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An aqueous solution is 1.33 molal in met...

An aqueous solution is 1.33 molal in methanol. Determine the mole fraction of methanol & `H_(2)O`.

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molality `="mole fraction of solute"/("mole fraction of solvent" times "mol. Wt of solvent") times 1000`
`1.333=x_(A)/(x_(B) times M_(B)) times 1000`,
`(1.33 times 18)/1000=x_(A)/x_(B),23.94/1000=x_(A)/x_(B)`
`rArr x_(A)=0.02394 x_(B), x_(A)+x_(B)=1`
`rArr 1.02394 x_(B)=1`
`x_(B)=1/1.02394=0.98, x_(A)=0.02`
Second Method :
Let wt of solvent = 1000 gm molarity = 1.33
`" "=` moles of solute
mole fraction of solute
`="moles of solute"/("moles of solute + moles of solvent")
`=m/(m+1000/18)=1.33/(1.33+1000//18)`
mole of fraction of solute = 0.02
mole fraction of solvent = 1 - 0.02 = 0.98
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