To solve the problem of calculating the volume of a 5.0% (w/v) dextrose solution that contains 1.5 grams of dextrose, we need to apply the concept of percentage concentration and convert it appropriately to determine the volume.
Here's a step-by-step solution:
1. Understand the Given Data:
- You are given a concentration of 5.0% (w/v). This means there are 5.0 grams of dextrose in every 100 mL of solution.
- You are also given the mass of dextrose, which is 1.5 grams.
2. Set Up the Relationship:
- The concentration percentage (5.0%) indicates 5.0 grams in 100 mL.
- To find the volume that contains 1.5 grams, we need to set up the ratio based on the given concentration.
3. Set Up a Proportion:
- Use the concentration to set up a proportion to find the volume (V) needed for 1.5 grams of dextrose:
[tex]\[ \text{Volume} = \frac{\text{Mass of dextrose}}{\text{Concentration fraction}} \][/tex]
4. Calculate the Concentration Fraction:
- Convert 5.0% to a fraction:
[tex]\[ 5.0\% = \frac{5.0}{100} = 0.05 \][/tex]
5. Calculate the Volume:
- Plug in the given values into the relationship:
[tex]\[ \text{Volume} = \frac{1.5 \text{ grams}}{0.05} \][/tex]
- Perform the division:
[tex]\[ \text{Volume} = 30 \text{ mL} \][/tex]
6. Verify Significant Figures:
- According to the given data:
- The concentration (5.0%) has two significant figures.
- The mass (1.5 grams) also has two significant figures.
- Thus, the final answer should be rounded to two significant figures.
Final Answer:
The volume of the 5.0% (w/v) dextrose solution that contains 1.5 grams of dextrose is 30 mL.
This result aligns perfectly with all necessary considerations and steps to ensure accuracy.
