * Volume Moles of \(\mathrm{HNO}_{3}\) = 0.200 M * 0.100 L (Note: We converted mL to L by dividing by 1000) Moles of \(\mathrm{HNO}_{3}\) (2) = 0.020 mol

Calculate the Total Moles of Nitric Acid

Now, we will combine the moles of \(\mathrm{HNO}_{3}\) from both solutions to find the total moles of nitric acid in the final solution. Total moles of \(\mathrm{HNO}_{3}\) = Moles of \(\mathrm{HNO}_{3}\) (1) + Moles of \(\mathrm{HNO}_{3}\) (2) Total moles of \(\mathrm{HNO}_{3}\) = 0.005 mol + 0.020 mol = 0.025 mol

Calculate Final Volume of the Solution

We need the volume of the final solution. Since the volumes are additive in this case, we simply add the volumes of both initial solutions to find the total volume. Total Volume = Volume of Solution 1 + Volume of Solution 2 Total Volume = 0.050 L + 0.100 L = 0.150 L

Calculate the Molarity of the Final Solution

Now that we have the total moles of \(\mathrm{HNO}_{3}\) and the total volume of the final solution, we can calculate the molarity. Final Molarity = Total moles of \(\mathrm{HNO}_{3}\)/Total Volume Final Molarity = 0.025 mol / 0.150 L Final Molarity = 0.167 M So, the molarity of the final solution of nitric acid is \(0.167 \ \mathrm{M}\).

Key concepts

Nitric Acid

Nitric acid, represented by the chemical formula \(\mathrm{HNO}_{3}\), is a highly corrosive mineral acid. It has a wide range of applications, primarily in the production of fertilizers and explosives. When dissolving in water, nitric acid dissociates into hydrogen ions \(\mathrm{H}^{+}\) and nitrate ions \(\mathrm{NO}_{3}^{-}\). These ions are responsible for its strong acidic properties.
This property makes \(\mathrm{HNO}_{3}\) a useful reagent in various chemical reactions and industrial processes. However, due to its corrosive nature, it must be handled with care. Safety precautions, such as wearing gloves and goggles, are essential when working with nitric acid to avoid skin burns and respiratory issues. Always store it in a secure, labeled container to prevent accidents. Understanding the basic properties and safety measures of nitric acid lays a solid foundation for mastering its role in chemistry.

Solution Mixing

Solution mixing is the process of combining two or more liquid solutions to form a uniform mixture. It's a common practice in laboratories and industries. Understanding how to mix solutions correctly is crucial for accurate scientific results.
In this exercise, two solutions of nitric acid are mixed. Here's what you need to understand about mixing solutions:

• **Volume Additivity**: When solutions are mixed, their volumes usually add together without a significant change in total volume. However, always confirm, as some chemical reactions can cause volume changes.
• **Concentration Change**: The resulting concentration of the mixture will be different from the original solutions. This requires calculating total moles and total volume to find the new molarity.

By calculating the total amount of solute (in moles) from each solution and dividing by the total volume of the mixture, you can determine the final concentration. Properly controlled mixing ensures the desired concentration and properties of the final solution.

Chemical Concentration

Chemical concentration reflects how much solute is present in a given volume of solution. Molarity, denoted as \(\mathrm{M}\), is a common way to quantify concentration. It's defined as the number of moles of solute in one liter of solution. To calculate molarity, you need:

• The amount of solute, measured in moles.
• The total volume of the solution, measured in liters.

For example, if you dissolve \(0.020 \ \mathrm{mol}\) of \(\mathrm{HNO}_{3}\) in \(0.100 \ \mathrm{L}\), the molarity is \(0.200 \ \mathrm{M}\).
In a situation like the one given, after mixing, you need to find the total moles of solute and the final volume to compute the new molarity of the solution. Understanding chemical concentration allows chemists to prepare solutions of precise properties, crucial for reactions where the concentration affects the rate or yield. Always carefully measure both solute and solvent while calculating concentration for accurate and meaningful chemical analysis.