To prepare 5.0 L of a 0.22 M aqueous sodium hydroxide, NaOH, solution from 2.5 M aqueous sodium hydroxide stock solution, what volume of the stock solution should you add to a 5.0 L volumetric flask?
The Correct Answer and Explanation is:
To prepare a diluted solution from a stock solution, you can use the dilution equation:M1V1=M2V2M_1 V_1 = M_2 V_2M1V1=M2V2
Where:
- M1M_1M1 is the concentration of the stock solution (2.5 M).
- V1V_1V1 is the volume of stock solution you need to take (this is what we’re solving for).
- M2M_2M2 is the concentration of the diluted solution (0.22 M).
- V2V_2V2 is the final volume of the diluted solution (5.0 L).
Step 1: Plug in the known values.
(2.5 M)(V1)=(0.22 M)(5.0 L)(2.5 \, \text{M}) (V_1) = (0.22 \, \text{M}) (5.0 \, \text{L})(2.5M)(V1)=(0.22M)(5.0L)
Step 2: Solve for V1V_1V1.
V1=(0.22 M)(5.0 L)2.5 MV_1 = \frac{(0.22 \, \text{M}) (5.0 \, \text{L})}{2.5 \, \text{M}}V1=2.5M(0.22M)(5.0L)V1=1.12.5=0.44 LV_1 = \frac{1.1}{2.5} = 0.44 \, \text{L}V1=2.51.1=0.44L
Step 3: Convert the result to milliliters.
Since 1 L=1000 mL1 \, \text{L} = 1000 \, \text{mL}1L=1000mL, we get:V1=0.44 L×1000=440 mLV_1 = 0.44 \, \text{L} \times 1000 = 440 \, \text{mL}V1=0.44L×1000=440mL
Final Answer:
You should add 440 mL of the 2.5 M NaOH stock solution to the 5.0 L volumetric flask. After adding the stock solution, fill the flask to the 5.0 L mark with distilled water to make the final 0.22 M NaOH solution.
Explanation:
The dilution equation ensures that the moles of NaOH in the stock solution and the moles in the final solution are the same, just spread over a larger volume. By calculating the required volume of the concentrated stock solution, we can ensure that we achieve the desired concentration without waste or errors in measurement.
