Colligative property: Relative Lowering in V.P

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COLLIGATIVE PROPERTIES

The properties of the solution which depend upon the number of solute particles are called colligative properties. These properties help in the determination of molar mass of non-volatile solutes. These are inversely proportional to the molar mass.

colligative properties ∝ 1/M

TYPES:COLLIGATIVE PROPERTIES

1.) RELATIVE LOWERING IN VAPOR PRESSURE

2) ELEVATION IN BOILING POINT

3) DEPRESSION IN FREEZING POINT

4) OSMOSIS

1.) RELATIVE LOWERING IN V.P

This colligative property is also known as Raoult’s law for the solution containing non-volatile solute.It states that relative lowering in vapor pressure for the solution containing non-volatile solute is equal to mole fraction of the solute in the solution.

Here the term on the left hand side of the above equation is called relative lowering in vapor pressure and the term on the right hand side is the mole fraction of non-volatile solute.

DERIVATION

P_S = P_A + P_B            equation number (i)

P_A =  P_A°. χ_A

P_B  = P_B°. χ_B

P_B° = 0 (because solute is non-volatile)

P_B  = ₀ . χ_B

_{PB  = 0}

P_S = P_A

now  P_A =  P_A°. χ_A equation number (ii)

and  χ_A = 1 - χ_B

now put the value of χ_A in equation number (ii)

  P_A =  P_A°.(1- χ_B)

  P_A =  P_A° - P_A° .  χ_B

  P_A   + P_A°. χ_B  =  P_A° equation number (iii)

As solute is non-volatile hence P_A° is greater than P_A

P_A° > P_A hence equation number (iii) become :

 P_A°. χ_B  =  P_A° - P_A    equation number (iv)

Here P_A° - P_A is the lowering in vapor pressure.when we rearrange equation number 4 we get relative lowering in vapor pressure as follow :

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