If the vapor pressure at the normal boiling point of an aqueous ideal binary mixture is 740 torr, what is the mol fraction of the nonvolatile solute that was dissolved within it?

1 Answer
Truong-Son N.
Nov 9, 2017

Well, this solution probably doesn't quite allow us to use Debye-Huckel theory of dilute solutions, but... I guess it's fairly dilute...

Well, do you know the boiling point of water is #100^@ "C" ~~ "373 K"#?

If so, you should recall that the vapor pressure of pure water at its boiling point MUST be equal to the atmospheric pressure of #"1 atm"#. That is of course an assumption, as we may very well be at an entirely nonstandard pressure, so the question is not clear.

Given that assumption, we can use Raoult's Law for ideal solutions:

#P_j = chi_(j(l))P_j^"*"#

where:

  • #P_j# is the vapor pressure of solvent #j# containing solute #i# in it.
  • #"*"# indicates for the pure substance.
  • #chi_(j(l))# is the mol fraction of component #j# in the liquid phase.

Therefore, the mol fraction of the (which substance?) is:

#chi_(j(l)) = P_j/P_j^"*"#

#= "740 torr"/"760 torr" = 0.9737#

And so, the mol fraction of the (which substance?) is:

#color(blue)(chi_(i(l)) = 0.0263 = 20/760 = ???)#

What is the change in vapor pressure for the solvent? What should its sign be?

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