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

Explanation

Here `M_(2)= 58.5" g "mol^(-1), w_(1) = 65" g, "w_(2) = ? `
` DeltaT_(f) = 7.5^(@)C, i= 1.87, K_(f) = 1.86" K "kg mol^(-1)`
Using the formula, ` Delta T_(f) = i K_(f) m`
`DeltaT_(f) = i K_(f) xx(w_(2)xx1000)/(M_(2)xxw_(1))`
` 7.5 = 1.87 xx 1.86 xx(w_(2)xx1000)/(58.5 xx 65)`
` w_(2)=(7.5 xx58.5 xx 65)/(1.87 xx 86 xx 1000) = (28518.75)/(3478.2) = 8.199 g`