What is the mass of NaCl in 64.7 mL of a 10.0% w/v solution?
The correct answer and explanation is:
Answer:
The mass of NaCl in 64.7 mL of a 10.0% w/v solution is 6.47 grams.
Explanation (300 words):
To find the mass of NaCl in a given volume of a 10.0% w/v (weight/volume) solution, we first need to understand what the percentage concentration means.
A 10.0% w/v solution means that there are 10.0 grams of solute (NaCl) dissolved in every 100 milliliters of the solution. The notation “w/v” literally stands for weight per volume.
Given this, the concentration tells us:
- 10.0 g NaCl / 100 mL solution
Now, we want to find the mass of NaCl in 64.7 mL of this solution.
We can use a simple proportion based on the definition of concentration: mass of NaCl=(10.0 g NaCl100 mL solution)×64.7 mL solution\text{mass of NaCl} = \left(\frac{10.0 \text{ g NaCl}}{100 \text{ mL solution}}\right) \times 64.7 \text{ mL solution}
Calculate: mass of NaCl=0.10 g/mL×64.7 mL=6.47 g\text{mass of NaCl} = 0.10 \text{ g/mL} \times 64.7 \text{ mL} = 6.47 \text{ g}
Therefore, 64.7 mL of a 10.0% w/v NaCl solution contains 6.47 grams of sodium chloride.
Additional points to consider:
- The w/v percentage is often used in solutions where the solute is a solid dissolved in a liquid, and the volume of the solution is measured in milliliters.
- The density of the solution is not necessarily needed here because the w/v percentage is based on total volume of solution, not just the solvent.
- This calculation assumes the solution is well mixed and homogeneous.
- If the problem asked for a different unit (such as molarity or mass in different units), additional steps would be needed.
This method can be applied for any w/v percentage solution if you know the volume and want to find the mass of solute.