Chapter 16.4, Problem 34SP

Interpretation Introduction

Interpretation: The mass of sodium fluoride required to prepare a $0.400\text{ m NaF}$ that contains $750\text{ g H2O}$ is to be determined.

Concept introduction: Molality is the number of moles of solute present in a kilogram of a solvent. Molality is the way of measuring the concentration of the solution. Concentration is defined as the amount of solute present in the given quantity of solvent.

Answer to Problem 34SP

The mass of sodium fluoride required is $12.6\text{ g}$ .

Explanation of Solution

The data given in the question to determine the mass required of sodium fluoride to prepare a $0.400\text{ m NaF}$ that contains $750\text{ g H2O}$ is as follows:

• Molality of sodium fluoride solution is $0.400\text{ m}$ .
• Mass of the solvent is $750\text{ g}$ .

The formula of molality is as follows:

  $\text{Molality = }\frac{\text{Number of moles of solute}}{\text{Mass of solvent ( in Kg)}}$

Substitute the value of molality and mass of solvent to find out the number of moles of solute present in the solution.

  $\text{0}\text{.400 m = }\frac{\text{Number of moles of solute}}{\text{0}\text{.750 Kg}}$

  $\begin{array}{l}\text{Number of moles of solute}=0.400\text{ m }\times \text{ 0}\text{.750 Kg}\\ \text{Number of moles of solute}=0.3\text{ moles}\text{.}\end{array}$

The formula for the number of moles is explained below:

  $\text{Number of moles =}\frac{\text{Given mass}}{\text{Molar mass}}$

Substitute the value of the number of moles and molar mass to calculate the mass required to make the desired solution.

  $\begin{array}{l}\text{Given mass = Number of moles }\times \text{ Molar mass}\\ \text{Given mass = 0}\text{.3 moles }\times \text{ 41}\text{.99 }\frac{g}{\text{mol}}\\ \text{Given mass = 12}\text{.6 g}\end{array}$

Conclusion

The mass of sodium fluoride required is $12.6\text{ g}$ .