Expression of Concentration of Solutions - Practice Questions & MCQ

The concentration of a solution gives us an idea about the relative amount of solute and solvent present in the solution. The concentration can be expressed either qualitatively or quantitatively. For example, qualitatively we can say that the solution is dilute (i.e., relatively very small quantity of solute) or it is concentrated (i.e., relatively very large quantity of solute). But in reality, the qualitative description can cause confusion, and hence there is a need for a quantitative description of the solution.     

There are several ways by which we can describe the concentration of the solution quantitatively.

 

(1) Mass percentage (w/w):

It is the mass of any component present in 100 g of solution. 

Mathematically, it can be defined as:

For example, a solution described by 20% by mass of glucose in water, it means that 20 g of glucose is dissolved in 80 g of water resulting in a 100 g solution.

The mass % can also be expressed in terms of the mass fraction by simply removing the 100 from the above given formula

Concentration described by mass percentage is commonly used in industrial chemical applications.

 

(2) Volume percentage (V/V):

It is the volume of any solute present in 100 ml of the solution. Mathematically it is defined as:

For example, a 20% Methanol solution in water means that 20 mL of Methanol is dissolved in water such that the total volume of the solution is 100 mL. Solutions containing liquids are commonly expressed in this unit.

 

(3) Mass by volume percentage (w/V):

It is the mass of solute dissolved in 100 mL of the solution. Mathematically, it is defined as: 

For example, a 20% weight by volume solution of Glucose in water means that 20 g of Glucose was dissolved in water to obtain a 100ml solution.

This concentration term is commonly used in medicine and pharmacy.

 

(4) Parts per million (ppm):

When a solute is present in trace quantities, it is convenient to express concentration in parts per million (ppm) and is defined as:

As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume, and mass to volume.

This is generally used in expressing the hardness of water and in expressing the concentration of dissolved oxygen in water etc.

For example, if the hardness of a hard water sample is 100pm in CaCO₃, it means that 100 g of CaCO₃ is present in 10⁶ g of the water sample.

 

(5) Mole fraction:

It is the ratio of the moles of any component present in solution to the total moles present in solution. A commonly used symbol for mole fraction is X and the subscript used on the right-hand side of X denotes the component.

It is defined as: 

For example, in a binary mixture, if the number of moles of A and B is n_A  and n_B respectively, the mole fraction of A will be:

It can be shown that in a given solution sum of all the mole fractions is unity, i.e.

Mole fraction unit is very useful in relating some physical properties of solutions, say vapour pressure with the concentration of the solution, and quite useful in describing the calculations involving gas mixtures.

 

(6) Molality(m):

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

For example, 1 molal solution of NaOH means that 1 mol (40 g) of NaOH is dissolved in 1 kg of water.

 

(7) Molarity (M):

It is defined as the number of moles of solute dissolved in one litre of solution

For example, 0.5 mol L^-1 (or 0.5 M) solution of NaOH means that there is 0.5 mol of NaOH dissolved in water to obtain one litre of solution.

Each method of expressing the concentration of the solutions has its own merits and demerits. Mass %, ppm, mole fraction, and molality are independent of temperature, whereas molarity is a function of temperature. This is because volume depends on temperature and the mass does not.