Calculation of Molality:

Molality is defined as the number of moles of solute per kilogram of solvent. In this case, one molal aqueous solution means that one mole of solute is dissolved in one kilogram of water.

Therefore, Molality = 1 mole / 1 kg = 1 mol/kg

Calculation of Mole Fraction:

Mole fraction is defined as the ratio of moles of solute to the total number of moles of solute and solvent in a solution.

Let's assume that the molar mass of the solute is 'x' g/mol. Then, the number of moles of solute in one kilogram of water is given by:

Number of moles of solute = (1 mol / 1000 g) * (1000 g / 1 kg) * x g = x/1000 mol

The total number of moles in the solution is given by:

Number of moles of solute + Number of moles of solvent = x/1000 mol + 1000/18 mol

Here, we have assumed that the density of water is approximately 1 g/mL and its molar mass is 18 g/mol.

Therefore, the mole fraction of the solute is given by:

Mole fraction of solute = (Number of moles of solute) / (Number of moles of solute + Number of moles of solvent)

= x/1000 mol / (x/1000 mol + 1000/18 mol)

= (18x) / (1000x + 18000)

Putting x = 36 g/mol (as given in the question), we get:

Mole fraction of solute = (18*36) / (1000*36 + 18000)

= 0.018

Hence, the correct option is C) 0.018.

Mole fraction =molality /molality +55.5 so 1/1+55.5 =1/56.5=0.017