Asolution is prepared by dissolving 38.6 g sucrose (c12h22o11) in 495 g of water. determine the mole fraction of sucrose if the final volume of the solution is 508 ml.

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:

Molar mass of C₁₂H₂₂O₁₁ = (12×12) + (1×22) + (16×11)

= 144 + 22 + 176

= 342 g/mol

Mass of C₁₂H₂₂O₁₁ = 38.6 g

Mole = mass / molar mass

Mole of C₁₂H₂₂O₁₁ = 38.6/342

Molar mass of H₂O = (2×1) + 16

= 18 g/mol

Mass of H₂O = 495 g

Mole = mass / molar mass

Mole of H₂O = 495 / 18

Next, we shall determine the total mole.

Mole of C₁₂H₂₂O₁₁ = 0.113 mole

Mole of H₂O = 27.5 mole

Total mole = 0.113 + 27.5

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,

Moles = 0.113

Similarly, for water:

Moles = 27.5

Now, total moles of the solution is:

Total moles = 27.613 mole

Calculating the mole fraction, we get:

Therefore, the mole fraction of sucrose for the given solution is 0.004.

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