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A solution is prepared by dissolving 38.6 g of sucrose (C₁₂H₂₂O₁₁) in 495 g of water. Determine the mole fraction of sucrose if the final volume of the solution is 508 mL.

Answer :

Answer:

[tex]x_{suc}=0.00406[/tex]

Explanation:

Hello!

In this case, since the mole fraction relates the moles of solute and the moles of solution, and for sucrose it is:

[tex]x_{suc}=\frac{n_{suc}}{n_{suc}+n_{water}}[/tex]

Whereas we need to compute the moles of both sucrose and water based on their molar masses (342.3 and 18.02 respectively) as shown below:

[tex]n_{suc}}=\frac{38.6g}{342.3g/mol}=0.113mol\\\\ n_{water}}=\frac{495g}{18.02g/mol}=27.5mol\\[/tex]

Thus, the mole fraction sucrose turns out:

[tex]x_{suc}=\frac{0.112}{0.112+27.5}\\\\x_{suc}=0.00406[/tex]

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