Chemistry ELEVATION OF BOILING POINT AND OSMOTIC PRESSURE
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ELEVATION OF BOILING POINT AND OSMOTIC PRESSURE

Elevation in Boiling Point :

The boiling points elevates when a non-volatile solute is added to a volatile solvent which occurs due to lowering of vapour pressure. The boiling point of a liquid may be defined as the temperature at which its vapour pressure becomes equal to atmospheric pressure.

So, when a non-volatile solute is added to a volatile solvent results lowering of vapour pressure and consequent elevation of boiling point.

where

`DeltaT_b = T_b - T_b^o`

`DeltaT_b =` elevation in B.P.

`Delta P =` lowering of V.P.

`X_B =` mole fraction of solute

`K =` elevation constant

`T_b^o =` boiling point of solvent

`T_b =` boiling point of solution

It is found that elevation of boiling point is directly proportional to the number of moles of the solute in given amount of the solvent(`m`).

`Delta T_b prop m`

`DeltaT_b prop K_b m`

Where 'm' is the molality of solution.

Where `K_b` is ebullioscopic or boiling point elevation constant. When molality of the solution is equal to one, then

`DeltaT_b = K_b`

Hence molal elevation constant of the solvent may be defined as the elevation in its boiling point when one mole of non-volatile solute is dissolved per kg (`1000` gm) of solvent. The unit of `K_b` are `K` `kg` `mol^(-1)`.

Because molality of solutron `m = W_B/M_B * 1000/W_A`

So `Delta T_b =K_b W_B/M_B * 1000/W_A` or `M_B = (1000 xx K_b xx W_B)/(DeltaT_b xx W_A)`

Where `W_A=` mass of solvent, `W_B =` mass of solute,

`M_A =` Molar mass of solvent, `M_B =` Molar mass of solute.

Determination of `K_b` of Solvent :

`K_b = (RT_b^2)/(1000L_v)`

where `R` is molar gas constant, `T`, is the boiling point of the solvent on Kelvin scale and `L_v`, the latent heat of vaporization of solvent in calories per gram.

For water `K_b =2 x(373)^2/1000xx540 = 0.5 15 K-kg//mol`

If energy is taken in joule then use `R= 8.314 JK^(-1) text(mole)^(-1)`
Energy is taken in calorie then use `R = 2 cal K^(-1) text(mole)^(-1)`

Osmotic Pressure

(a) `text(Osmosis)` : Spontaneous flow of solvent molecules through a semipermeable membrane from a pure solvent to the solution (or from a dilute solution to a concentrated solution) is termed as osmosis.

`(b)` `text(Osmotic Pressure)` : When a solution is separated from the pure solvent with the help of a semipermeable membrane, there
occurs the flow of solvent molecules from the pure solvent to the solution side. The flow of solvent molecules from a region of higher concentration of solvent to the region of lower concentration of solvent is termed as the phenomenon of osmosis. This also happens when two solution of different concentrations are separated by a semipermeable membrane.

As a result of osmosis a pressure is developed which is termed as osmotic pressure. It is defined in various methods.

(i) The excess hydrostatic pressure which builds up as a result of osmosis is called osmotic pressure.

(ii) The excess pressure that must be applied to the solution side to prevent the passage of solvent into it through a semipermeable membrane.

(iii) Osmotic pressure of a solution is equal to the negative pressure which must be applied to the solvent in order to just stop the osmosis.

(iv) The osmotic pressure of a solution may be defined as the extra pressure which should be applied to the solution to increase the chemical potential of solvent in solution equal to the chemical potential of the pure solvent at the same temperature.

(c) `text(Theory of Dilute Solutions)` : The osmotic pressure of a dilute solution was the same as the solute would have exerted if it were a gas at the same temperature as of the solution and occupied a volume equal to that of the solution. This generalization is known as Van't Hoff theory of dilute solutions.

The osmotic pressure is a colligative property. So the osmotic pressure is related to the number of moles of the solute by the following relation

`pi V = n R T`

`pi = n/V RT` `[n/V = C]`

`pi = CRT`

Here `C` = concentration of solution in moles per litre;
`R` = solution constant;
`T` = temperature in Kelvin degree;
`n` = number of moles of solute; and
`V` = volume of solution.

This equation is called Van't Hoff's equation.

(d) `text(Determination of molecular mass from osmotic pressure)` : The molecular mass of a substance i.e. solute can be calculated by applying the following formula.

`M = (WRT)/(pi V)`

Accurate molecular mass will only be obtained under following conditions
(i) The solute must be non-volatile;
(ii) The solution must be dilute; and
(iii) The solute should not undergo dissociation or association in the solution.

`text(Solution constant R)`- The solution constant `R` has the same significance and value as the gas constant. i.e.

`R = 0.0821 litre-atm K^(-1) mol^(-1)`
`= 8.314 xx 10^(-7) erg K-lmol^(-1)`
`= 8.314 J K^(- 1) mol^(-1)`
`= 8.314 Nm K^(-1) mol^(-1)`

(e) `text(Type of solutions)` :

(i) `text(Isotonic solution)` : The two solutions having equal osmotic pressure are termed as isotonic solution.

(ii) `text(Hypertonic solution)` : A solution having higher osmotic pressure than some other solution is said to be called hypertonic solution.

(iii) `text(Hypotonic solution)` : A solution having a lower osmotic pressure relative to some other solution is called hypotonic solution.

(f) `text(Semipermeable membrane)` : A membrane which allows the passage of solvent molecules but not that of solute. When a solution is separated from the solvent by it is known as semipermeable membrane. Some example of it are as follows

(i) Copper ferrocyanide `Cu_2[Fe(CN)_6]`;
(ii) Calcium phosphate membrane; and
(iii) Phenol saturated with water.

(g) `text(Reverse Osmosis)` : If a pressure greater than the osmotic pressure is applied on the concentrated solution, the solvent starts
to flow from concentrated solution to dilute solution (or pure solvent). This is reverse osmosis. One of its chief uses is desalination of sea water to get pure drinking water.
 
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