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?

1 Answer
Dec 28, 2016

Answer:

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

Explanation:

#"Raoult's Law"# tells us that in an ideal solution, the vapour pressure of a component is proportional to the mole 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 or acetone as the solvent rather than water, given that these organic solvents would have expressed a REDUCED mole fraction with respect to water, and thus a GREATER diminution in vapour pressure with respect to that of the pure solvent....