12 Class Chapter 2- Solution

SOLUTION

                                                          Solution: - 

               A solution is homogeneous mixture of two or more chemically non-reacting substances, whose composition can be varied within certain limits.

Expressing concentration of solutions

1.      Percentage:-

=>  mass percentage (%) of a component  (W/W)

                  = Mass of the component in solution*100 / Total mass of the solution

=>  volume percentage (%) of the component (V/V)

           = Volume of the component * 100 / Total volume of the solution

=>  Mass/Volume percentage (%) of the component (W/V)

           =Mass of the component in solution * 100 / Total volume of the solution

2.      Strength:-

Strength of the solution ( gl^-1 or gdm^-3)

= Mass of the solute in grams / Volume of the solution in litre

3.      Molarity (M) :- 

                                No. of moles of the solute / Volume of the solution in litre

    M = strength in gram per litre / Molar mass of the solute

4.      Mole fraction :-   

                                It is obtained by dividing the no. of moles of the solute or solvent by the total no. of moles of the solution.

Mole fraction,    X₁ = n₁/n₁+n₂

                           X₂ = n₂/n₁+n₂

 n₁ = no. of moles of the solvent

 n₂ = no. of moles of the solute

X₁+X₂ = 1

5.      Mass fraction: - 

                                Mass of the given component per unit mass of the solution denoted by X.

X_A = W_A / W_A+W_B

X_B = W_B / W_A+W_B

W_A = Mass of the solvent

W_B = Mass of the solute

X_A+X_B = 1

Solution of solids in liquids

Solubility of a solid in a liquid :- It is defined as the maximum amount of the solid (solute) in grams which can dissolve in 100 grams of liquid (solvent) to form the saturated solution at the particular temperature.

Factors affecting the solubility of a solid in a liquid

        i.            Nature of the solute & the solvent :- “Like dissolves Like”

=> The polar (ionic) compounds like NaCl dissolve in polar solvent like water.

=>  The non polar (covalent or organic) compounds dissolve in non polar compounds like Anthracene dissolve in Benzene.

      ii.            Effect of temperature :-

=>  The solubility increases with increase of temperature when the process of dissolution is endothermic.

Solute + Solvent + Heat -> Solution

Ex:- NaNo₃, KNO₃, NaCl, KCl

=>  The solubility Decreases with increase in temperature when the process of dissolution is exothermic.

Solute + Solvent -> Solution + Heat

              Ex:- Sodium carbonate mono hydrate (Na₂CO₃.H₂O).

=>  Those whose solubility does not increases or decreases continuously

Ex:- CaCl₂.6H₂O -> CaCl₂.4H₂O -> CaCl₂.2H₂O

Solution of Gases in liquids

1)      Solubility of a gas in a liquid :- The solubility of a gas in a particular liquid is the volume of the gas in CC’s (centimetre cubes CM³) that can dissolve in unit volume of the liquid to form the saturated solution at the temperature of the experimented under a pressure of one atmosphere.

Factors affecting the solubility of a liquid in a gas

i)        Nature of the gas & the solvent:- Gases like Hydrogen, Oxygen, Nitrogen etc. dissolve in water only to a small extent but gases like CO₂, HCl, NH₃ are highly soluble.

The greater solubility of later gases they react with solvent. the greater solubility of the gas in a solvent due to their chemical similarity.

ii)      Nature of temperature:- The solubility of gases decreases with increase  in temperature.

iii)    Effect of pressure (Henry’s Law):- By increasing the pressure solubility also increases.

Henry’s Law:-  

                      The mass of a gas dissolved in the given volume of liquid at constant temperature is directly proportional to the pressure of the gas present in equilibrium with the liquid.

                                        m ∝ p

                                        m=K_HP

Also,

The partial pressure of gas in vapour phase (P) is proportional to the mole fraction of gas (x) in the solution.

                                    P=K_HX

Limitations of Henry’s law

Henry’s law is applicable only if the the following conditions are satisfied:-

a)      Pressure should be low and temperature should be high i.e. gas behaves as an ideal gas.

b)      The gas should not go under compound formation with solvent or association or dissociation in the solvent.

Vapour Pressure of liquid solution:-   

                                                         Vapour pressure of liquid/solution is the pressure exerted by the vapour in equilibrium with the liquid/solution at a particular temperature.

Raoults Law:-

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

For component A

                        P_A ∝ X_A

                        P_A = P⁰_AX_A

Where, P⁰_A = Vapour pressure of pure component A at the same temperature

For component B,

                        P_B = P⁰_BX_B

By Daltons law of partial pressure:-

            P_total = P_A+ P_B

            P_total = P⁰_AX_A + P⁰_BX_B

                         = (1-X_B) P⁰_A+ P⁰_BX_B

                     = P⁰_A - P⁰_AX_B + P⁰_BX_B

                              = P⁰_A+ (P⁰_B- P⁰_A)X_B

If Y_A  & Y_B represents the mole fraction of component A & B respectively.

