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

What mass of NaCl (molar mass = `58.5" g "mol^(-1)` be dissolved in 65 g of water to lower the freezing point by `7.5^(@) C`? The freezing pont depression constant, `K_(f)`, for water is 1.86 K kg `mol^(-1)` . Assume van't Hoff factor for Nacl is 1.87.

Text Solution

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For electrolytes,
`DeltaT_(f)= i xx K_(f) xx m = (i xx K_(f)xx W_(B) xx 1000)/(W_(A) xx M_(B))`
Here, `i=1.87 , K_(f) = 1.86 "K kg mol"^(-1)`,
`M_(B) = 58.5" g mol"^(-1), DeltaT_(f) = 7.5^(@)C or 7.5K`
`W_(A) = 65g, W_(B) = ?`
`7.5=(1.87 xx 1.86 xx W_(B) xx 100)/(65 xx 58.5)`
or `W_(B) = (7.5 xx 65 xx 58.5)/(1.87 xx 1.86 xx 1000) = 8.2 g`
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