Question

A solution of ethanol in water is 10 % by volume. If the solution and pure ethanol have densities of 0.9866 g/cc and 0.785 g/cc respectively. The percent by weight is nearly?
(A) 7.95 %
(B) 17 %
(C) 9.86 %
(D) 16.2 %

Answer 1

Solution is represented in terms of relative percent concentration of solute in a solution. This calculation provides information about the concentration of the solution. The percentage expresses the number of parts of a particular substance per 100 total parts.

Complete Solution :
We know that the volume percent is used to express the concentration of a solution when the volume of a solute and the volume of a solution is given.
And we write the equation as:
$\text{Volume}\,\text{percentage=}\dfrac{\text{Volume}\,\text{of}\,\text{solute}}{\text{Volume}\,\text{of}\,\text{solution}}\text{ }\\!\\!\times\\!\\!\text{ 100 }\\!\\!$
Since it is given that, 10% of the total solution has ethanol.

Now take the total volume of solution as 100ml, then the volume of ethanol will be 10ml.
Volume of ethanol = 10ml
Volume of solution = 100ml
$\text{Density =}\dfrac{\text{Mass}}{\text{Volume}}$
By rearranging the above equation, the mass of ethanol and solution can be derived.
And the equation becomes,
Weight of ethanol = Volume$\times$density
Weight of ethanol = $10\times 0.785=7.85g$
Weight of solution = $100\times 0.9866=98.66g$
$\text{Weight}\,\text{percent}\,\text{of}\,\text{ethanol=}\dfrac{\text{Weight}\,\text{of}\,\text{ethanol}}{\text{Weight}\,\text{of}\,\text{solution}}\text{ }\\!\\!\times\\!\\!\text{ 100 }\\!\\!$
Weight percent of ethanol = $\dfrac{7.85}{98.66}\times 100$
Weight percent of ethanol = 7.95%
So, the correct answer is “Option A”.

Note: We generally express concentration in terms of relative units. And the three different types of percentage concentration which is commonly used are as follows:
1. Mass percent: The mass percent is used to express the concentration of a solution when the mass of a solute and the mass of solution is given.
2. Volume percent: The volume percent is commonly used to express the concentration of a solution when the volume of a solute and the volume of a solution is provided.
3. Mass/Volume percent: This measures the mass or weight of solute in grams vs. the volume of solution.