Class 12 Chemistry Study Notes Chapter 2 - Solutions

A solution is simply a homogeneous mixture of two or more substances.

Solutions can be solid, liquid and gaseous.

Alloy is an example of a solid solution, while air is a gaseous solution.

A mixture is called solution when it has homogeneity at the particle level.

Examples of solutions

Types of Solutions

Properties of Solutions

·        They are homogeneous mixtures of solutes and solvents.

·        The solute particles in a solution are extremely small in size. They are less than 1 nm (10⁻⁹ m) in diameter.

·        The solute particles are not visible to the naked eye.

·        As a result of the small size of the solute particles, a solution does not scatter a beam of light passing through it.

·        Being small in size, the solute particles get dissolved in the solvent. Hence, the solute cannot be separated from the solvent by filtration.

·        The solute particles do not settle down when left undisturbed.

Vapour Pressure

Like a gas, a liquid exerts pressure of its own due to evaporation. This pressure is known as the vapour pressure of the liquid.

Ways to represent Concentration

(i) Mass percentage (w/w):

   

(ii) Volume percentage (V/V):

   

(iii) Mass by volume percentage (w/V): Another unit which is commonly used in medicine and pharmacy is mass by volume percentage. It is the mass of solute dissolved in 100 mL of the solution.

(iv) Parts per million:

   

(v) Mole fraction:

   

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

             

(vi) Molarity: Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution,

   

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

   

Solubility

·        Solubility of a substance is the maximum amount of the substance that can be dissolved in a specified amount of a solvent at a given temperature.

·        Factors on which solubility depends:

·        Nature of solute and solvent

·        Temperature

·        Pressure

Solubility of a Solid in a Liquid

When a solute is dissolved in a solvent, the following dynamic equilibrium is established.

        Solute + Solvent  Solution

This equilibrium follows Le Chatelier’s Principle.

·        Effect of temperature:

According to Le Chatelier’s principle, in a nearly saturated solution, if the dissolution process is

·        Endothermic (Δ_solH > 0), then the solubility will increase with the increase in temperature

·        Exothermic (Δ_solH < 0), then the solubility will decrease with the increase in temperature

·        Effect of pressure:

·        Pressure has no significant effect on the solubility of solids in liquids.

·        Reason − Solids and liquids are negligibly affected by pressure as they are highly incompressible.

Solubility of a Gas in a Liquid

·        The solubility of gases in liquids increases with the increase in pressure.

Henry’s law

The solubility of a gas in a liquid is directly proportional to the pressure of the gas.

Or

The partial pressure of a gas in vapour phase (p) is directly proportional to the mole fraction of the gas (x) in the solution, i.e.,

        p = K_H x

Where, K_H = Henry’s law constant

The plot of the partial pressure of HCl vs. its mole fraction in a solution of cyclohexane is given below.

Some important applications of Henry’s law

(i) Bottles are sealed under high pressure to increase the solubility of CO₂ in soft drinks and soda water.

(ii) Henry’s law states that the solubility of gas increases with an increase in pressure. Therefore, when a scuba diver dives into the sea, the increased sea pressure causes the nitrogen present in air to dissolve in his blood in great amounts. As a result, when he comes back to the surface, the solubility of nitrogen again decreases and the dissolved gas is released, leading to the formation of nitrogen bubbles in the blood. This results in the blockage of capillaries and leads to a medical condition known as ‘bends’, which are painful and dangerous to life. Hence, the oxygen tanks used by scuba divers are filled with air and diluted with helium to avoid bends.

(iii) The concentration of oxygen is low in the blood and tissues of climbers or people living at high altitudes. This is because at high altitudes, the partial pressure of oxygen is less than that at ground level. Low blood oxygen causes climbers to become weak and prevents them from thinking clearly. These are symptoms of ‘anoxia’.

·        Effect of temperature

Solubility of gases in liquids decreases with the increase in temperature.

Vapour Pressure of Liquid Solutions

·        Let p₁, p₂ = Partial vapour pressure of two volatile components 1 and 2 of a mixture

     = Vapour pressure of pure components 1 and 2

    x₁, x₂ = Mole fractions of the components 1 and 2

    p_total = Total vapour pressure of the mixture

Raoult’s law

For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction.

         p₁ ∝  x₁

That is, for component 1,

        

For component 2,

          

According to Dalton’s law of partial pressures,

          

                      

                      

        

·        From the above equation, it can be concluded that:

·        p_total can be related to mole fraction of any one component.

·        p_total varies linearly with x₂.

·      Depending upon  and ,  increases or decreases with the increase of x₁.

·        The plot of vapour pressure and mole fraction of an ideal solution at constant temperature is shown below.

    Here, maximum value of .

    Minimum value of .

    Here,  because it is assumed that component 1 is less volatile than component 2.

·        The component of vapour phase in equilibrium with the solution is determined by the partial pressures of the components.

