NaOH is commonly used in the manufacturing of paper. how many millimeters of a 5.25% (w/v) NaOH solution must be used to prepare 250 mL of a 0.175% (w/v) NaOH solution?
The correct answer and explanation is:
To find how many milliliters of a 5.25% (w/v) NaOH solution are needed to prepare 250 mL of a 0.175% (w/v) NaOH solution, we can use the dilution formula: C1V1=C2V2C_1V_1 = C_2V_2
Where:
- C1C_1 = concentration of the stock solution (5.25%)
- V1V_1 = volume of the stock solution needed (this is what we are solving for)
- C2C_2 = concentration of the final solution (0.175%)
- V2V_2 = volume of the final solution (250 mL)
Step-by-step calculation:
(5.25%)⋅V1=(0.175%)⋅(250 mL)(5.25\%) \cdot V_1 = (0.175\%) \cdot (250\ \text{mL}) V1=0.175⋅2505.25V_1 = \frac{0.175 \cdot 250}{5.25} V1=43.755.25≈8.33 mLV_1 = \frac{43.75}{5.25} \approx 8.33\ \text{mL}
✅ Correct Answer: 8.33 mL
🧪 Explanation (Approx. 300 Words):
Sodium hydroxide (NaOH), also known as lye or caustic soda, is widely used in paper manufacturing during the pulping process. In labs or industry, NaOH solutions are often prepared by dilution from a more concentrated stock. To ensure precise results, chemists rely on the dilution formula: C1V1=C2V2C_1V_1 = C_2V_2
This equation maintains the amount of solute (NaOH) constant before and after dilution. The term “w/v” refers to weight per volume, meaning the concentration is expressed as grams of solute per 100 mL of solution.
In this problem, we are given:
- A stock solution of 5.25% NaOH,
- A target solution of 0.175% NaOH,
- A final volume of 250 mL.
The goal is to find how much of the concentrated (5.25%) solution is required to prepare the desired diluted solution. By substituting into the dilution formula, we calculate that 8.33 mL of the stock solution contains the right amount of NaOH to reach 0.175% when diluted to 250 mL.
This method is commonly used in laboratories for preparing standard solutions efficiently and safely. Once the 8.33 mL of concentrated NaOH is measured, it should be added to a volumetric flask and diluted with water to a total of 250 mL. This approach ensures both accuracy and chemical safety, which are essential in industrial and laboratory settings.