A solution of ammonia in water is called "ammonium hydroxide" because of the equilibrium: NH3 + H2O = NH4+ + OH-. The Density of the concentrated ammonium hydroxide, which contains 28.0 wt % NH3, is 0.899 g/mL. What volume of this reagent should be diluted to 500.0 mL to make 0.250 M NH3? Give the volume to 3 s.f and describe in detail the preparation of this volume.

Answer 1

To determine the volume of concentrated ammonium hydroxide (NH₃) needed to make a 500 mL solution with a concentration of 0.250 M NH₃, we will first need to find out how many moles of NH₃ are present in that final volume and then use the properties of the concentrated solution to calculate the required volume.

Step 1: Calculate the moles of NH₃ needed

\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution (L)}} \]

We can rearrange this formula to find the moles of solute:

\[ \text{moles of NH₃} = \text{Molarity} \times \text{Volume (L)} \]

Substituting the desired concentration and final solution volume:

\[ \text{moles of NH₃} = 0.250 , \text{mol/L} \times 0.500 , \text{L} = 0.125 , \text{mol} \]

Step 2: Find the mass of NH₃ needed

Using the molar mass of NH₃ (approximately 17.03 g/mol):

\[ \text{mass of NH₃} = 0.125 , \text{mol} \times 17.03 , \text{g/mol} = 2.12875 , \text{g} \approx 2.13 , \text{g} \]

Step 3: Use the density and concentration of the concentrated solution to determine the volume required

The concentrated ammonium hydroxide solution contains 28.0 wt% NH₃, which means 28 g of NH₃ per 100 g of solution.

To find out how many grams of solution we need to obtain 2.13 g of NH₃, we set up the following relationship:

\[ \text{mass of solution} = \frac{\text{mass of NH}_3}{\text{wt%}} = \frac{2.13 , \text{g}}{0.28} \approx 7.607 , \text{g} \]

Step 4: Calculate the volume of the concentrated solution needed

Now using the density of concentrated ammonium hydroxide (0.899 g/mL), we can find the volume of the solution:

\[ \text{Volume (mL)} = \frac{\text{mass of solution}}{\text{density}} = \frac{7.607 , \text{g}}{0.899 , \text{g/mL}} \approx 8.45 , \text{mL} \]

Summary of steps to prepare the solution

1. Measure out approximately 8.45 mL of concentrated ammonium hydroxide (28.0% NH₃) carefully using a pipette or a graduated cylinder.
2. Transfer the measured concentrated solution into a 500 mL volumetric flask or a suitable container.
3. Add distilled water gradually to the container. Start by adding a small amount of water to the flask containing concentrated solution to dilute it.
4. Once the concentrated solution has been mixed with some water, continue to fill the flask with distilled water until the total volume reaches exactly 500.0 mL.
5. Mix the solution thoroughly to ensure uniform distribution of NH₃ throughout the solution.

Answer

The volume of concentrated ammonium hydroxide needed is 8.45 mL (to 3 significant figures).