Colligative Properties and Determination of Molar Mass | Solutions | Notes | Summary - Zigya

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Colligative Properties and Determination of Molar Mass

Properties of ideal solution which depends upon a number of particles of solute but independent of the nature of the particles are called colligative properties.

Depression of Freezing Point

increment straight T subscript straight f space equals space straight K subscript straight f straight m
where comma space increment straight T subscript straight f space equals space straight T subscript straight f superscript 0 space minus straight T subscript straight f
straight K subscript straight f space equals space fraction numerator molal space depression over denominator Cryoscopic space constant end fraction
straight m space equals space molality
straight M space equals space fraction numerator straight k subscript straight f space straight x space 1000 space straight x space straight W subscript straight B over denominator increment straight T subscript straight f space straight x space straight W subscript straight A end fraction

Elevation of Boiling Point

increment straight T subscript straight b space equals space straight k subscript straight b straight m
Where comma space increment straight T subscript straight b space equals space straight T subscript straight b space minus space straight T subscript straight b superscript 0
straight K subscript straight b space equals space fraction numerator Molal space elevation space constant over denominator Ebllioscopic space constant end fraction
straight m space equals molality
straight M space equals fraction numerator straight k subscript straight b space straight x space 1000 space straight x space straight W subscript straight B over denominator increment straight T subscript straight b space straight x space straight W subscript straight A end fraction

Osmosis and Osmotic Pressure

The excess pressure that must be applied to a solution side to prevent osmosis i.e. to stop passage of solvent molecules into it through a semi-permeable membrane.

straight pi space equals space CRT
straight pi space equals space Osmotic space pressure
straight R space equals space gas space constant
straight pi space equals space straight n subscript 2 over straight V RT

Here V is the volume of a solution in litres containing n2 moles of solute.If w2 grams of solute, of molar mass, M2 is present in the solution, then n2 = w2 / M2 and we can write,

πV space equals space fraction numerator straight w subscript 2 RT over denominator straight M subscript 2 end fraction
or
space straight M subscript 2 space equals space fraction numerator straight w subscript 2 RT over denominator πV end fraction

Relative Lowering of Vapour Pressure

fraction numerator straight P subscript straight A superscript 0 space minus space straight P subscript straight A over denominator straight P subscript straight A superscript 0 end fraction space equals space straight X subscript straight B
straight X subscript straight B space equals space fraction numerator straight n subscript straight B over denominator straight n subscript straight A space plus space straight n subscript straight B end fraction

For dilute solution, nB<<nA, hence nB is neglected in the denominator.

fraction numerator straight P subscript straight A superscript 0 space minus straight P subscript straight A over denominator straight P subscript straight A superscript 0 end fraction space equals space straight n subscript straight B over straight n subscript straight A
fraction numerator straight P subscript straight A superscript 0 minus straight P subscript straight A over denominator straight P subscript straight A superscript 0 end fraction space equals space fraction numerator straight W subscript straight B space straight x space straight M subscript straight A over denominator straight M subscript straight B space straight x space straight W subscript straight A end fraction

 

Reverse Osmosis and Water Purification

The phenomenon of reversal of the direction of osmosis by the application of a pressure larger than the osmotic pressure on the solution side is known as reverse osmosis. In this case, the pure solvent flows out of the solution through a semi-permeable membrane.

Reverse osmosis takes place only when external energy is applied to the more saline solution.

Reverse osmosis is used in the desalination of sea-water.

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