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What mass of NaCl ("molar mass =58.5 g m...

What mass of NaCl `("molar mass =58.5 g mol"^(-1))` dissolved in 50g of water will lower the freezing point by `5^@C?` The freezing point depression constant, `K_p` for water is `1.86" K kg mol"^(-1)`, van't Hoff factor for NaCl is 1.87.

Text Solution

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Here `M_(B)=58.5 g mol^(-1), w_(A)= 50g, w_(B)`= ?
`Delta T_(f)=5^(@)C, i=1.87, K_(f)=1.86K kg mol^(-1)`
Depression of freezing point, `Delta T_(f)= iK_(f) m`
`Delta T_(f)= i xx K_(f)xx (w_(B) xx 1000)/(M_(B) xx w_(A)) rArr 5= 1.87 xx 1.86 xx (w_(B) xx 1000)/(58.5 xx 50)`
`therefore` Mass of solute `w_(B)= (5 xx 58.5 xx 50)/(1.87 xx 1.86 xx 1000)= 4.205g`
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