Question

1 molal NaCl solution has the density 1.21 gm/cc. Find the molar concentration of the same solution.

• A. 1 M
• B. 0.95 M
• C. 0.87 M
• D. 1.14 M

Hint:

To find molarity from molality, first calculate the volume of solution using density and total mass, then divide by the total moles of solute.

Answer 1

The Correct Option is B

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:
\[ \text{Density of solution} = 1.21 \, \text{g/mL} \times 1000 = 1210 \, \text{g/L} \]
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: \[ \text{Mass of NaCl} = 1 \, \text{mol} \times 58.5 \, \text{g/mol} = 58.5 \, \text{g} \] Thus, the mass of the solvent (water) is: \[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of NaCl} = 1210 \, \text{g} - 58.5 \, \text{g} = 1151.5 \, \text{g} = 1.1515 \, \text{kg} \]

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: \[ \text{Molarity} = \frac{\text{moles of NaCl}}{\text{volume of solution in L}} = \frac{1 \, \text{mol}}{1 \, \text{L}} = 1 \, \text{M} \] 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: \[ Molarity = 0.95 \]