In vapour phase,

Y_A = P_A/ P_A+ P_B = P_A/ P_total         ……………………..(i)

Y_B = P_B/ P_A+ P_B = P_B/ P_total         ……………………..(ii)

From eq. (i) & (ii)………

P_A = Y_A * P_total

P_B = Y_B * P_total

In general,

            P_i = Y_i * P_total

Raoults Law for non volatile liquid:-

Vapour pressure of each component is directly proportional to its mole fraction.

            P₁  µ X₁

            P₁ = P⁰₁X₁

            P₁/P⁰₁ = X₁

Ideal solutions:-  

                        An ideal is that solution which obeys raoults law in all conditions of temperature an concentration.

i.e. ∆ V_mixing = 0

       ∆ H_mixing = 0

Also, forces of attraction between components are same as in pure state.

A-A = A-B = B-B

Non ideal solutions:-  

                               The solutions which not obeys the Raoults Law is known as non ideal solutions.

∆ V_mixing ≠ 0, ∆ H_mixing ≠ 0

v  The force of interaction between solvent/solute is different than in pure state.

Positive deviation:-  

Positive Deviation

                              In this A-B interaction are weaker than A-A, B-B

i.e. interaction between solute-solvent is weaker than solute-solute or solvent-solvent. This means in such solutions the molecules of A or B (A-B) will find it easier to escape than in pure state.

 

Negative deviation:-  

Negative Deviation

                               Intra molecular attraction force between A-A and B-B are weaker than those between A-B. this decreases the escaping tendency of molecules for each component (A-B) and consequently the vapour pressure decreases resulting in –Ve deviation from raoults law.

Colligative Properties: -  

                                     Those properties of ideal solutions which depends only on the no. of particles of the solute dissolve in the definite amount of solvent and do not depend upon nature of solute.

The important colligative properties are:-

1)      Relative lowering of vapor pressure

2)      Osmotic pressure

3)      Elevation in boiling point

4)      Depression in freezing point

Relative lowering of vapour pressure: -  

                                                               from Raoults law for solutions of solids in liquids.

        Where, P⁰ = vapour pressure of pure solvent

            P_S = vapour pressure of solution

            n₂ = no. of moles of solute

            n₁ = no. of moles of solvent

For dilute solutions n₂<<n₁

Hence, neglecting n₂ in the denominator we have,

Here, w₁ & w₂ are the masses and m₁ & m₂ are masses of solvent & solute respectively.

Osmotic Pressure:-  

                               The process of the flow of the solvent molecules from solvent to solution through semi permeable membrane (SPM) is called osmosis the flow of the solvent molecules can be stopped if some extra pressure is applied on the solution. This pressure that just stops the flow of solvent molecules is called osmotic pressure of the solution.

=>> Osmotic pressure of the solution is directly proportional to the molar concentration or molarity (C) of the solution and its temperature (T).

Mathematically,

                 i.e.      

Or,                      π = R*C*T

Where, R is solution constant equal to the gas constant

            π = CRT

   Hence,         π = (n₂/v) RT

this equation is called von’t hoff equation for dilute solutions.

Also, πv = n₂RT

Elevation in boiling point:-  

                                              It is found that the boiling point of the solution is always higher than that of pure solvent. The increase is called elevation in boiling point.

Elevation in boiling point

 From figure,   we known       ∆T_b = T_b - T⁰_b

Where, T⁰_b  & T_b is the temperature at which the vapour pressure of the solvent and solution becomes equal to the atmospheric pressure and ∆T_b is called elevation in boiling point.

Also, ∆T_b is directly proportional to m

          ∆T_b = k_bm

Where, k_b is called molal elevation constant or ebullioscopy constant and ‘m’ is the molality of the solution.

=>  Calculation of molecular mass of the solute:- 

                                                                             As molality is the no. of moles of the solute dissolve per 100 gm of the solvent. If w₂ grams of the solute of molecular mass m₂ are dissolve in w₁ gram of the solvent

                             m = (W₂/M₂)(1000/W₁)

                        ∆T_b = K_b(W₂/M₂)(1000/W₁)

Depression in freezing point:- 

                                               It is observed that the freezing point of the solution is always lower than that of pure solvent. And the decrease is called the depression in freezing point.

Depression in freezing point

From figure,     ∆T_f = T⁰_f –T_f

Where,  T⁰_f = freezing point of pure solvent

              T_f = freezing point of solution

            ∆T_f = Depression in freezing point

Also,

            ∆T_{f  is directly proportional to} m

            ∆T_f  = k_f m

Where, k_f is molal depression constant or cryoscopic constant and m is molality of the solution.

=>  Calculation of molecular mass of solute:-

∆T_f = K_f(w₂/m₂)(1000/W₁)

                       

Vant hoff factor:-  

                           It is defined as the ratio of the experimented value to the calculated property of the colligative property known as vant hoff factor.