SOLUTION:

Step 1: Calculate the number of moles of solvent (water).

The molar mass of water is 18.02 g/mol.

[tex]\begin{aligned} & n_{\text{solvent}} = \text{250 g} \times \frac{\text{1 mol}}{\text{18.02 g}} = \text{13.87 mol} \\ \end{aligned}[/tex]

Step 2: Calculate the mole fraction of solvent.

[tex]\begin{aligned} X_{\text{solvent}} & = 1 - X_{\text{solute}} \\ & = 1 - 0.13 \\ & = 0.87 \end{aligned}[/tex]

Step 3: Calculate the number of moles of solution.

[tex]\begin{aligned} n_{\text{solution}} & = \frac{n_{\text{solvent}}}{X_{\text{solvent}}} \\ & = \frac{\text{13.87 mol}}{0.87} \\ & = \text{15.94 mol} \end{aligned}[/tex]

Step 4: Calculate the number of moles of solute.

[tex]\begin{aligned} n_{\text{solute}} & = n_{\text{solution}} - n_{\text{solvent}} \\ & = \text{15.94 mol} - \text{13.87 mol} \\ & = \text{2.07 mol} \end{aligned}[/tex]

Step 5: Calculate the mass of solute (glucose).

The molar mass of glucose is 180.15 g/mol.

[tex]\begin{aligned} & \text{mass}_{\text{solute}} = \text{2.07 mol} \times \frac{\text{180.15 g}}{\text{1 mol}} = \boxed{\text{373 g}} \\ \end{aligned}[/tex]

Hence, 373 g of glucose must be dissolved in 250 g of water so that the mole fraction of glucose is 0.13.

[tex]\\[/tex]

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