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A 10% solution of sucrose (molar mass 34...

A 10% solution of sucrose (molar mass 342) is isotonic with 1.754% solution of urea. Calculate the molecular mass of urea.

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First solution. Weight of cane sugar `(W_(1)) = 10 g`
Volume `V =(100)/(1000)=0.1L `
Mol. wt. of cane sugar `(C_(12)H_(22)O_(11))=342" g mol"^(-1)`
`R=0.0821" L atm. K"^(-1)" mol"^(-1)`
`pi_(1)=(W_(1)xxRT)/(M_(1)V)=(10xxRT)/(342xx0.1)`
(b) Second Solution. Weight of urea `(W_(2))=1.754g`
Volume of solution `=(100)/(1000)=0.1L`
Mol. wt. of urea `=M_(2)` (say)
`pi_(2)=(W_(2)RT)/(M_(2)xx V)=(1.754 xx RT)/(M_(2)xx0.1)`
Since the solutions are isotonic, `pi_(1)=pi_(2)`
or `(10 xx RT)/(342xx0.1)=(1.754RT)/(M_(2)xx 0.1) or (10)/(342)=(1.754)/(M_(2))`
or `M_(2)=(342 xx 1.754)/(10)=60"g mol"^(-1)`
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