Explanation:


Molality: It is defined as the number of moles of solute present in 1000 g of solvent. It is represented by the symbol 'm'.

Mole fraction: It is defined as the ratio of the number of moles of one component to the total number of moles in the solution.


Formula:

Molality (m) = Number of moles of solute / Mass of solvent (kg)

Mole fraction of solute = Number of moles of solute / Total number of moles in solution


Given:

Molality (m) = 1.00 mol/kg


Assuming:

Mass of solvent = 1000 g (1 kg)


Calculation:

Let us assume that the solute is represented by 'A' and the solvent is represented by 'B'.

Let the number of moles of solute be 'x'.

Mass of solute (A) = Number of moles of solute (x) * Molar mass of solute (MA)

Mass of solvent (B) = Mass of solvent in kg (1 kg) * Molar mass of solvent (MB)

Molality (m) = Number of moles of solute (x) / Mass of solvent (kg)

Therefore, the equation becomes:

m = x / (1000 g * MB)

x = m * 1000 g * MB


Total number of moles in solution = Number of moles of solute + Number of moles of solvent

Number of moles of solvent = Mass of solvent / Molar mass of solvent

Number of moles of solvent = 1000 g / MB


Total number of moles in solution = x + (1000 g / MB)

Mole fraction of solute = x / (x + 1000 g / MB)

Mole fraction of solute = (m * 1000 g * MB) / ((m * 1000 g * MB) + 1000 g)

Mole fraction of solute = (m * MB) / (m * MB + 1)


Answer:

Mole fraction of solute in a 1.00 molal aqueous solution is (1 * 18) / (1 * 18 + 1) = 0.947.

Answer is 0.0177 by using formula mole fraction of solute = moles of solute/moles of solute+(1000/molar mass of solvent)