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The problem asks you to calculate the volume of a 7.0% (w/v) NaCl solution that contains 0.50 g of NaCl. Here's the step-by-step solution:

### Step 1: Understand the meaning of 7.0% (w/v)
- 7.0% (w/v) means there are 7.0 grams of NaCl in 100 mL of solution.

### Step 2: Set up the proportion
You need to find how much solution (in mL) contains 0.50 grams of NaCl. Use a proportion based on the concentration:
\[
\frac{7.0 \text{ g NaCl}}{100 \text{ mL solution}} = \frac{0.50 \text{ g NaCl}}{V \text{ mL solution}}
\]
Where \( V \) is the volume you want to calculate.

### Step 3: Solve for \( V \)
\[
V = \frac{0.50 \text{ g NaCl} \times 100 \text{ mL solution}}{7.0 \text{ g NaCl}} = \frac{50.0}{7.0} \text{ mL} = 7.14 \text{ mL}
\]

### Final Answer:
The volume of the solution is **7.14 mL**.

Would you like more details on any part of the solution, or do you have additional questions?

Here are 5 related questions to expand your understanding:
1. How would the volume change if the solution concentration were 5.0% instead of 7.0%?
2. What is the relationship between the weight/volume percentage and molarity for this solution?
3. How would you calculate the mass of NaCl in a 500 mL solution with a 7.0% (w/v) concentration?
4. What is the role of NaCl in medical applications such as hypertonic saline?
5. How would you prepare 1 L of a 7.0% NaCl solution starting with solid NaCl?

**Tip:** Always ensure you match the number of significant digits in your final answer with the given data to maintain precision.

To reduce dangerous swelling in the brain, physicians sometimes administer intravenous hypertonic saline, a 7.0% (w/v) solution of salt (NaCl) in water. Calculate the volume of this solution that contains 0.50 g of NaCl. Be sure your answer has a unit symbol and is rounded to the correct number of significant digits.

Learn how to calculate the volume of a 7.0% (w/v) NaCl solution containing 0.50 g of NaCl. This problem covers key mathematical concepts such as percentage concentration and proportions. Suitable for high school students in Grades 9-12.

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