Question

Density of $$3M$$ of $$NaCl$$ is$$1.25g/mL$$ . Calculate the volume of water required to make $$1000mL$$ of this $$NaCl$$ solution. [Consider the density of water as $$1g/mL$$ ]
A. $$1074.5mL$$
B. $$1250mL$$
C. $$824.5mL$$
D. $$1000mL$$

Answer 1

Hint: Molarity and density are different ways of expressing essentially the same thing. Density is the mass of a solid, liquid or gas divided by its volume whereas molarity is the number of moles of solute per liter of solution. Density is not a term used for the concentration of any solution, whereas molarity is a concentration term.

Complete step by step answer:
According to the question,
Density ($$d$$ ) of sodium chloride ($$NaCl$$) = $$1.25g/mL$$
Concentration of sodium chloride = $$3M$$= $$3moles$$ in one liter of the solution
Molar mass of sodium chloride $=NaCl=23+35.5=58.5g$
The volume of the solution is given as = $1L=1000mL$
As we know that the density is defined as the mass per unit volume of any substance. So, mathematically it can be written as:
$d={\displaystyle \frac{m}{V}}$
Thus, $m=d\times V$
Substituting the values for sodium chloride in the above equation, we have:
$m=1.25g/mL\times 1000mL=1250g$
The mass of sodium chloride solution is found to be = $m=1250g$
We know that the mole of any substance is the ratio of the weight of the solute and the molar mass of the solute. Mathematically, this can be written as:
$n={\displaystyle \frac{w}{M_w}}$
Thus, $w=n\times M_w$
Substituting the values, we have:
$m=3\times 58.5=175.5g$
Thus, the mass of the sodium chloride dissolved (solute) in the solvent is found to be = $w=175.5g$ .
We know that, mass of solution = mass of solvent + mass of solute
Hence, the mass of the solvent = mass of solution – mass of solute
Mass of solvent = $(1250-175.5)g=1074.5g$

Thus, the correct option is A. $$1074.5mL$$ .

Note:
Density is the amount of particles of the solute present in the solution when the particles dissolve in the solvent. Concentration is a specific term used for defining the strength of a solution and the various and most common concentration terms used in analytical chemistry include molarity, normality, molality, etc.