Question

What volumes of $90\%$ alcohol by weight $(d = {\text{0}}{\text{.8gm}}{{\text{l}}^{{\text{ - 1}}}})$ must be used to prepare 80ml of $10\%$ alcohol by weight $(d = {\text{0}}{\text{.9gm}}{{\text{l}}^{{\text{ - 1}}}})$ .

Answer 1

Calculate the mass of $10\%$ alcohol solution. Using the mass of $10\%$ alcohol solution calculate the mass of alcohol in it. Using the density and mass of $90\%$ alcohol solution calculate the total volume of solution. Finally, calculate the volume of $90\%$ alcohol solution require to prepare 80 ml solution containing $10\%$ alcohol by weight and having density ${\text{0}}{\text{.9gm}}{{\text{l}}^{{\text{ - 1}}}}$ .

Formula Used: $d = \dfrac{m}{v}$

Complete step-by-step answer:
We have to prepare an 80 ml solution containing $10\%$ alcohol by weight and having density ${\text{0}}{\text{.9gm}}{{\text{l}}^{{\text{ - 1}}}}$ .
First, we will calculate the mass of 80 ml $10\%$ alcohol solution using the given density and volume of the solution.
$d = \dfrac{m}{v}$
Where,
$d$ = density
$m$ = mass
$v$ = volume
So we will substitute 80 ml for the volume of the solution, ${\text{0}}{\text{.9gm}}{{\text{l}}^{{\text{ - 1}}}}$ for the density of the solution and will calculate the volume of the solution as follows:
${\text{0}}{\text{.9gm}}{{\text{l}}^{{\text{ - 1}}}} = \dfrac{m}{{{\text{80 ml}}}}$
$v{\text{ = 72g}}$
Using this mass of solution we will calculate the mass of alcohol.
$10\%$ alcohol by weight indicates ${\text{100g}}$ the solution contains ${\text{10g}}$ of alcohol
So, ${\text{mass of alcohol = }}\dfrac{{{\text{72g }} \times 1{\text{0g}}}}{{100{\text{g}}}} = 7.2{\text{g}}$
Now we have to calculate the volume of $90\%$ alcohol solution that contains 7.2g of alcohol.
$90\%$ alcohol by weight indicates ${\text{100g}}$ the solution contains ${\text{90g}}$ of alcohol.
Using mass and density of solution we calculate the volume of $90\%$ alcohol solution as follows :
$v = \dfrac{m}{d}$
Substitute ${\text{100g}}$ for the mass of the solution and ${\text{0}}{\text{.8gm}}{{\text{l}}^{{\text{ - 1}}}}$ for the density of the solution and calculate the volume of the solution.
$v = \dfrac{{100}}{{0.8}}$
${\text{v = 125ml}}$

We can say that 125 ml solution contain 90 g of alcohol so calculate the volume of $90\%$ alcohol solution that contains 7.2g of alcohol as follows:
{\text{Volume of 90% alcohol = }}\dfrac{{{\text{7}}{\text{.2g x 125ml}}}}{{{\text{90g}}}} = {\text{10ml}}

So, 10ml $90\%$ alcohol by weight $(d = {\text{0}}{\text{.8gm}}{{\text{l}}^{{\text{ - 1}}}})$ must be used to prepare 80ml of $10\%$ alcohol by weight $(d = {\text{0}}{\text{.9gm}}{{\text{l}}^{{\text{ - 1}}}})$ .

Note: Concentration of solution is the amount of solute in a given amount of solution. There are various units to express concentration. Weight% is one of the units of concentration that indicate the amount of solute present in 100g of solution. The method of preparation of a solution of lower concentration from higher concentration is known as dilution.