Question

On mixing 15.0 ml of ethyl alcohol of density \[0.792gm{{l}^{-1}}\] with 15 ml of pure water at \[4{}^{\circ }C\], the resulting solution is found to have a density of \[0.924gm{{l}^{-1}}\]. The percentage contraction in volume is:
a.) 8%
b.) 2%
c.) 3%
d.) 4%

Answer 1

Hint: For finding the final concentration of solution we'll use the relationship between volume, density and mass. And here density and volume data is given in the question.


Complete step by step solution:

Given that, for ethyl alcohol:
Volume = 15.0 ml
Density = \[0.792gm{{l}^{-1}}\]
For water:
Volume = 15.0 ml
And we know that density of water = 1
density of resulting solution =\[0.924gm{{l}^{-1}}\]
now we know that, density = mass / volume
by rearranging:
mass = density x volume
now, mass of ethyl alcohol = volume of ethyl alcohol x density of ethyl alcohol
                     = 15 ml x \[0.792gm{{l}^{-1}}\]
                     = 11.88 g
Mass of water = 15 x 1 = 15 g
Now total mass of solution = mass of ethyl alcohol + mass of water
                         = 11.88 g + 15 g
                          = 25.88 g
Density = mass of solution / volume of solution
\[\frac{0.909}{30}\times 100\]= 25.88 g / volume of solution
Volume of solution = 29.09 ml
Expected volume = 30 ml
Concentration = 30 – 29.09
              = 0.909 ml
% of concentration = \[\frac{0.909}{30}\times 100\]
                   = 3.03 %
So, the correct answer is option “C”.


Note: Here the question is asking for volume concentration not for that molar concentration, so don’t get confused. Here no need to change the units of ml.