We are given:
Molality of the solution = 1 molal = 1 mole of NaCl per 1 kg of solvent (water).
Density of the solution = 1.21 gm/cc = 1.21 g/mL.
The molar mass of NaCl = 58.5 g/mol.
Step 1: Convert the density to g/L.
Since 1 cc = 1 mL, the density is
given as 1.21 g/mL. To convert it to g/L, we multiply by 1000:
Step 2: Calculate the mass of 1 L of solution.
The mass of 1 L of solution is 1210 g.
Step 3: Calculate the mass of the solvent (water).
Since the solution is 1 molal, it contains 1 mole of NaCl per 1000 g (1 kg) of solvent. The mass of NaCl in the solution is:
Thus, the mass of the solvent (water) is:
Step 4: Calculate the molarity.
Molarity (M) is defined as the number of moles of solute per liter of solution. We already know the number of moles of NaCl is 1 mole, and the volume of the solution is 1 L. The molarity is:
However, we need to correct the molarity using the total mass of the solution and the solvent: 1. The density is 1210 g/L and the mass of the solvent is 1.1515 kg. The concentration is: