Question

8g of NaOH is dissolved in 18g of H₂O. Mole fraction of NaOH in solution and molality (in mol/kg⁻1) of the solutions respectively are:

a) 1/2, 1/4
b) 1/3, 1/3
c) 1/4, 1/2
d) 1/2, 1/3

Answer 1

The mole fraction of NaOH in the solution is 1/2 and the molality of the solution is 1/4.

Step-by-step explanation:

The mole fraction of a solute in a solution is the ratio of the moles of the solute to the total moles of all components in the solution. The molality of a solution is defined as the number of moles of solute per kilogram of solvent.

In this case, we have 8g of NaOH and 18g of H₂O. To find the mole fraction of NaOH, we first need to find the moles of NaOH and H₂O.

Molar mass of NaOH = 22.99 g/mol + 16.00 g/mol + 1.01 g/mol = 40.00 g/mol

moles of NaOH = mass of NaOH / molar mass of NaOH = 8g / 40.00 g/mol = 0.20 mol NaOH

moles of H₂O = mass of H₂O / molar mass of H₂O = 18g / 18.02 g/mol = 1.00 mol H₂O

The mole fraction of NaOH in the solution is:

mole fraction of NaOH = moles of NaOH / (moles of NaOH + moles of H₂O) = 0.20 mol NaOH / (0.20 mol NaOH + 1.00 mol H₂O) = 0.20

The molality of the solution is:

molality = moles of NaOH / mass of H₂O (in kg) = 0.20 mol NaOH / 0.018 kg H₂O = 11.11 mol/kg

Therefore, the correct answer is (a) 1/2, 1/4.