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Chapter 9 Exercise 12 Using % m/v as a Conversion Factor

Chapter 9 Exercise 12: Using % m/v as a Conversion Factor

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Introduction

This video covers Chapter 9, Exercise 12, which explains how to use the mass/volume percent (% m/v) as a conversion factor to determine the mass of a solute in a solution. The example used involves calculating the grams of mannitol a patient receives from a given volume of solution.

Main Points
  1. Problem Overview

- Given: 

     - 100 milliliters of a 20% mass/volume (m/v) mannitol solution.

- Asked: 

     - How many grams of mannitol are in that 100 milliliters.
  1. Understanding the Conversion Factor

- 20% m/v Solution: Means there are 20 grams of mannitol in every 100 milliliters of solution.

- Formula:

     \[
     \% \text{ m/v} = \left( \frac{\text{grams of solute}}{\text{milliliters of solution}} \right) \times 100
     \]

- Application: This percentage can be used as a conversion factor between grams of solute and milliliters of solution.

  1. Conversion Steps

- Given Volume: 100 milliliters of solution.

- Conversion Factor:

     \[
     \frac{20 \text{ grams of mannitol}}{100 \text{ milliliters of solution}}
     \]

- Calculation: 

     \[
     100 \text{ mL} \times \left( \frac{20 \text{ grams}}{100 \text{ mL}} \right) = 20 \text{ grams of mannitol}
     \]

- Result: The patient receives 20 grams of mannitol per 100 milliliters of solution.

  1. Extended Calculation

- Given: How many grams of mannitol does the patient receive in 12 hours?

- Assumption: The same amount is received every hour.

- Calculation: 

     \[
     20 \text{ grams/hour} \times 12 \text{ hours} = 240 \text{ grams of mannitol}
     \]
Conclusion

The video demonstrates how to use the % m/v as a conversion factor to determine the mass of a solute in a given volume of solution. By understanding and applying this method, one can accurately calculate the amount of solute in various solution scenarios.

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