Methods of Expressing Concentration of Solution for IIT JEE

The measure of the amount of solute, in a given amount of solvent of the solution, that has been dissolved is known as the concentration of the solution. If the solute that is dissolved has a relatively large amount, then the solution is said to be concentrated while if the solute that is dissolved has a relatively small amount, then the solution is said to be diluted. 

To determine the quantitative concentration of a solution, there are various methods which are listed below-

1. Concentration in parts per million

2. Mass Percentage

3. Volume Percentage

4. Mass by Volume Percentage

5. Molarity

6. Molality

7. Normality

8. Formality

9. Mole Fraction

Let us study each method in detail.

Concentration in Parts Per Million (ppm)

One part by volume or by weight of a solute in million parts by volume or by weight of solution equals 1 ppm. Weight/ weight or weight/volume concentrations are expressed in parts per million when the solutions are very dilute. 

The concentration for a solution is given by-

\[ C = \frac{weight of solute in g}{volume of solution in l}\]

Concentration in parts per million 106for a solution-

\[ ppm = \frac{mass of solute}{total mass of the solution}*10^{6}\]

Mass Percentage (w/w)

Mass percentage of a solution is referred to the concentration of the solution that is expressed as the percent of one component in the solution by mass. Let us say a solution consists of two components: a solute and a solvent which are A and B respectively. The mass percentage of solute A will be-

\[Mass~percentage~of~A = \frac{Mass of solute A in the solution}{Total mass of the solution}* 100\]

Volume Percentage (V/V)

The volume percentage of a solution is referred to as the concentration of the solution that is expressed as the percent of one component in the solution by volume. Let us say a solution consists of two components: a solute and a solvent which are A and B respectively. The mass percentage of solute A will be-

\[Volume~percentage~of~A = \frac{Volume of solute A in the solution}{Total volume of the solution}* 100\]

Mass by Volume Percentage (w/V)

The mass by volume percentage is most commonly used in the pharmaceutical industry. When the mass of solute is dissolved per 100 mL of the solution, it is referred to as mass by volume percentage. It is given by-

\[ Mass~by~Volume~percentage = \frac{Mass of solute}{Volume of solution}* 100\]

Molarity (M)

The molarity of a solution refers to the number of moles that are dissolved in a solution of 1 liter. To find the molarity of a solution, moles of solute are divided by the volume of the solution. 

\[ Molarity = \frac{Moles of solute }{liters of solution} = mol L^{-1}\]

Molality (m)

The concentration of the solution in which the moles of solute and the mass of the solvent are represented is known as molality. To find the molality of the solution, moles of solute is dissolved per kg of the solvent. 

\[ Molality = \frac{Moles of solute }{Mass of solvent in kg}\]

Normality

Normality is referred to as the number of gram equivalents of the solute in a solution present in 1 liter of the solution.

\[ Normality=\frac{Weight of solute in grams}{Equivalent mass * Volume in liter}\]

Formality

Formality is the number of gram formulas that is present in one liter of solution. 

\[ Formality=\frac{Weight of solute in gram}{formula weight * Volume in liter}\]

Mole Fraction

A mole fraction gives the concentration, when the solution has a solute and a solvent, as the ratio of moles of one component to the total moles that are present in the solution. Mole fraction for two components A and B in a solution where A is the solute and B is the solvent. So the mole fractions of A and B are given as-

\[ x_{A}= \frac{n_{A}}{n_{A}+n_{B}}\]

\[ x_{A}= \frac{x_{A}}{x_{A}+x_{B}}\]

More about the Topic

1. Percent by Mass or Mass Percentage

Mass percentage is defined as the amount of solute (in gram) present in 100 grams of the solution. This can be calculated by using the following formula:

Mass percentage or percent by mass = (Mass of solute / Mass of solution) X 100

Here, the mass of solution can be expressed by the following formula:

Mass of solution = Mass of solute + Mass of solvent

The mass of solution can also be expressed as:

Mass of solution = Volume of solution X Density of solution

Mass Fraction:

Mass fraction can be expressed as the ratio of mass of solute and mass of solution.

Mass fraction = Mass of solute / Mass of solution

Hence, the mass percentage of solute can be calculated by multiplying a mass fraction by 100.

20% solution of glucose means that 20 grams of glucose (solute) is present in 100 grams of the solution, i.e., 20 gram of glucose has been dissolved in 80 gram of water (solvent). 

2. Percent by Volume:

This term is defined as the solute volume present in 100 mL of solution. This can be expressed by following formula:

Percent of solute by volume = (Volume of solute / Volume of solution) X 100

3. Percent Mass by Volume:

This term is defined as the solute mass present in 100 mL of solution. This can be expressed by following formula:

Percent of solute of mass by volume = (Mass of solute / Volume of solution) X 100

4. Strength or Solution Concentration (Concentration in Gram per Liter):

This term can be defined as the amount of the solute mass (in gram) present in one liter of the solution. So, the unit of this term is gram per liter. It can be expressed by the following formula:

Concentration of solution = (Solute mass in gram / Solution volume in liters)

If the unit of volume is in mL, then the overall formula should be multiplied by 1000.