Let y₁, y₂ = Mole fractions of the components 1 and 2 respectively in the vapour phase.

According to Dalton’s law of partial pressures,

      p₁ = y₁ p_total

      p₂ = y₂ p_total

In general, we can write

     p_i = y_i p_total

Raoult’s Law as a Special Case of Henry’s Law

·        According to Raoult’s law, the vapour pressure of a volatile component in a given solution is .

·        According to Henry’s law, the partial vapour pressure of a gas (the component is so volatile that it exists as gas) in a liquid is

        p = K_H x

·        It can be observed that in both the equations, the partial vapour pressure of the volatile component varies directly with its mole fraction. Only the proportionality constants K_H and  are different. Thus, Raoult’s law becomes a special case of Henry’s law in which K_H is equal to  .

Vapour Pressure of Solutions of Solids in Liquids

·        When a non-volatile solute is added to a solvent, the vapour pressure of the liquid decreases.

·        Reason: The number of solvent molecules on the surface decreases and as a result, number of solvent molecules escaping from the surface decreases.

·        Raoult’s law in general form: For any solution, the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.

·        Let us take a binary solution made by dissolving a non-volatile solute in a solvent. Since the solute is non-volatile, only the solvent molecules contribute to vapour pressure.

Let  = Vapour pressure of the solvent

 = Vapour pressure of the solvent in pure state

      x₁ = Mole fraction of the solvent

Then, according to Raoult’s law,

                   

Here, the proportionality constant is equal to the vapour pressure of the solvent in pure state.

The plot of vapour pressure vs. mole fraction of the solvent, which is linear, is shown below.

Ideal Solution

·        Solutions which obey Raoult’s law over the entire range of concentrations

·        For ideal solution:

·        Enthalpy of mixing of the pure components to form the solution,

        Δ_mix H = 0

·        Volume of mixing, Δ_mix V = 0

·        An ideal solution will be formed when intermolecular forces of attraction between the molecules of solute (A − A) and those between the molecules of solvent (B − B) are nearly equal to those between solute and solvent molecules (A − B).

·        Examples: n-Hexane and n-heptane, bromoethane and chloroethane, benzene and toluene

Non-Ideal Solutions

·        Solutions which do not obey Raoult’s law over the entire range of concentration

·        The vapour pressure of a non-ideal solution is either higher or lower than that predicted by Raoult’s law.

Positive deviation from Raoult’s law

(When vapour pressure of solution is higher)

·        The plot of vapour pressure of two component solutions as a function of mole fraction is shown below.

·        The intermolecular forces of attraction between solute-solvent molecules are weaker than those between solute-solute molecules and solvent-solvent molecules. Therefore, solvent molecules can easily escape, resulting in increase in vapour pressure.

·        Example: Ethanol and acetone mixture.

Negative deviation from Raoult’s law

(When vapour pressure of solution is lower)

·        The plot of vapour pressure of two component solutions as a function of mole fraction is shown below.

·        The intermolecular forces of attraction between solute-solute molecules and solvent-solvent molecules are weaker than those between solute-solvent molecules. This results in the decreasing of vapour pressure.

·        Example − Chloroform and acetone mixture

The intermolecular attractive forces between solute-solvent molecules increase due to the formation of H-bond.

Azeotropes

·        Binary mixtures which have the same composition in liquid and vapour phase, and have constant boiling points

·        Not possible to separate the components by fractional distillation

·        Two types –     (i) Minimum boiling azeotrope (ii) Maximum boiling azeotrope

·        Minimum boiling azeotrope − Solution showing a large positive deviation from Raoult’s law of specific composition

·        Example: Ethanol-water mixture containing ethanol approximately 95% by volume

·        Maximum boiling azeotrope − Solution showing a large negative deviation from Raoult’s law at specific composition

·        Example: Nitric acid-water mixture containing 68% nitric acid and 32% water by mass

The boiling point of this azeotrope is 393.5 K.

Colligative Properties and Determination of Molar mass

·        Properties which depend upon the number of solute particles present in the solution irrespective of their nature, relative to the total number of particles present in the solution

·        Examples: Relative lowering of vapour pressure of the solvent, depression of freezing point of the solvent, elevation of boiling point of the solvent, osmotic pressure of the solution.

Relative Lowering of Vapour Pressure

·        Relative lowering of vapour pressure is equal to the mole fraction of the solute.

      i.e.,

Where,

       = Vapour pressure of the solvent

      p₁ = Vapour pressure of the solution

      x₂ = Mole fraction of the solute

However,

Where, n₂ = Number of moles of solute

            n₁ = Number of moles of solvent

        

For dilute solution, n₁ >> n₂ , therefore

       

       

       

         Where, w₂ = Mass of solute

               M₂ = Molar mass of solute

                w₁ = Mass of solvent

               M₁ = Molar mass of solvent

Elevation of Boiling Point

·        With addition of non-volatile solute, vapour pressure decreases and hence, boiling point increases.

