https://file.aiquickdraw.com/mathbot/file/1727751244271apnctc49.jpg

We are given a 10.0% (w/v) ketamine solution and are asked to calculate the volume of this solution that contains 15 mg of ketamine. 

### Step-by-step solution:

1. **Understanding the concentration**:
   A 10.0% (w/v) solution means that 10.0 g of ketamine is present in 100 mL of solution. This can be expressed as:
   \[
   \frac{10.0 \, \text{g ketamine}}{100 \, \text{mL solution}} = 0.1 \, \text{g/mL}
   \]
   So, the concentration of the solution is 0.1 g of ketamine per mL.

2. **Convert mg to g**:
   We are given 15 mg of ketamine. Since 1 g = 1000 mg:
   \[
   15 \, \text{mg} = 0.015 \, \text{g}
   \]

3. **Set up the proportion**:
   Using the concentration, we know:
   \[
   0.1 \, \text{g} \text{ of ketamine is in } 1 \, \text{mL of solution}.
   \]
   We need to find the volume of solution that contains 0.015 g of ketamine:
   \[
   \frac{0.1 \, \text{g}}{1 \, \text{mL}} = \frac{0.015 \, \text{g}}{x \, \text{mL}}.
   \]

4. **Solve for \(x\)**:
   Cross-multiply and solve for \(x\):
   \[
   x = \frac{0.015 \, \text{g} \times 1 \, \text{mL}}{0.1 \, \text{g}} = 0.15 \, \text{mL}.
   \]

### Final answer:
The volume of the solution required to contain 15 mg of ketamine is **0.15 mL**.

Would you like further details or have any questions? 

Here are 5 related questions to further explore:
1. What does (w/v) stand for in a solution concentration?
2. How would the answer change if the concentration was 5% instead of 10%?
3. What are other common ways of expressing solution concentration (e.g., molarity)?
4. How do you convert between weight/volume percent and molarity?
5. How would you calculate the volume for a solution with a solute measured in micrograms?

**Tip**: Always make sure the units match when solving proportion problems with solution concentrations!

Ketamine, sometimes used as an adjuvant to general anesthesia, is available as a 10.0% (w/v) solution. Calculate the volume of this solution that contains 15 mg of ketamine.

Learn how to calculate the volume of a 10.0% (w/v) ketamine solution that contains 15 mg of ketamine. This problem involves key concepts such as unit conversion, proportions, and concentration calculations. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation