The vapor pressure of water at 20 C is 17.5mmHg. What is the vapor pressure of water over a solution prepared from 200g of sucrose (##C_12H_22O_11##) and 112.3 g of water?

We use ##"Raoult's Law..........."## and calculate a solution vapour pressure of ##16*mm*Hg##.

##"Raoult's Law"## tells us that in an ideal solution, the vapour pressure of a component is proportional to fraction of that component in solution.

##"Mole fraction of sucrose:"## ##="Moles of sucrose"/"Moles of sucrose + moles of water"##

##chi_"sucrose"=((200*g)/(342.13*g*mol^-1))/((200*g)/(342.13*g*mol^-1)+(112.3*g)/(18.01*g*mol^-1))=0.0857##

##"Mole fraction of water:"##

##chi_"water"=((112.3*g)/(18.01*g*mol^-1))/((200*g)/(342.13*g*mol^-1)+(112.3*g)/(18.01*g*mol^-1))=0.914##

Note that by definition, ##chi_"sucrose"+chi_"water"=1##

Because sucrose is involatile, the vapour pressure of the solution is proportional to the mole fraction of water:

##P_"solution"=chi_"water"xx17.5*mm*Hg##

##=0.914xx17.5*mm*Hg=16*mm*Hg##

We might have got better results if we used ethyl alcohol as the rather than water.