To determine the volume of concentrated ammonium hydroxide needed to prepare 500.0 mL of a 0.250 M NH\(_3\) solution, we will first need to find out how much NH\(_3\) is required in moles, and then use the concentration and density of the concentrated solution to find the required volume.
Step 1: Calculate Moles of NH\(_3\) Needed
The concentration (Molarity, M) of the diluted solution is given by:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in L}} \]
To find the moles of NH\(_3\) needed for 500.0 mL (which is 0.500 L) at a concentration of 0.250 M:
\[ \text{moles of NH}_3 = \text{Molarity} \times \text{Volume (L)} = 0.250 , \text{mol/L} \times 0.500 , \text{L} = 0.125 , \text{mol} \]
Step 2: Calculate the Mass of NH\(_3\) Required
The molar mass of ammonia (NH\(_3\)) is approximately 17.03 g/mol. Therefore, the mass of NH\(_3\) needed is:
\[ \text{mass of NH}_3 = \text{moles} \times \text{molar mass} = 0.125 , \text{mol} \times 17.03 , \text{g/mol} = 2.12875 , \text{g} \]
Step 3: Determine the Amount of Concentrated Ammonium Hydroxide Required
The concentrated ammonium hydroxide solution has a concentration of 28.0% NH\(_3\) by weight. Therefore, in 100 g of this solution, there are 28.0 g of NH\(_3\).
To find out the mass of the concentrated ammonium hydroxide solution required to obtain 2.12875 g of NH\(_3\):
\[ \text{mass of concentrated solution} = \frac{\text{mass of NH}_3}{\text{fraction of NH}_3} = \frac{2.12875 , \text{g}}{0.280} = 7.603125 , \text{g} \]
Step 4: Calculate the Volume of Concentrated Ammonium Hydroxide Required
Using the density of concentrated ammonium hydroxide (0.899 g/mL), we can convert mass to volume:
\[ \text{Volume (mL)} = \frac{\text{mass (g)}}{\text{density (g/mL)}} = \frac{7.603125 , \text{g}}{0.899 , \text{g/mL}} \approx 8.448 , \text{mL} \]
Step 5: Report Final Volume and Description of Preparation
Final Volume: Approximately 8.45 mL (to 3 significant figures).
Detailed Preparation Steps
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Measure Concentrated NH\(_4\)OH: Using a pipette or a graduated cylinder, carefully measure approximately 8.45 mL of the concentrated ammonium hydroxide solution.
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Dilution Process:
- Obtain a clean 500 mL volumetric flask.
- Add the measured volume of concentrated ammonium hydroxide solution into the flask.
- Carefully add distilled water to the flask, filling it up to the 500 mL mark. It is important to add the water gradually and mix gently to ensure proper dilution while avoiding overheating or excessive release of ammonia gas.
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Mix the Solution: Stopper the flask and invert it several times to mix thoroughly. Ensure that the solution is homogeneous before use.
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Label: Label the flask with the contents (0.250 M NH\(_3\)) and the date of preparation.
This will give you a 500 mL solution of 0.250 M NH\(_3\) suitable for use in experiments or further dilutions.
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