Question

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

Answer 1

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 = $3M$= $3{\text{ }}moles$ 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:
$d = \dfrac{m}{V}$
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:
$n = \dfrac{w}{{{M_w}}}$
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. $1074.5{\text{ }}mL$ .

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.