Question

On mixing 15 ml of ethyl alcohol density 0.792 g/ml with 15 ml of pure water at 4°c, the resulting solution is found to have a density 0.924g/ml.The % contraction in volume is:-​

Answer 1

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Given:

• On mixing 15 ml of ethyl alcohol density 0.792 g/ml with 15 ml of pure water at 4°c, the resulting solution is found to have a density 0.924g/ml.

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To find:

• The % contraction in volume.

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Solution:

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We know that,

$\: \: \: \: \: \: \: \: \bullet\bf\: \: \: {Mass = Volume \times Density}$

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Therefore,

• → Mass of alcohol = 15 × 0.792
• → Mass of alcohol = 11.88 g

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Similarly,

• → Mass of water = 15 × 1
• → Mass of water = 15 g

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Now,

• → Total mass = 11.88 + 15
• → Total mass = 26.88 g

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Using Formula:

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$\bf\to{Volume\: of\: Solution = \dfrac{Mass\: of\: component}{Density\: of\: solution}}$

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$\tt\longmapsto{Volume\: of\: solution = \dfrac{26.88}{0.924}}$

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$\tt\longmapsto{Volume\: of\: solution = 29.0909\: mL}$

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Now,

• Expected volume = (15 + 15)mL
• Expected volume = 30 mL

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Finding the difference

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• → Difference = (30 - 29.0909) mL
• → Difference = 0.909 mL

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As we know that,

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$\small\bf{\to{\%\: concentration\: in \: volume = \dfrac{Difference}{Expected\: volume} \times 100}}$

$\tt\longmapsto{\%\: concentration\: in \: volume = \dfrac{0.909}{30} \times 100}$

$\tt\longmapsto{\%\: concentration\: in \: volume = 0.0303 \times 100}$

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$\bf\longmapsto{\%\: concentration\: in \: volume = 3.03\: \%}$

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Hence,% concentration in volume is 3.03%.

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