How many grams of sucrose, c12h22o11, (mm= 342.3 g/mol), must be added to 631. g of water at 20°c to lower the vapor pressure by 0.963 mm hg? the vapor pressure of water at 20°c is 17.5 mmhg

The fraction of vapor pressure lowering is 0.963 mmHg/17.5 mmHg = 0.05503. This should be equal to the mole fraction of the sucrose in the water. The number of moles of water is 631 g / 18.02 g/mol = 35.02 moles. If we have x grams of sucrose, then we have x/342.3 moles of sucrose, and the mole fraction of sucrose would be equal to 0.05503:
(x/342.3) / (x/342.3 + 35.02) = 0.05503
x = 698.0789 g sucrose

The phase where ice changes directly to gas is called sublimation