Problem 16 - Chemistry: Principles and Reactions

Question

A bottle of commercial concentrated aqueous ammonia is labeled "29.89\% \(\mathrm{NH}_{3}\) by mass; density \(=0.8960 \mathrm{~g} / \mathrm{mL}\)." (a) What is the molarity of the ammonia solution? (b) If \(250.0 \mathrm{~mL}\) of the commercial ammonia is diluted with water to make \(3.00 \mathrm{~L}\) of solution, what is the molarity of the diluted solution?

Step-by-Step Solution

Answer

Solution: The molarity of the commercial ammonia solution is 15.74 M. After dilution, the molarity of the diluted solution is 1.31 M.

Step 1: Find moles of ammonia in 1 L of solution

First, we need to find the mass of \(\mathrm{NH}_{3}\) in 1 L of solution. We are given that the mass percentage of \(\mathrm{NH}_{3}\) in the solution is \(29.89\%\). We also know the density of the solution is \(0.8960 \mathrm{~g} / \mathrm{mL}\), so its mass in 1 L is: \(1000\mathrm{~mL} \times 0.8960 \mathrm{~g} / \mathrm{mL} = 896\mathrm{~g}\). We can then find the mass of \(\mathrm{NH}_{3}\) in 1 L of solution: \(896\mathrm{~g} \times 29.89\% = 267.95\mathrm{~g}\). Now, we can convert the mass of \(\mathrm{NH}_{3}\) to moles using its molar mass, which is \(17.03\mathrm{~g/mol}\): \(\displaystyle\frac{267.95\mathrm{~g}}{17.03\mathrm{~g/mol}} = 15.74\mathrm{~mol}\).

Step 2: Find molarity of ammonia solution

Now that we have the moles of ammonia in 1 L of solution, we can calculate the molarity. The formula for molarity is: \(M = \displaystyle\frac{n}{V}\) Plugging our values, we have: \(M = \displaystyle\frac{15.74\mathrm{~mol}}{1\mathrm{~L}} = 15.74\, \mathrm{M}\). So, the molarity of the ammonia solution is \(15.74\, \mathrm{M}\).

Step 3: Find molarity of diluted solution

In the second part of the problem, we are asked to find the molarity of the diluted solution after adding the concentrated ammonia to water. We know the volume of the commercial ammonia added is \(250.0\mathrm{~mL}\) and the final volume of the diluted solution is \(3.00\mathrm{~L}\). We can use the dilution formula to find the molarity of the diluted solution: \(M_{1}V_{1} = M_{2}V_{2}\) Our initial molarity \(M_{1}\) is \(15.74\, \mathrm{M}\), and the initial volume \(V_{1}\) is \(250.0\mathrm{~mL}\). The final volume \(V_{2}\) is \(3.00\mathrm{~L}\). We can plug in the values and solve for \(M_{2}\): \(15.74\mathrm{M} \times 250.0\mathrm{~mL} = M_{2} \times 3.00\mathrm{~L}\) We need to convert \(V_{1} = 250.0\mathrm{~mL}\) to liters to match the units with \(V_{2}\): \(V_{1} = 250.0\mathrm{~mL} \times \displaystyle\frac{1\mathrm{~L}}{1000\mathrm{~mL}} = 0.250\mathrm{~L}\) Now we can solve for \(M_{2}\): \(M_{evential} = \displaystyle\frac{15.74\mathrm{M} \times 0.250\mathrm{~L}}{3.00\mathrm{~L}} = 1.31\, \mathrm{M}\). Therefore, the molarity of the diluted solution is \(1.31\, \mathrm{M}\).

Key Concepts

Aqueous Ammonia

Aqueous ammonia is a solution of ammonia gas (\(\mathrm{NH}_3\)) dissolved in water. This type of solution is common in both household cleaning products and industrial applications. Ammonia, when dissolved in water, results in a clear and colorless liquid with a characteristic pungent smell. When we talk about aqueous ammonia, the percentage typically refers to how much ammonia is present in the solution in terms of mass.

• Industrial Use: Used for manufacturing chemicals and as a refrigerant.
• Household Use: Common in cleaning solutions due to its effectiveness in grease removal.

Understanding aqueous ammonia is crucial for calculations involving the concentration of ammonia in such solutions, which can then be further used in stoichiometric calculations or preparing diluted solutions.

Density Calculation

Density is a key concept when dealing with solutions. It is defined as the mass per unit volume and can significantly help determine other attributes, such as mass from volume. In the exercise we're analyzing, density is crucial because it allows us to determine how much of the solution's total mass is composed of \(\mathrm{NH}_3\).
Given:

• Density of aqueous ammonia: \(0.8960 \, \text{g/mL}\)

To calculate the mass in a given volume, you multiply the density by the volume, which we did for a 1-liter volume of solution, leading to a total mass of \(896 \, \text{g}\).

• Formula: \(\text{Mass} = \text{Density} \times \text{Volume}\)
• Application: Used to convert volume measures to mass when the density is known.

This calculated mass is critical for finding out the mass of the ammonia component in the solution, fundamental for subsequent steps.

Dilution Formula

When we take a concentrated solution and add solvent to decrease its concentration, we have performed a dilution. This is very common in labs and industries to achieve solutions suitable for various applications.
The dilution formula helps in finding the new concentration of a solution after dilution:

• The formula can be written as: \(M_1V_1 = M_2V_2\)

Where \(M_1\) and \(V_1\) are the molarity and volume of the original solution, while \(M_2\) and \(V_2\) pertain to the diluted solution. By rearranging this formula, one can solve for the unknown final molarity \(M_2\).
In our exercise, this formula was used to find how the concentration changed when \(250.0 \, \text{mL}\) of the ammonia solution was diluted to a final volume of \(3.00 \, \text{L}\).

• Practical Use: Allows researchers and technicians to prepare specific molarity solutions from more concentrated stock solutions efficiently.

Mass Percentage Calculation

Mass percentage is an important metric in chemistry that lets you know what fraction of a solution’s mass is comprised of a specific component. It is expressed as a percentage and is calculated using the formula:

• \[\text{Mass Percentage} = \left(\frac{\text{mass of component}}{\text{total mass of solution}}\right) \times 100\% \]

In our example, the ammonia is 29.89\% by mass. This means that out of every 100g of the solution, about 29.89g is ammonia.

• Importance: Useful in understanding the strength/purity of a solution.
• Application: Helps in quality control and ensuring consistency in formulation.

By determining the mass of the ammonia using its mass percentage and the solution's total mass, you can then calculate other variables, including molarity.