Question

If the density of methanol is $0.793kg{L}^{-1}$, what is its volume needed for making $2.5L$ of its $0.25M$ solution?

Answer 1

Hint: At first think about the definition of density and molarity of the solution. Density of a molecule is defined as the ratio of mass of a substance to its volume. Molarity of a solution is defined as the moles of a solute per litres of a solution.

Complete step by step answer:
In the question, we have given that
Density of methanol $=0.793kg{L}^{-1}$
Molarity of solution $=0.25M$
Volume of solution$=2.5L$
We know that, molarity of a solution is given by
$M={\displaystyle \frac{n}{v}}$
$$\begin{gathered} 0.25={\displaystyle \frac{n}{2.5}} \\ n=0.625 \end{gathered}$$
So from the above calculation $0.625$ moles of methanol is needed.
Molar mass of methanol is $30g/mol$
One mole of a molecule is defined as the ratio of given weight by actual weight of a molecule. It is represented by n.
$n={\displaystyle \frac{m}{32}}$
$$\begin{gathered} 0.625={\displaystyle \frac{m}{32}} \\ m=20 \end{gathered}$$
The mass of methanol is $20g$
Density of methanol is given by,
$$\begin{gathered} d={\displaystyle \frac{m}{v}} \\ 0.793={\displaystyle \frac{20}{v}} \end{gathered}$$
$v=25.2mL$
From the above calculation, we can say that the required volume is $25.2mL$.
Additional Information:-
Concentration is the abundance of a constituent divided by the total volume of a mixture. The molar concentration is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. Molar concentration is also called molarity. The sum of molar concentrations gives the total molar concentration, the density of the mixture divided by the molar mass of the mixture or by the reciprocal of the molar volume of mixture.

Note:
Don’t get confused with the term molar concentration. Molar concentration of a solution is nothing but molarity of that solution. In the question, the density of a molecule and molarity of solution are interrelated.