Concentration of solution = (Solute mass in gram / Solution volume in mL) X 1000

The strength of the solution can be defined as the concentration of solution in grams per liter. Suppose, 10 g of glucose (solute) is present in 1 L of solution, then the strength or concentration of the solution is 10 g/L.

5. PPM (Parts per Million):

This method is particularly important when the solute is present in trace quantities. It is easy to express concentration of solution in that case. Parts per million can be defined as the amount of the solute in grams present in 106 gram of the solution.

ppm = (Mass of solute / Mass of solution) X 106

The example in which the solute is present in trace quantities is the atmospheric pollution in cities. This concentration refers to the pollutant volume in 106 units of air volume. 20 ppm of sulfur dioxide (SO2) in air means that 10 mL of SO2 is present in 106 mL of air volume. 

6. Mole Fraction:

Mole fraction method can be used in the case when the solution is composed of two or more components. It is defined as the ratio of total moles of one component to the total number of moles of the given solution. (Note- The total number of moles of the solution includes the moles of all the components present in the solution.) 

Suppose there are three components present in the solution, namely component A, B and C. The moles of component A is a, the moles of component B is b, and the moles of component C is c. Hence, the total moles of solution is (a + b + c).

According to the definition of mole fraction, the mole fraction of component A, B, and C can be calculated in the following way:

Mole fraction of A = f A = a / (a + b + c)

Mole fraction of B = f B = b / (a + b + c)

Mole fraction of C = f C = c / (a + b + c)

Fact on Mole fraction: The addition of mole fraction of all components is always equal to 1, i.e., 

f A+ f B + f C = 1

In case of binary solution (i.e. the condition when the solution is made up of only one solute and remaining is solvent.), 

Total mole fraction = Mole fraction of solute + Mole fraction of solvent = 1

Consider the case of a solution that is made up of solute A and solvent B. The moles of solute A are a and the moles of solvent B is b. Then the mole fraction is:

Mole fraction of solute A = X A= a / (a + b)

Mole fraction of solute B = X B= b / (a + b)

Hence, the total mole fraction is:

Total Mole Fraction = X A + X B = 1

Note- The mole fraction of solution is independent of temperature of the solution.

7. Molality:

Molality of the solution can be defined as the number of solute moles available or present in total of 1 kg of the solvent. The symbol of molality is ‘m’. 

Molality can be represented by the following formula:

Molality (m) = Number Of Solute Moles/Number Of Kilograms(kg)of the solvent present

Suppose, a gram of solute of molecular mass b be present in c gram of the solvent, then the molality can be calculated as:

Molality (m) = a/(bXc) X 1000

Molality (m) = A/c X 1000

Where A is the total number of moles of solute i.e. a / b. 

Please note the following points on molality:

1. Molality involves the mass of liquids during the calculation rather than involving volumes of liquids. Hence, this method is the most convenient method of expressing the concentration of a solution.

2. This method is, unlike mole fraction, independent of the variation in temperature.

There is a relation between the molality and solubility which can be mentioned as follow:

Molality = (Solubility X 10) / Molecular mass of solute

Solubility can be expressed as:

Solubility = (Mass of solute in gram / Mass of solvent in gram) X 100

8. Molar Concentration (Molarity):

Molar concentration i.e. also known as molarity can be defined as the total number of solute moles per liter or say per dm3 of the solution.

According to the definition, it can be calculated by using the following formula:

Molarity (M) = Number of moles of solute / Number of liters of solution

OR

Molarity (M) = (Number of moles of solute / Number of mL of solution) X 1000

OR

Number of moles of solute = Molarity (M) X Number of liters of solution

Consider a solution containing a gram of solute of molecular mass b and it is dissolved in a V liter of solution. 

Then, the molarity of the solution is

Molarity (M) = a / (b X V)

OR

Molarity of solution X b = a / V = Strength of the solution

If the volume component is taken in mL unit, then the following modification is needed:

Molarity (M) of the solution = a/(bXV) X 1000

The formula can also be written as:

Molarity (M) = (1000 X Weight of solute in gram) / (Molecular mass of solute X Volume of solvent in mL) 

9. Normality:

The term ‘normality’ can be defined as the number of gram equivalents of solute present per liter of the solution. Normality is denoted by ‘N’. 

According to definition, it can be expressed by the following formula:

Normality (N) = number of gram equivalents of solute / Number of liters of the solution

OR 

Number of gram equivalents of solute = Normality X Number of liters of the solution

Let A gram of the solute of equivalent mass B be present in V liter of the final solution, then the normality can be calculated by:

Normality (N) = (A / B) / V

OR

Normality (N) = A / (B X V)

OR

Normality (N) X Equivalent mass = A / V = Strength of the solution in g/L

The solutions are expressed as 1 N, 2 N, etc. 

10. Formality:

The formality of the solution can be defined as the formula mass (in gram) present per liter of solution. When the formula mass is equal to the molecular mass, formality is equal to the molarity. Formality is also dependent on temperature, just like normality and molarity of the solution. Formality is particularly useful when the solution contains ionic compounds in which the molecule does not exist. (Formole is known as the mole of ionic compounds and formality is the molarity of ionic compounds.)