# Solution

A homogeneous mixture of two or more substances having uniform properties such as density, refractive index etc., is known as solution. The substance which is present in smaller quantity in the solution is called solute and which is present in larger quantity is called solvent.

E. g. In the aqueous solution of sugar, sugar is solute and water is solvent. The concentration of solutions is expressed by following different ways:

1. As percentage by weight: If w g of solute is present in W g of solution then

$\text{Percentage of solute} = \dfrac{\text{Mass of solute} \times 100}{\text{Mass of solution}} = \dfrac{w \times 100}{W}$

2. As gram per litre $(gL^{-1})$ : It is the number of gram of solute present in one lire of the solution.

$gL^{-1} = \dfrac{\text{Mass of solute}}{\text{Volume of solution in litre}}$

3. As parts per million (ppm): This unit is used for very dilute solutions. It may be expressed as:

$\text{ppm of a substance} = \dfrac{\text{Mass of the solute}}{\text{mass of the solution}} \times 10^6$

4. As normality (N): It is the number of gram equivalent of the solute present in one litre of the solution. Thus

$N = \dfrac{\text{Gram equivalent}}{\text{Litres of solution}} \\[3mm] = \dfrac{\text{Mass of the solute(g)}}{\text{Eq. mass of solute} \times _{litre}} \text{or} \dfrac{w}{EV}$

When the gram equivalent of the substance per litre of solution are 1/5, 1/10, 1/20, 5 etc. they are indicated as N / 5, N / 10, N / 20, 5N etc. respectively.

Strength of the solution in gram per litre is determined by the following formula:

Strength,

$g L^{-1} =\text{Normality} \times \text{Gram Eq. mass}$

5. As molarity (M): It may be defined as, the number of moles of solute present in one litre of solution. This is called its molarity. Thus

$\text{Molarity} = \dfrac{\text{Mass of solute} (g) / \text{Mol. Mass of solute}}{\text{Volume of solution (L)}}$

Molarity is related with normality as:

$\text{Molarity} = \text{Normality} \times \text{Eq. mass / Mol. Mass}$

6. As molality (m): It may be defined as, the number of moles of solute present in 1000 g (1 kg) of solvent. This in called its molality.

Thus,

$\text{Molarity} = \dfrac{\text{Mass of the solute} (g) / \text{Mol mass of solute}}{\text{Mass of solvent} (kg)}$

7. As mole fraction: It may be defined as the ratio of the number of moles of the solute to the total number of moles in the solution. This is called mole fraction or molar fraction of the solute.  Let n be the number of moles of solute dissolved in ‘N’ moles of the solvent.

Thus,

$\text{Mole fraction of solute} = \dfrac{n}{(n + N)}$

And $\text{Mole fraction of solvent} = \dfrac{N}{(n + N}$

It is evident that:

Mole fraction of solute + Mole fraction of solvent =1

8. Formality (F): It is the number of gram formula weight of solute present in one litre of the solution

$\text{Formality} = \dfrac{\text{No. of gram formula weight of solute}}{\text{Volume of solution} (L)}$

Morality, mass fraction, mole reaction do not depend upon temperature, so these are preferred over molarity and normality which depend upon temperature.

• Molality, mole reaction, mass fraction are temperature independent as weight does not change with temperature.

Representations of concentrations

 S. No System Definition 1. Percentage (%) Parts of solute in 100 parts of solution (w/w, w/v, v/w, v/v). 2. Gram per liter No. of solute in 1 L of solution 3. Parts per million (PPM) No. of g of solute in 106g of solution. 4. Normality (N) No. of equivalent of solute in 1 L of solution. 5. Molarity (M) No. of moles of solute in 1 L of solution. 6. Molality (m) No. of moles of solute in 1 Kg of solvent. 7. Mole fraction (x) Fraction of mole of component in 1 mole of the mixture. 8. Formality (F) No. of formula weight of solute in 1 L of solution.

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