Start by writing the three equations that you're going to use to solve for the boiling point, freezing point, and vapor pressure of the solution.
- Freezing point depression
#DeltaT_"f" = i * K_f * b#, where
#K_f# - the cryoscopic constant - depends on the solvent;
#b# - the molality of the solution;
#i# - the van't Hoff factor - the number of ions per individual molecule of solute.
#DeltaT_"f"# - the freezing point depression - defined as
#T_"f"^@ - T_"f sol"#.
In your case, the van't Hoff factor will be equal to 1 because you're dealing with a non-electrolyte.
Plug in your values and solve for #DeltaT_"f"#
#DeltaT_"f" = 1 * 1.86^@"C"/cancel("molal") * 0.750cancel("molal") = 1.40^@"C"#
The freezing point of the solution will be
#T_"f sol" = T_"f"^@ - DeltaT_"f" = 0^@"C" - 1.40^@"C" = color(green)("-1.40"^@"C")#
#DeltaT_b = i * K_b * b#, where
#i# - the van't Hoff factor;
#K_b# - the ebullioscopic constant;
#b# - the molality of the solution.
#DeltaT_b# - the poiling point elevation - defined as #T_"b sol" - T_"b"^@#
Once again, plug in your values and solve for #DeltaT_"b"#
#DeltaT_"b" = 1 * 0.51^@"C"/cancel("molal") * 0.750cancel("molal") = 0.383^@"C"#
The boiling point of the solution will be
#T_"b sol" = T_"b"^@ + DeltaT_"b" = 100^@"C" + 0.383^@"C" = color(green)(100.4^@"C")#
#P_"solution" = chi_"[solvent](http://socratic.org/chemistry/solutions-and-their-behavior/solvent)" * P_"solvent"^@#, where
#P_"solution"# - the vapor pressure of the solution;
#chi_"solvent"# - the mole fraction of the solvent;
#P_"solvent"^@# - the vapor pressure of the pure solvent.
Since you didn't provide the mass of water used to make your solution, I'll assume that you have a 1-kg sample.
The number of moles of water present in 1000 g will be
#1000cancel("g") * "1 mole water"/(18.02cancel("g")) = "55.5 moles"#
The mole fraction of water, which is defined as the number of moles of water divided by the total number of moles in the solution, will be
#chi_"water" = (55.5cancel("moles"))/((55.5 + 0.750)cancel("moles")) = 0.9867#
SIDE NOTE Since molality is defined as moles of solute per kg of solvent, the 1 kg of water implies that you have 0.750 moles of sucrose.
Therefore, the vapor pressure of the solution will be
#P_"solution" = 0.9867 * "23.76 torr" = color(green)("23.44 torr")#
