Question

Density of 2 m aqueous solution of naoh is 1.28 g/cm3. The molality of the solution is [given that molecular mass of naoh = 40 g molâ1]

Answer 1

Explanation:

The given data is as follows.

      Molarity = 2 M,       Density = 1.28 $g/cm^{3}$ = 0.00128 g/L (as 1 $cm^{3}$ = 0.001 L)

      Molar mass = 40 g/mol

Therefore, it means that there are 2 moles present in 1 liter. Hence, calculate the mass of solution as follows.

              Density = $\frac{mass}{volume}$

                     1280 $g/L$ = $\frac{mass}{1 L}$

                                           mass = 1280 g

As it is known that, number of moles = $\frac{mass}{Molar mass}$

Therefore, mass of solute (NaOH) is as follows.

                     number of moles = $\frac{mass}{Molar mass}$

                            2 = $\frac{mass}{40 g/mol}$                                                  

                       mass = 80 g/mol

Now, mass of solute + mass of solvent = mass of solution.

                80 g + mass of solvent = 1280 g

                        mass of solvent = 1280 g - 80 g

                                                    = 1200 g

or,                                                 = $\frac{1200}{1000}$ = 1.2 kg

Now, calculate the molality as follows.

                     Molality = $\frac{\text{no. of moles of solute}}{\text{mass of solution in kg}}$

                                   = $\frac{2}{1.2}$

                                   = 1.6 mol/kg

Thus, we can conclude that molality of the given solution is 1.6 mol/kg.

Answer 2

Given that, the density of 2 M aqueous solution of NaOH is 1.28 g/cm³.

{ Density (d) is 1.28 g/cm³ and Molarity (M) is 2M }

We have to find molality (m) of the solution.

Now,

The relation between Molality, Molarity and Density is:

m = 1000M/(1000d - 2m.m.)

Here, m = molality, M = Molarity, d = density and m.m. = molar mass

Also given that, Molar Mass (m.m.) of NaOH = 40 g/mol

Substitute the known values in the above formula,

→ m = [1000(2)]/[1000(1.28) - 2(40)]

→ m = 2000/(1280.00 - 80)

→ m = 2000/(1280 - 80)

→ m = 2000/1200

→ m = 20/12

→ m = 5/3

→ m = 1.67

Therefore, the molality of the solution is 1.67 Molal.