# Solutions Class 12 Notes Chemistry Chapter 2

Introduction, Types of Solutions, Expressing the Strength of Solution, Solubility, Vapour Pressure of Solution, Raoult’s Law, Colligative Properties

## Introduction

In this chapter, we will discuss about liquid solutions and their formation. This will be followed by studying the properties of solutions, like vapour pressure and colligative properties. We will begin with types of solutions and expressions for concentration of solutions in different units.

Thereafter, we will state and explain Henry’s law and Raoult’s law, distinguish between ideal and non-ideal solution and deviation of real solutions from Raoult’s law. We will also discuss abnormal colligative properties alongwith association and dissociation of solute.

## Types of Solutions

All the three states of matter (solid, liquid and gas) may behave either as solvent or solute. When a solution is composed of only two chemical substances, it is termed as binary solution. Depending upon the state of solute or solvent, binary solutions can be classified as

## Some Important Definitions

### 1. Mixture

When two or more chemically non-reacting substances are mixed, they form mixture.

### 2. Heterogeneous Mixture

It consists of distinct phases, and the observed properties are just the sum of the properties of individual phases.

### 3. Homogeneous Mixture

It consists of a single phase which has properties that may differ from one of the individual components.

### 4. Solution

The homogeneous mixture of two or more components such that at least one component is a liquid is called solution.

### 5. Solvent

It is the constituent of solution which has same physical state as that of solution and generally present in greater amount than all the other components.

### 6. Solute

The component of a solution other than solvent is called solute, may or may not have same physical state as that of solution. Generally it is in smaller amount.

Ex- In a sugar syrup (liquid solution) containing 60% sugar (solid) and 40% water (liquid), water is termed as solvent, due to same physical state as that of solution.

## Expressing the Strength of Solution

For a given solution the amount of solute dissolved per unit volume of solution is called concentration of solute. Strength of solution is the amount of solute in grams dissolved in one litre of solution. It is generally expressed in g/litre.

Other methods of expressing the strength of solution are:

## Solubility

### 1. Mass percentage

Mass % of solute = \frac{Mass-of-solute}{Total-mass-of-solution}\times 100

Mass % of solvent = \frac{Mass-of-solvent}{Total-mass-of-solution}\times 100

### 2. Volume percentage

Volume % of solute = \frac{Volume-of-solute}{Total-volume-of-solution}\times 100

Volume % of solvent = \frac{Volume-of-solvent}{Total-volume-of-solution}\times 100

### 3. Molality (m)

It is no. of moles of solute dissolved in 1 kg of the solvent.

m = (Number of moles of solute) / (Mass of solvent {in kg})

### 4. Molarity (M)

It is no. of moles of solute dissolved in 1 litre of solution.

M = (Number of moles of solute ) / (Volume of solution {in litre})

### 5. Normality (N)

It is no. of gram-equivalents of solute dissolved in 1 litre of solution

N = (Number of gram equivalents of solute) / (Volume of solution {in litre})

### 6. Formality

Ionic solutes do not exist in the form of molecules These molecular mass is expressed as Gram-formula mass. Molarity for ionic compounds is actually called as formality.

### 7. Mole fraction

Mole fraction of solute = (Number of moles of solute) / (Total moles of solution)

Mole fraction of solvent = (Number of moles of solvent) / (Total moles of solution)

For a binary solution,

mole fraction of solute + mole fraction of solvent = 1.

### 8. Parts per million (ppm)

It is defined in two ways

ppm = mass fraction × 10^6

ppm = mole fraction × 10^6

## Solubility

Solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent at a specified temperature. It depends upon the nature of solute and solvent as well as temperature and pressure. Let us consider the effect of these factors in solution of a solid or a gas in a liquid.

### 1. Solubility of Solid in Liquid

A solute dissolves in a solvent if the intermolecular interactions are similar in them, i.e., like dissolves like. Polar solute dissolves in polar solvent and non-polar solute in non-polar solvent. For e.g., sodium chloride and sugar dissolves readily in water and napthalene and anthracene dissolves readily in benzene.

Solute + Solvent ⟶ Solution

(i). Dissolution: When a solid solute is added to the solvent, some solute dissolves and its concentration increases in solution. This process is called dissolution.

(ii). Crystallization: Some solute particles collide with solute particles in solution and get separated out. This process is called crystallization.

(iii). Saturated solution: Such a solution in which no more solute can be dissolved at the same temperature and pressure is called a saturated solution.

(iv). Unsaturated solution: An unsaturated solution is one in which more solute can be dissolved at the same temperature.

(vi) Effect of temperature: In general, if in a nearly saturated solution, the dissolution process is endothermic, the solubility should increase with rise in temperature, if it is exothermic, the solubility should decrease with rise in temperature.

