The freezing point of diluted milk sample is found to be $-0.2^{0} \mathrm{C}$, while it should have been $-0.5^{\circ} \mathrm{C}$ for pure milk. How much water been added to pure milk to make the diluted sample?

(B) 3 cups of water to 2 cups of pure milk

(A) 1 cup of water to 2 cups of pure milk

(C) 1 cup of water to 3 cups of pure milk

(D) 2 cups of water to 3 cups of pure milk

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Solutions

The freezing point of diluted milk sample is found to be

- 0. 2^{0} C

, while it should have been

- 0. 5^{\circ} C

for pure milk. How much water been added to pure milk to make the diluted sample?

(A)1 cup of water to 2 cups of pure milk
(B)3 cups of water to 2 cups of pure milk✓ Correct
(C)1 cup of water to 3 cups of pure milk
(D)2 cups of water to 3 cups of pure milk

Answer: (B)

Solution

Freezing-point depression is proportional to the solute concentration, so the ratio of depressions equals the ratio of concentrations. Pure milk gives

0. 5^{\circ}

and the diluted sample

0. 2^{\circ}

, a factor of

\frac{0.5}{0.2} = 2.5

, meaning the milk has been diluted

2.5

times. So

2

cups of milk become

5

cups of mixture, which means

3

cups of water were stirred into the

2

cups of pure milk.

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option

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