To calculate the molality of the solution, we first need to determine the number of moles of solute. The molar mass of cane sugar is 342.3 g/mol, so the number of moles of cane sugar in 38.0 g is:
$$38.0 \text{ g cane sugar} \times \frac{1 \text{ mol cane sugar}}{342.3 \text{ g cane sugar}} = 0.111 \text{ mol cane sugar}$$
Next, we need to determine the mass of the solvent in kilograms. The mass of the water is 175 g, which is equivalent to 0.175 kg.
Finally, we can calculate the molality of the solution by dividing the number of moles of solute by the mass of the solvent in kilograms:
$$\text{Molality} = \frac{0.111 \text{ mol cane sugar}}{0.175 \text{ kg water}} = 0.634 \text{ mol/kg}$$
Therefore, the molality of the solution is 0.634 mol/kg.
