What should be the mole fraction of sucrose (C12H22O11) in an aqueous solution at 20°C so that the vapor pressure of water above the solution is 2.0 mmHg less than the vapor pressure of pure water at the same temperature. The vapor pressure of pure water at 20 °C is 17.5 mmHg.

The mol fraction of sucrose in an aqueous solution at 20°C  is 0.114

Explanation:

Step 1: Data given

The vapor pressure of water above the solution is 2.0 mmHg

The vapor pressure of pure water at 20 °C is 17.5 mmHg

Step 2: Calculate the mol fraction of sucrose

Psolution = (χsolvent) (P°solvent)

⇒with Psolution = the vapor pressure of the solution is 2.0 mmHg

⇒with χsolvent = the mol fraction of sucrose = TO BE DETERMINED

⇒with P°solvent = the vapor pressure of pure water at 20 °C =17.5 mmHg

2.0 mmHg = X * 17.5 mmHg

X = 2.0 mmHg / 17.5 mmHg

X = 0.114

The mol fraction of sucrose in an aqueous solution at 20°C  is 0.114

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