Chapter U4.83, Problem 4E

Interpretation Introduction

Interpretation:

The solution with the highest molarity and highest density needs to be identified from 1.0 g KCl in 1.0 L water, 5.0 g KCl in 0.5 L water and 10.0 g KCl in 0.3 L.

Concept Introduction:

Molarity is defined as the moles of solute in 1-liter volume of a solution

  $\begin{array}{l}\text{Molarity = }\frac{\text{moles of solute}}{\text{L of solution}}\text{ -----(1)}\end{array}$

   $\begin{array}{c}\text{moles = }\frac{\text{mass of solute (m)}}{\text{molar mass of solute (mol}\text{. wt)}}\text{ -----(2)}\end{array}$

  $\begin{array}{c}\text{i}\text{.e}\text{.}\end{array}$

  $\begin{array}{c}\text{Molarity = }\frac{\text{mass of solute}}{\text{molar mass }\times \text{L of solvent}}\end{array}$

   $\begin{array}{c}\text{i}\text{.e}\text{. M = }\frac{\text{m}}{\text{mol}\text{.wt × V}}\text{ ------(3)}\end{array}$

The density of a solution is the ratio of its mass and volume i.e.

  $\text{Desnity(D) = }\frac{\text{Mass (m)}}{\text{Volume (V)}}\text{ -----(4)}$

Answer to Problem 4E

The solution of 10.0 g KCl in 0.3 L water has the highest molarity and density.

Explanation of Solution

a)

Given:

Mass of KCl = 1.0 g

The volume of water solvent = 1.0 L

Calculation:

Based on equation (1) and (2):

  $\text{Molarity = }\frac{\text{mass of solute}}{\text{molar mass }\times \text{L of solution}}$

Molar mass of KCl = 74.55 g/mol

  $\text{Molarity = }\frac{\text{1}\text{.0 g}}{\text{74}\text{.55 g/mol }\times \text{1}\text{.0 L}}=1.3\times {10}^{-2}\text{ mol/L}$

b)

Given:

Mass of KCl = 5.0 g

The volume of water solvent = 0.5 L

Calculation:

Based on equation (1) and (2):

  $\text{Molarity = }\frac{\text{mass of solute}}{\text{molar mass }\times \text{L of solution}}$

Molar mass of KCl = 74.55 g/mol

  $\text{Molarity = }\frac{\text{5}\text{.0 g}}{\text{74}\text{.55 g/mol }\times \text{0}\text{.5 L}}=1.3\times {10}^{-1}\text{ mol/L}$

c)

Given:

Mass of KCl = 10.0 g

The volume of water solvent = 0.3 L

Calculation:

Based on equation (1) and (2):

  $\text{Molarity = }\frac{\text{mass of solute}}{\text{molar mass }\times \text{L of solution}}$

Molar mass of KCl = 74.55 g/mol

  $\text{Molarity = }\frac{\text{10}\text{.0 g}}{\text{74}\text{.55 g/mol }\times \text{0}\text{.3 L}}=4.5\times {10}^{-1}\text{ mol/L}$

The solution of 10.0 g KCl in 0.3 L water has the highest density.

Molarity can be expressed in terms of the solution density and solute molecular weight by combining equations (3) and (4) i.e.

  $\text{M = }\frac{\text{D}}{\text{mol}\text{.wt }}$

Therefore,the molarity of a solution is directly proportional to its density.

Since 10.0 g of KCl in 0.3 L of water has the highest molarity; correspondingly it will also have the highest density.

Conclusion

The solution of 10.0 g of KCl in 0.3 L of water has the highest molarity and the highest density.