Calculation of Molality of 3M NaCl Solution

Density of a solution can be used to calculate its molality. The following steps can be followed to calculate the molality of a 3M NaCl solution:

1. Determine the molar mass of NaCl
The molar mass of NaCl can be calculated by adding the atomic masses of sodium (Na) and chlorine (Cl). The atomic masses of Na and Cl are 22.99 g/mol and 35.45 g/mol, respectively. Therefore, the molar mass of NaCl is:

Molar mass of NaCl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol

2. Convert the density of the solution from g/cc to g/mL
Since the density of the solution is given in g/cc, it needs to be converted to g/mL. Since 1 cc = 1 mL, the density of the solution in g/mL is:

Density of solution = 1.28 g/cc = 1.28 g/mL

3. Calculate the mass of NaCl in 1 L of solution
Since the solution is 3M NaCl, it means that 1 L of solution contains 3 moles of NaCl. The mass of NaCl in 1 L of solution can be calculated as follows:

Mass of NaCl = 3 moles x 58.44 g/mol = 175.32 g

4. Calculate the mass of solvent (water) in 1 kg of solution
Since the density of the solution is 1.28 g/mL, it means that 1 L of solution weighs 1.28 kg. Therefore, 1 kg of solution contains:

Volume of solution = 1 kg / 1.28 g/mL = 0.781 L

Since the solution is 3M NaCl, it means that 1 L of solution contains 997 g of water and 3 x 58.44 g = 175.32 g of NaCl. Therefore, 0.781 L of solution contains:

Mass of water = 0.781 L x 997 g/L = 776.36 g

5. Calculate the molality of the solution
Molality is defined as the number of moles of solute (NaCl) per kilogram of solvent (water). Therefore, the molality of the solution can be calculated as:

Molality = moles of NaCl / kg of water = 3 moles / 0.776 kg = 3.86 mol/kg

Therefore, the molality of the 3M NaCl solution is 3.86 mol/kg.