Respuesta :
The mole fraction of sucrose in the final solution prepared by dissolving 38.6 g sucrose ( C₁₂H₂₂O₁₁) in 495 g of water is 0.004
We'll begin by calculating the number of mole sucrose and water in the solution. This can be obtained as follow:
For sucrose:
Molar mass of C₁₂H₂₂O₁₁ = (12×12) + (1×22) + (16×11)
= 144 + 22 + 176
= 342 g/mol
Mass of C₁₂H₂₂O₁₁ = 38.6 g
Mole of C₁₂H₂₂O₁₁ =?
Mole = mass / molar mass
Mole of C₁₂H₂₂O₁₁ = 38.6/342
Mole of C₁₂H₂₂O₁₁ = 0.113 mole
For water:
Molar mass of H₂O = (2×1) + 16
= 18 g/mol
Mass of H₂O = 495 g
Mole of H₂O =?
Mole = mass / molar mass
Mole of H₂O = 495 / 18
Mole of H₂O = 27.5 mole
Next, we shall determine the total mole.
Mole of C₁₂H₂₂O₁₁ = 0.113 mole
Mole of H₂O = 27.5 mole
Total mole =?
Total mole = 0.113 + 27.5
Total mole = 27.613 mole
Finally, we shall determine the mole fraction of sucrose.
Mole of Sucrose, C₁₂H₂₂O₁₁ = 0.113 mole
Total mole = 27.613 mole
Mole fraction of sucrose =?
Mole fraction = mole of element / total mole
Mole fraction of sucrose = 0.113 / 27.613
Mole fraction of sucrose = 0.004
Therefore, the mole fraction of sucrose in the solution is 0.004
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Mole fraction is defined as the ratio of number of moles of a constituent of a solution to the total amount of all constituent in a mixture. The mole fraction of sucrose in 508 ml of solution will be 0.004.
Given that,
- Molar mass of C[tex]_{12}[/tex]H[tex]_{22}[/tex]O[tex]_{11}[/tex] = 144 + 22 + 176 = 342 g/mol
- Given Mass of C[tex]_{12}[/tex]H[tex]_{22}[/tex]O[tex]_{11}[/tex] = 38.6 g
- [tex]\text{moles}&=\dfrac{\text{given mass}}{\text{molar mass}}[/tex]
- [tex]\text{moles}&=\dfrac{38.6}{342}[/tex]
Moles = 0.113
Similarly, for water:
- Molar Mass of Water = 2 + 16 = 18 g/mol
- Given Mass of Water = 495 g
- [tex]\text{moles}&=\dfrac{\text{given mass}}{\text{molar mass}}[/tex]
- [tex]\text{moles}&=\dfrac{495}{18}[/tex]
Moles = 27.5
Now, total moles of the solution is:
- Total moles = 0.113 + 27.5
Total moles = 27.613 mole
Calculating the mole fraction, we get:
- [tex]\text{Mole Fraction}&=\dfrac{\text{Moles of sucrose}}{\text{Total moles}}\\\\\text{Mole Fraction}&=\dfrac{0.113}{27.613}[/tex]
- Mole fraction of sucrose = 0.004
Therefore, the mole fraction of sucrose for the given solution is 0.004.
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