(vii) Effect of pressure: Solids and liquids are highly incompressible, so pressure does not have any significant effect on solubility of solids and liquids.

(vii) Supersaturated solution: When more solute can be dissolved at higher temperature in a saturated solution, then the solution becomes supersaturated.

### 2. Solubility of Gas in Liquid

All gases are soluble in water as well as in other liquids to a greater or lesser extent. The solubility of a gas in liquid depends upon the following factors Nature of the gas, Nature of solvent, Temperature and Pressure.

Generally, the gases which can be easily liquified are more soluble in common solvents. For e.g., CO2 is more soluble than hydrogen or oxygen in water. The gases which are capable of forming ions in aqueous solutions are much more soluble in water than other solvents. For e.g., HCl and NH3 are highly soluble in water but not in organic solvents (like benzene) in which they do not ionize.

(i) Effect of temperature: Solubility of most of the gases in liquids decreases with rise in temperature. In dissolution of a gas in liquid, heat is evolved and thus this is an exothermic process. The dissolution process involves dynamic equilibrium and thus follows Le Chatelier’s principle. As dissolution is exothermic the solubility of gas should decrease with rise in temperature.

(ii) Effect of pressure: Henry’s law - At constant temperature, the solubility of a gas in a liquid is directly proportional to the pressure of the gas.

p = KH x,

KH = Henry’s law constant.

### Applications of Henry’s law

1. In manufacture of soft drinks and soda water, CO2 is passed at high pressure to increase its solubility.
1. To minimise the painful effects accompanying the decompression of deep sea divers. O2 diluted with less soluble. He gas is used as breathing gas.
1. At high altitudes, the partial pressure of O2 is less then that at the ground level. This leads to low concentrations of O2 in the blood of climbers which causes ‘anoxia’.

## Vapour Pressure of Solution

It is the pressure exerted by vapour on the surface layer of liquid at equilibrium between vapour and liquid.

### Factors affecting Vapour Pressure

#### i). Nature of liquid

Liquid with higher intermolecular attraction forces form less amount of vapour and hence lower vapour pressure and vice-versa.

#### ii). Temperature

Vapour pressure increases with temperature of liquid. This is because, as temperature increases, kinetic energy of the molecules increases, hence, more molecules leave the surface of the liquid and come into vapour phase.

## Raoult’s Law

According to Raoult’s law, for a solution of volatile liquids, the relative lowering of vapour pressure of solution is directly proportional to its mole fraction of dissolved solvent in solute.

\frac{P°-P}{P°}=X_A

### Ideal Solution

The solution which obeys Raoult’s law at all compositions of solute and solvent and at all temperature is called an ideal solution. Ex- Benzene and Toluene, n-hexane and n-heptane.

#### Characteristics of an ideal Solution

1. Raoult’s law is obeyed by it.

2. ΔHmixing = 0 i.e., no heat should be absorbed or evolved during mixing.

3. ΔVmixing = 0, i.e., no change in volume (expansion or contraction) on mixing.

### Non-ideal Solution

Those solutions which deviate from ideal behaviour are called non-ideal solutions or real solutions. Acetone and CS2, Acetone and C2H5OH

#### Characteristics of an non-ideal Solution

1. Raoult’s law is not obeyed by it.

2. ΔHmixing ≠ 0 i.e., solution may absorb or release heat.

3. ΔVmixing ≠ 0 i.e., solution may expand or contract on mixing of solute and solvent.

### Azeotropic Mixture

At the constant boiling temperature, liquid mixture vapouries without change in composition and the condensate contains same composition, i.e., mixture distills like a pure liquid, which has same composition. At this point, solution or mixture is called an azeotropic mixture.

## Colligative Properties

The properties of dilute solution which depends only on number of particles of solute (molecules or ions) present in the solution and not on their nature, are called colligative properties. The important colligative properties are;

1. Relative lowering of vapour pressure
2. Elevation of boiling point
3. Depression in freezing point
4. Osmotic pressure

### i). Relative Lowering of Vapour Pressure

When a non-volatile solute is added to a solvent, its vapour pressure gets lowered. If this pressure is divided by pressure of pure solvent, this is called relative lowering of vapour pressure

According to Raoult’s law,

\frac{P°-P}{P°}=X_A

where, P° = V.P. of pure solvent

P° - P = lwering in vapour pressure

\frac{P°-P}{P°}=\frac{n_A}{n_{A}+n_{B}} ...[X_A=\frac{n_A}{n_{A}+n_{B}}]

For dilute solution nA + nA ≈ nA

\frac{P°-P}{P°}=\frac{n_A}{n_{B}}

\frac{P°-P}{P^0}=\frac{W_A}{M_{A}}\times\frac{M_B}{W_B}

where, WA = weight of solute

WB = weight of solvent

MA = molecular weight of solute

MB = molecular weight of solvent

### ii). Elevation of boiling point

A liquid boils at the temperature at which its vapour pressure is equal to the atmospheric pressure. The boiling point of a solution of non-volatile solute is always higher than that of the boiling point of pure solvent in which the solution is prepared. Similar to lowering of vapour pressure, the elevation of boiling point also depends on the number of solute particles rather than their nature.

