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 can be calculated using the following steps: 1. Calculate moles of HNO3 in each solution: Moles1 = 0.100 M × 0.050 L = 0.005 mol Moles2 = 0.200 M × 0.100 L = 0.020 mol 2. Calculate total moles of HNO3: Total moles of HNO3 = 0.005 mol + 0.020 mol = 0.025 mol 3. Calculate the total volume of the final solution: Total volume = 0.050 L + 0.100 L = 0.150 L 4. Calculate molarity of the final solution: Final molarity = 0.025 mol / 0.150 L = 0.167 M Therefore, the molarity of the final solution of nitric acid is \(0.167 M\).

Step-by-step solution

Find moles of solute in each solution separately

To find the moles of HNO3 in each solution, we'll use the molarity formula: Moles of solute = Molarity × volume (in liters) Moles of HNO3 in first solution: volume1 = 50.00 mL = 0.050 L Molarity1 = 0.100 M Moles of HNO3 in second solution: volume2 = 100.00 mL = 0.100 L Molarity2 = 0.200 M

Calculate total moles of HNO3

Add the moles of HNO3 from both solutions to find the total moles of solute: Total moles of HNO3 = Moles1 + Moles2

Calculate the total volume of the final solution

To find the total volume, simply add the volumes of the two solutions: Total volume = volume1 + volume2

Calculate molarity of the final solution

Now that we know the total moles of solute and the total volume of the solution, we can calculate the final molarity: Final molarity = Total moles of HNO3 / Total volume (in liters) Plug in the values from Steps 2 and 3 to calculate the final molarity.

Key concepts

Solution Concentration

Solution concentration is about how much solute, like a salt or acid, is present in a given amount of solution. A common way to express this is through molarity. Molarity (M) is defined as the number of moles of solute per liter of solution.
The formula to calculate molarity is:
\[\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}\]

• Moles of solute refer to the amount of substance, measured in moles.
• Volume of solution is simply the amount of the liquid solution, usually in liters, that contains the solute.

For example, when mixing two solutions of different concentrations, like in the above exercise, it's essential to calculate the total concentration by considering both the amount (moles) of solute and the total final volume of the solution.

Moles of Solute

Calculating the moles of solute is crucial in determining the concentration of any solution. A mole is a unit that measures the amount of substance, based on the number of atoms or molecules rather than mass or volume alone.
Here's how you can determine it:
When you know the molarity and volume of a solution, you can calculate the moles of solute by using:

• Formula: Moles = Molarity x Volume (in liters)
• This calculation helps in knowing how much solute is present in a given volume.

In the given exercise, we found the moles of nitric acid \( \mathrm{HNO_3} \) present in two different solutions first, before mixing. It allows us to precisely figure out how much nitric acid is present in each solution before moving on to find out their combined molarity.

Volumetric Analysis

Volumetric analysis is a quantitative analytical method to determine the concentration of a solution. It involves adding a solution of known concentration, called the titrant, to another solution to reach an equivalence point, where the reactants are present in stoichiometric amounts.
In the context directly related to the exercise, volumetric analysis also involves:

• The addition of different solution volumes to understand how concentrations change.
• Correctly measuring volumes is pivotal since any error can affect results.

Using volumetric principles in mixing solutions helps ensure accurate concentration measurements by taking into account the total volume after mixing.

Acid-Base Chemistry

Acid-base chemistry is a branch of chemistry dealing with acids, bases, and pH levels. Acids, like nitric acid used in the example, can donate protons (H\(^+\)) in a chemical reaction.
Understanding acids and bases is essential in various chemical reactions and calculations. In acid-base chemistry:

• Acids release hydrogen ions (H\(^+\)) in solution.
• Bases accept hydrogen ions or release hydroxide ions (OH\(^-\)).
• The strength of an acid or base is determined by how completely it dissociates in water.

In the exercise problem, we work with nitric acid solutions and calculate the molarity to understand how concentrated and effective the acid is in various chemical reactions.