·      Here,  = Elevation of boiling point

      Where, T_b = Boiling of solution.   T_b° = Boiling point of solvent

          ΔT_b ∝ m (for dilute solution)

    ⇒ ΔT_b = K_b m

    Where, m = Molality

                K_b = Proportionality constant known as Boiling Point Elevation Constant

                        or Molal Elevation Constant or Ebullioscopic constant

                        (Unit = K kg mol⁻¹)

             

             

       Where,

                w₂ = Mass of solute

                M₂ = Molar mass of solute

                w₁ = Mass of solvent

      Hence,

               

               

Depression of Freezing point

With addition of non-volatile solute, vapour pressure decreases, which leads to a decrease in freezing point.

    Here,  = Depression of freezing point

    Where,      = Freezing point of solvent

                     T_f  = Freezing point of solution

For dilute solution (ideal solution),
           ΔT_f  ∝ m

          ⇒ ΔT_f = K_f  m

    Where, m = Molality

                K_f = Proportionality constant known as Freezing Point Constant

                       or Molal Depression Constant or Cryoscopic constant

                       (Unit = K kg mol⁻¹)

             

             

     Where,

                w₂ = Mass of solute

                M₂ = Molar mass of solute

                w₁ = Mass of solvent

    Hence,

               

               

    The value of K_b and K_f can be determined by the following relations:

               

               

    Where,

                M₁ = Molar mass of the solvent

                 R = Gas constant

                Δ_vapH = Enthalpy of vaporisation

                Δ_fusH = Enthalpy of fusion

Antifreeze

Antifreeze solutions are added to a liquid in a cooling system (such as the water in an automobile engine) to lower its freezing point and prevent ice build-up in the system at cooler temperatures.

Functions of Antifreeze

·        It contains chemicals that prevent corrosion and scale formation in the engine and radiator of a vehicle.

·        It provides protection against boiling during summers. At 1 atmosphere pressure, water boils at 100 °C; but a 50-50 blend of water−ethylene glycol boils at 106 °C.

·        A mixture of antifreeze and distilled water (in the ratio, one part antifreeze to one part water) provides freeze protection down to −36.67 °C and boils over protection up to 129.4 °C.

Precautions 

·        Avoid using concentrated antifreeze in a cooling system. At least 40% of the mixture should be water.

·        Do not increase the concentration of antifreeze above 60% as it damages the freezing and overheating protection of the engine. 

·        Do not add too much water to the cooling system as it lowers the concentration of the corrosion inhibitor and antifreeze. This results in decreased protection against corrosion and freezing.

Osmosis and Osmotic Pressure

·        The process of flow of solvent molecules from pure solvent to solution or from solution of lower concentration to solution of higher concentration through a semi-permeable membrane is called osmosis.

·        The pressure required to just stop the flow of solvent due to osmosis is called osmotic pressure (π) of the solution.

·        Osmotic pressure π has to be applied to the solution to prevent osmosis.

·        For dilute solution, osmotic pressure is directly proportional to the molarity C of the solution at a given temperature T.

That is, π = CRT (R = Gas constant)

             

        Where,

            n₂ = Number of moles of solute

            V = Volume of the solution in litres

             

        Where, w₂ = Mass of the solute

                    M₂ = Molar mass of the solute

           

           

           

 

·        Isotonic solutions − Solutions having same osmotic pressure. These solutions have same concentration of solute. Osmosis does not occur between two isotonic solutions.

·        Hypotonic solution − Solution having a low concentration of solute relative to another.

·        Hypertonic solution − Solution having a high concentration of solute relative to another.

Reverse Osmosis and Water purification

·        If the pressure applied on the solution is greater than its osmotic pressure, then the direction of osmosis is reversed i.e., the solvent starts passing from solution to solvent. The phenomenon is called reverse osmosis.

·        This phenomenon is used in purification (desalination) of sea water.

       

·        Due to association or dissociation of molecules, the molar mass of a substance calculated from its colligative property is either lower or higher than the expected or normal value. Such molar mass is called abnormal molar mass.

         Dissociation:

             KCl  K⁺ + Cl⁻

         Association:

             2CH₃COOH ⇌ (CH₃COOH)₂

            

·        To account for the extent of dissociation or association, van’t Hoff introduced a factor i, known as the van’t Hoff factor.

           

              

              

·        Value of i:

      For association, i < 1

      For dissociation, i > 1

      No association or dissociation, i = 1

·        Modified equations for colligative properties after inclusion of van’t Hoff factor

·        Relative lowering of vapour pressure of solvent,

             

·        Elevation of boiling point, ΔT_b = iK_b m

·        Depression of freezing point, ΔT_f = iK_f m

·     Osmotic pressure of solution,

Online Tuitions & Self-Study Courses for Grade 6 to 12 & JEE / NEET