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

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 = \[3M\]= \[3{\text{ }}moles\] 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.