The freezing point of a diluted milk sample i | vedclass

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(B) The depression in freezing point $\Delta T_f$ is directly proportional to the concentration of the solute in the milk. Let $V_p$ be the volume of

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$3$ cups of water to $2$ cups of pure milk

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(B) The depression in freezing point $\Delta T_f$ is directly proportional to the concentration of the solute in the milk. Let $V_p$ be the volume of pure milk and $V_w$ be the volume of added water.For pure milk,the freezing point depression is proportional to the concentration $C_p = \frac{n}{V_p} = 0.5$.For diluted milk,the concentration is $C_d = \frac{n}{V_p + V_w} = 0.2$.Taking the ratio: $\frac{C_p}{C_d} = \frac{V_p + V_w}{V_p} = \frac{0.5}{0.2} = 2.5$.This implies $V_p + V_w = 2.5 V_p$,so $V_w = 1.5 V_p$.If $V_p = 2$ cups,then $V_w = 1.5 	imes 2 = 3$ cups.Thus,$3$ cups of water are added to $2$ cups of pure milk.

The freezing point of a diluted milk sample is found to be $-0.2\ ^\circ C$,while it should be $-0.5\ ^\circ C$ for pure milk. How much water has been added to pure milk to make the diluted sample?

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