Chapter 21, Problem 93A

(a)

Interpretation Introduction

Interpretation: The 250 g of 0.90 % of NaCl solution mass by mass is given. The number of grams of NaCl required to make the solution needs to be determined.

Concept Introduction: In m/m solution, the number of grams of solute in 100 g of the solution is given. Thus, for 0.90 % NaCl m/m solution, there is 0.90 g of NaCl in 100 g of solution.

Explanation of Solution

The mass of the solution is given 250 g; thus, the mass of the solute can be calculated as follows:

For 100 g, 0.90 g of NaCl is used.

For 1 g, the number of grams of NaCl used will be:

  $m=\frac{0.90}{100}\text{ g}$

Thus, for 250 g, the mass of NaCl required will be:

  $\begin{array}{c}m=\left(250\right)\left(\frac{0.90}{100}\right)\text{g}\\ =2.25\text{ g}\end{array}$

Thus, the mass of NaCl (solute) required will be 2.25 g.

(b)

Interpretation Introduction

Interpretation: The mass of ${\text{KNO}}_{\text{3}}$ required to form the 500 mL of 2.0 M solution needs to be determined.

Concept Introduction: The molarity of a solution is defined as the number of moles of solute in 1 L of the solution.

Explanation of Solution

In the problem, 500 mL of 2.0 M ${\mathrm{KNO}}_3$ solution is given. Now, molarity is defined as the number of moles of solute in 1 L of solution.

  $M=\frac{n}{V\left(\text{L}\right)}$

Putting the values,

  $\begin{array}{c}2.0\text{ M}=\frac{n}{500\text{ mL}\left(\frac{1\text{ L}}{1000\text{ mL}}\right)}\\ \text{Or,}\\ n=\left(2.0\text{ M}\right)\left(500\text{ mL}\left(\frac{1\text{ L}}{1000\text{ mL}}\right)\right)\\ =1\text{ mol}\end{array}$

Thus, the number of moles of ${\text{KNO}}_{\text{3}}$ is required. Now, the molar mass of ${\text{KNO}}_{\text{3}}$ is 101.1 g/mol thus, the mass of ${\text{KNO}}_{\text{3}}$ can be calculated as follows:

  $m=n\times M$

Or,

  $\begin{array}{c}m=\left(1\text{ mol}\right)\left(101.1\text{ g/mol}\right)\\ =101.\text{1 g}\end{array}$

Therefore, 101.1 g of ${\text{KNO}}_{\text{3}}$ is dissolved in 1 L of water to form the given solution.