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

Hint: 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.