Problem 52 - Chemistry: The Central Science

Question

Commercial concentrated aqueous ammonia is \(28 \% \mathrm{NH}_{3}\) by mass and has a density of \(0.90 \mathrm{~g} / \mathrm{mL}\). What is the molarity of this solution?

Step-by-Step Solution

Answer

The molarity of the concentrated aqueous ammonia solution can be calculated as follows: 1. Mass of solution = \(0.90 \frac{\mathrm{g}}{\mathrm{mL}}\) × 1000 \(\mathrm{mL}\) = 900 g 2. Mass of \(\mathrm{NH}_{3}\) = 900 g × 28% = 252 g 3. Moles of \(\mathrm{NH}_{3}\) = \(\frac{252 \mathrm{~g}}{17 \mathrm{~g/mol}}\) = 14.82 moles 4. Molarity = \(\frac{14.82 \text{ moles}}{1 \text{ L}}\) = 14.82 M Therefore, the molarity of the concentrated aqueous ammonia solution is 14.82 M.

Step 1: Calculate the mass of \(\mathrm{NH}_{3}\) in 1 L of solution.

In order to accomplish this, we first need to find the mass of 1 L (1000 mL) of the solution. We can do this by multiplying the density of the solution by its volume: Mass of solution = Density × Volume Mass of solution = \(0.90 \frac{\mathrm{g}}{\mathrm{mL}}\) × 1000 \(\mathrm{mL}\) Next, we use the percentage composition of the solution to find the mass of \(\mathrm{NH}_{3}\) in it. To do this, we multiply the mass of the solution by the mass percentage of \(\mathrm{NH}_{3}\): Mass of \(\mathrm{NH}_{3}\) = Mass of solution × mass percentage of \(\mathrm{NH}_{3}\) Mass of \(\mathrm{NH}_{3}\) = Mass of solution × 28%

Step 2: Convert the mass of \(\mathrm{NH}_{3}\) to moles.

To convert the mass of \(\mathrm{NH}_{3}\) to moles, we divide it by its molar mass: Moles of \(\mathrm{NH}_{3}\) = \(\frac{\text{Mass of }\mathrm{NH}_{3}}{\text{Molar mass of }\mathrm{NH}_{3}}\) Molar mass of \(\mathrm{NH}_{3}\) = 14 (N) + 3 × 1 (H) = 17 \(\mathrm{g/mol}\)

Step 3: Calculate the molarity of the solution.

To find the molarity, we divide the moles of \(\mathrm{NH}_{3}\) by the volume of the solution in liters (since we are calculating the mass of the solution for 1 L): Molarity = \(\frac{\text{Moles of }\mathrm{NH}_{3}}{\text{Volume of solution}}\) Now, we can combine and calculate the steps above to find the molarity of the concentrated aqueous ammonia solution.