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Sagot :
SOLUTION:
Step 1: Determine the mass of solute (sucrose) and solvent (water).
Assuming that the mass of solution is 100 g, there are 25 g of sucrose in 75 g of water.
[tex]\begin{aligned} & mass_{\text{solute}} = \text{25 g} \\ & mass_{\text{solvent}} = \text{75 g} \end{aligned}[/tex]
Step 2: Calculate the number of moles of each component.
The molar masses of sucrose and water are 342.297 g/mol and 18.015 g/mol, respectively.
• For solute
[tex]\begin{aligned} n_{\text{solute}} & = \frac{mass_{\text{solute}}}{MM_{\text{solute}}} \\ & = \frac{\text{25 g}}{\text{342.297 g/mol}} \\ & = \text{0.073036 mol} \end{aligned}[/tex]
• For solvent
[tex]\begin{aligned} n_{\text{solvent}} & = \frac{mass_{\text{solvent}}}{MM_{\text{solvent}}} \\ & = \frac{\text{75 g}}{\text{18.015 g/mol}} \\ & = \text{4.1632 mol} \end{aligned}[/tex]
Step 3: Calculate the mole fraction of solute.
[tex]\begin{aligned} X_{\text{ethanol}} & = \frac{n_{\text{ethanol}}}{n_{\text{methanol}} + n_{\text{ethanol}}} \\ & = \frac{\text{0.073036 mol}}{\text{0.073036 mol + 4.1632 mol}} \\ & = 0.017241 & = \boxed{0.0172} \end{aligned}[/tex]
Hence, the mole fraction of 25% by mass sucrose solution is 0.0172.
[tex]\\[/tex]
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