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Question

The molality of an aqueous solution of Urea in which the mole fraction of Urea is 0.18, is


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Solution

Step 1 Mole fraction of water:

Mole fraction can be defined as the ratio of one component's moles to the total number of all the components present in the solution.

Molefractionofsolvent(χA)=Molesofsolute(n)Molesofsolute(n)+Molesofsolvent(N)

Molefractionofsolute(χB)=Molesofsolute(n)Molesofsolute(n)+Molesofsolvent(N)

Here, χA+χB=1

The mole fraction of Urea is 0.18

So the mole fraction of water is 1-0.18=0.82

Step 2 Molality:

Molality can be explained as the number of moles of solute present in 1000g of the solvent.

That is the relation between mole fraction and morality is;

Molality(m)=Molefractionofsolute×1000Molefractionofsolvent×Molarmassofsolvent

The molar mass of water is 18g

By substituting the values,

Molality(m)=0.18×10000.82×18Molality(m)=180.82×18Molality(m)=100.82Molality(m)=12.19molKg-1

Therefore, the Molality of an aqueous solution is12.19molKg-1


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