Chapter 14.2, Problem 31SSC

Interpretation Introduction

Interpretation:

Five quantitative ways to describe the composition of solution have to be compared and contrasted.

Concept introduction:

Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture.

Composition of a solution can be defined by expressing its concentration. Concentration can be expressed either qualitatively or quantitatively. Concentration can be described qualitatively using the words concentrated or dilute. The solution is either dilute or concentrated depends on the amount of solute present in the solution. In concentrated solution more amount of solute is present compare to dilute solution. There are several ways by which we can describe the concentration of the solution quantitatively. Some commonly used quantitative descriptions are percent by mass, percent by volume, molarity, molality and mole fraction.

Answer to Problem 31SSC

Quantitatively concentration of the solution can be expressed in five different ways such as percent by mass, percent by volume, molarity, molality and mole fraction. Among them, molarity, molality, and mole fraction are basedon moles of solute per some other quantity;percent by volume and molarity are defined by per volume of solution basis, molality and molefraction are based on per quantity of solvent basis, percent by mass and percent by volume are the only ratios involving percentages.

Quantitatively concentration of the solution can be expressed in five different ways-

Mass percentage or percent by mass (w/W): The mass percentage of a component of a solution is defined as:

$\mathrm{Mass}\%ofacomponent=\frac{Mass of the component in the solution}{Total mass of the solution}\times 100$

Volume/volume percentage (v/V percent): Percent by volume is expressed as the ratio of the volume of the solute to the total volume of the solution multiplied by 100.

In expression,

$\mathrm{Volume}percentage\left(v/V\right)\%ofacomponent=\frac{Volumeof the solute}{Total volume of the solution}\times 100$

Molarity: Molarity is defined as the number of moles of solute present in one litre of the solution and is expressed as:

$\mathrm{Molarity}ofthesolution=\frac{Numberofmolesof the solute}{ Volume of the solution(inlitre)}$

Molality: Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:

$\mathrm{Molality}ofthesolution=\frac{Numberofmolesof the solute}{Massof the solvent(inkg)}$

Mole fraction: Mole fraction defined as the number of moles of one component divided by total the number of moles in the mixture. Mole fraction is denoted as ‘ ${\chi }_i$ ’ where subscript ‘i’ represents the particular component. The sum of the mole fractions of the components in a mixture (or a solution) is unity. The mole fraction for the solvent ( ${\chi }_A$ )and the mole fraction for the solute ( ${\chi }_B$ )can be expressed as follows

Mole fraction ${\chi }_A=\frac{n_A}{ n_A+n_B}$ and ${\chi }_B=\frac{n_B}{ n_A+n_B}$ Where, ${\chi }_A$ and ${\chi }_B$ represent the mole fractions of each substance. n_A and n_Brepresent the number of moles of each substance.

$({\chi }_A+{\chi }_B)=1$

Molarity, molality, and mole fraction are based on moles of solute per some other quantity, percent by volume and molarity are defined by per volume of solution basis, molality and mole fraction are based on per quantity of solvent basis, percent by mass and percent by volume are the only ratios involving percentages. Mass percent, mole fraction and molality are independent of temperature, whereas volume percent and molarity are function of temperature. This is because volume depends on temperature and the mass does not.

Explanation of Solution

Quantitatively concentration of the solution can be expressed in five different ways-

Mass percentage or percent by mass (w/W): The mass percentage of a component of a solution is defined as:

$\mathrm{Mass}\%ofacomponent=\frac{Mass of the component in the solution}{Total mass of the solution}\times 100$

Volume/volume percentage (v/V percent): Percent by volume is expressed as the ratio of the volume of the solute to the total volume of the solution multiplied by 100.

In expression,

$\mathrm{Volume}percentage\left(v/V\right)\%ofacomponent=\frac{Volumeof the solute}{Total volume of the solution}\times 100$

Molarity: Molarity is defined as the number of moles of solute present in one litre of the solution and is expressed as:

$\mathrm{Molarity}ofthesolution=\frac{Numberofmolesof the solute}{ Volume of the solution(inlitre)}$

Molality: Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:

$\mathrm{Molality}ofthesolution=\frac{Numberofmolesof the solute}{Massof the solvent(inkg)}$

Mole fraction: Mole fraction defined as the number of moles of one component divided by total the number of moles in the mixture. Mole fraction is denoted as ‘ ${\chi }_i$ ’ where subscript ‘i’ represents the particular component. The sum of the mole fractions of the components in a mixture (or a solution) is unity. The mole fraction for the solvent ( ${\chi }_A$ )and the mole fraction for the solute ( ${\chi }_B$ )can be expressed as follows

Mole fraction ${\chi }_A=\frac{n_A}{ n_A+n_B}$ and ${\chi }_B=\frac{n_B}{ n_A+n_B}$ Where, ${\chi }_A$ and ${\chi }_B$ represent the mole fractions of each substance. n_A and n_Brepresent the number of moles of each substance.

$({\chi }_A+{\chi }_B)=1$

Molarity, molality, and mole fraction are based on moles of solute per some other quantity, percent by volume and molarity are defined by per volume of solution basis, molality and mole fraction are based on per quantity of solvent basis, percent by mass and percent by volume are the only ratios involving percentages. Mass percent, mole fraction and molality are independent of temperature, whereas volume percent and molarity are function of temperature. This is because volume depends on temperature and the mass does not.