What is the m...

Question

What is the molality of $C_{2} H_{5} O H$ in water solution which will freeze at $- 10^{o} C$ ? [Mol. wt. of $C_{2} H_{5} O H = 46, K_{f}$ for water $= 1.86 K k g m o l^{- 1}$ ]

6.315 m

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63.15 m

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3.540 m

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5.3 m

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Solution

The correct option is D $5.3 m$
The depression if the freezing point
$Δ T_{f} = i \cdot K_{f} \cdot m$
$Δ T_{f} = 10^{0} C = 10 K =$ the depression if the freezing point
$i = 1 =$ van't Hoff's factor (ethanol is non electrolyte and does not dissociate in aqueous solution).
$K_{f} = 1.86 K k g / m o l =$ molal depression in freezing point constant
$m =$ molality
$Δ T_{f} = i \cdot K_{f} \cdot m$
$10 K = 1 \times 1.86 K k g / m o l \times m$
$m = 5.3 m o l / k g = 5.3 m$
Hence, the molality of solution is 5.3 m.

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