The density of 3M solution of sodium chloride is 1.252 g mL$$^{-1}$$. The molality of the solution will be : (molar mass, NaCl = 58.5 g mol$$^{-1}$$)

We are given a 3M solution of sodium chloride, meaning it contains 3 moles of NaCl per liter of solution. The molar mass of NaCl is 58.5 g/mol, and the density of the solution is 1.252 g/mL. We need to find the molality, which is moles of solute per kilogram of solvent.

First, consider 1 liter (1000 mL) of the solution. The mass of this solution can be found using density:

Mass of solution = density × volume = 1.252 g/mL × 1000 mL = 1252 g.

In 1 liter of 3M solution, there are 3 moles of NaCl. The mass of this NaCl is:

Mass of NaCl = moles × molar mass = 3 mol × 58.5 g/mol = 175.5 g.

The mass of the solvent (water) is the total mass of the solution minus the mass of NaCl:

Mass of solvent = mass of solution - mass of NaCl = 1252 g - 175.5 g = 1076.5 g.

Convert this mass to kilograms:

Mass of solvent in kg = 1076.5 g ÷ 1000 = 1.0765 kg.

Molality is defined as moles of solute per kilogram of solvent:

Molality = moles of NaCl / mass of solvent in kg = 3 mol / 1.0765 kg.

Calculating this:

3 ÷ 1.0765 ≈ 2.786 m, which rounds to 2.79 m.

Comparing with the options:

A. 260 m

B. 2.18 m

C. 2.79 m

D. 3.00 m

Hence, the correct answer is Option C.