Let T° be the boiling point of pure solvent and T be the boiling point of solution. The increase in boiling point ΔTb = T – T° is known as elevation in boiling point.

For dilute solutions, the ΔTb is directly proportional to the molal concentration of the solute in a solution. Thus

ΔTb ∝ m

ΔTb = Kbm

Kb is molal elevation constant (Ebullioscopic constant). The unit of Kb is K kg mol–1.

Substituting the value of molality in above equation, we get

ΔT_{b}=\frac{K_{b}\times 1000\times w_{2}}{M_{2}\times w_{1}}

M_{2}=\frac{K_{b}\times 1000\times w_{2}}{ΔT_{b}\times w_{1}}

Where, w1 = mass of solvent, w2 = mass of solute and M2 = molar mass of solute

### iii). Depression in freezing point

Freezing point is the temperature at which vapour pressure of liquid phase becomes same as that of solid phase. The decrease in freezing point of a solvent on the addition of a non-volatile solute is known as depression in freezing point.

Let T° be the freezing point of pure solvent and T be the freezing point of solution. The decrease in freezing point ΔTf = T° -T is known as depression in freezing point.

For dilute solutions, the ΔTf is directly proportional to the molal concentration of the solute in a solution. Thus

ΔTf ∝ m

ΔTf = Kf ⋅ m

Here Kf is molal depression constant or cryoscopic constant

Substituting the value of molality in above equation, we get

ΔT_{f}=\frac{K_{}\times w_{2}\times 1000}{M_{2}\times w_{1}}

M_{2}=\frac{K_{}\times w_{2}\times 1000}{ΔT_{f}\times w_{1}}

Where, w1 = mass of solvent, w2 = mass of solute and M2 = molar mass of solute

### iv). Osmotic pressure

Osmosis is the spontaneous flow of the solvent molecules from a less concentrated solution (dilute) to a more concentrated solution through a semi-permeable membrane. The driving force of osmosis is called osmotic pressure. Osmotic pressure may be defined as “the minimum excess pressure that has to be applied on the solution to prevent the osmosis".

Osmotic pressure of a solution ∝ molar concentration of solute in that solution

π ∝ c

π = cRT

where, R = Gas constant = 0.0821 lit atm K-1 mole-1

T = Temperature

c = Molar concentration

π = \frac{n}{V}RT .....[c=\frac{n}{V}]

π = \frac{W_{B}}{M_{B}}\frac{RT}{V}

WB = wt. of solute

MB = Molar mass of solute

## van’t Hoff Factor

To calculate the extent of association or dissociation, van’t Hoff in 1886 introduced a factor ‘i’ called van’t Hoff factor. van’t Hoff factor ‘i’ is defined as ratio of the experimental value of colligative property to the calculated value of colligative property.

i.e., i = (Experiment ecolligatival properties) / (Calculated ecolligativ properties)

## Summary

1. A solution is a homogeneous mixture of two or more substances and are classified as solids, liquids and gaseous solutions.

2. Concentration of a solution is expressed in terms of mole fraction, molarity, molality and in percentages.

3. The dissolution of a gas in a liquid is governed by Henry’s law, according to which, at a given temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas.

4. The vapour pressure of the solvent is lowered by the presence of a non-volatile solute in the solution and this lowering is governed by Raoult’s law, according to which relative lowering of vapour pressure of solvent is equal to the mole fraction of non-volatile solute present in solution.

5. Solutions which obey Raoult’s law over the entire range of concentration are called ideal solutions. For non-ideal solutions, positive and negative deviations are observed from Raoult’s law. Azeotropes arise due to very large deviations from Raoult’s law.

6. Colligative properties are the properties of solutions which depends on the number of solute particles and independent of their chemical identity. These are relative lowering of vapour pressure, elevation in boiling point, depression in freezing point and osmotic pressure.

7. Solutes which dissociate in solution exhibit the molar mass lower than the actual molar mass and those which associate show higher molar mass.

8. van’t Hoff Factor ‘i’ is the extent to which a solute is dissociated or associated. This can be defined as ratio of observed colligative property to calculated colligative property.