Question

On mixing 15.0 mL of ethyl alcohol of density$\;{\text{0}}{\text{.792gm}}{{\text{1}}^{ - 1}}$ with 15 ml of pure water at $4^oC$, the solution is found to have a density of ${\text{0}}{\text{.924g}}{{\text{m}}^{ - 1}}$. The percentage contraction in volume is:
(A) 8%
(B) 2%
(C) 3%
(D) 4%

Answer 1

Hint: To solve the question we need to apply the formula of percentage concentration. For the formula we need to know the ideal volume and the observed volume.

Complete step by step solution:
-On mixing 15 mL of pure water and 15 mL of ethyl alcohol the ideal solution becomes 30mL.
15 mL of ethyl alcohol having a density of $\;{\text{0}}{\text{.792gm}}{{\text{1}}^{ - 1}}$ weighs 11.8 gram. 15 mL of pure water at $4^oC$ has a density of 1.0 gram per mL and weighs 15 grams.Therefore, the density of the solution is given to be ${\text{0}}{\text{.924g}}{{\text{m}}^{ - 1}}$. So its volume is about 29.09 mL
As we know that,
Percentage concentration is $\text{= }\dfrac{\left( \text{Ideal volume} \right)\text{ - }\left( \text{Observed volume} \right)}{\text{Ideal volume}}\text{ }\!\!\times\!\!\text{ 100}$
$\text{= }\dfrac{\text{30 }\!\!\times\!\!\text{ 29}\text{.9 }\!\!\times\!\!\text{ 100}}{\text{30}}$
$\text{= 3}\text{.03}$
$\text{Or 3 }\!\!%\!\!\text{ }$
So the correct answer is the percentage contraction in volume is 3%.
So the correct option is Option C.

Additional Information: We should be having a basic idea about the mixing of liquids and the volume contraction. By mixing different liquids together the volumes do not add. There occurs a volume contraction by binding forces between the molecules.
- When the two liquids are mixed the molecules of the liquids can go into the other liquids available spaces. That can do this because they are both polar and can mix freely. The mixture of the two liquids takes up less volume than the two liquid states separately.

Note: About the mixture that is mentioned in the question, here is something we should be knowing. When water and ethyl alcohol mix, there comes strong hydrogen bonding that draws the different molecules close together. The two different molecules are packed closer together than in pure solution. This results in the reduction of volume.