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QUESTION

# 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.