A sugar syrup of weight 214.2 g contains 34.2 g of sugar C₁₂H₂₂O₁₁. Calculate the mole fraction of the sugar in the syrup.

• If the answer is X then write 100011X

To find the mole fraction of sugar in the syrup, we first need to calculate the number of moles of sugar and the number of moles of water in the syrup.

Step 1: Calculate Moles of Sugar

The molar mass of sugar (C₁₂H₂₂O₁₁) is calculated as follows:

• Carbon (C): 12.01 g/mol × 12 = 144.12 g/mol
• Hydrogen (H): 1.008 g/mol × 22 = 22.176 g/mol
• Oxygen (O): 16.00 g/mol × 11 = 176.00 g/mol

Adding these together gives:

Molar mass of sugar = 144.12 + 22.176 + 176.00 = 342.296 g/mol

Now, calculate the moles of sugar:

Moles of sugar = mass / molar mass = 34.2 g / 342.296 g/mol ≈ 0.1000 moles

Step 2: Calculate Moles of Water

The total weight of the syrup is 214.2 g. The weight of water can be found by subtracting the weight of sugar:

Weight of water = 214.2 g - 34.2 g = 180.0 g

The molar mass of water (H₂O) is 18.015 g/mol. Now, calculate the moles of water:

Moles of water = 180.0 g / 18.015 g/mol ≈ 10.0 moles

Step 3: Calculate Mole Fraction of Sugar

The mole fraction of sugar (X) is given by the formula:

X = moles of sugar / (moles of sugar + moles of water)

Substituting the values:

X = 0.1000 / (0.1000 + 10.0) ≈ 0.0099

Final Calculation

To find 100011X:

100011X = 100011 × 0.0099 ≈ 990.10989

Thus, the final answer is approximately 990.11.