For two aqueous solutions, one containing urea and the other containing scandium(III) nitrate, with the same extent of freezing point depression, which of the following is true?
#a)# The boiling point elevation is the same.
#b)# The mass of dissolved solute is the same.
#c)# The number of ions in solution is the same.
#d)# The number of mols of particles dissolved are the same.
1 Answer
Well, try to go for the one that makes the most sense. If their freezing point depressions are the same, their boiling point elevations are the same.
The same number of dissolved solute particles cause both things to occur in the same way, regardless of their identity.
Since
As mentioned, if
#DeltaT_f# for the two solutions are equal,#DeltaT_b# for them is also equal.The relative extent to which boiling point increases compared to freezing point decreasing does not change based on what solute you use.
They cannot be the same mass of dissolved solute; if they did, it would be sheer coincidence. You have the same
#DeltaT_f# , the same#K_f# and#K_b# , and the same#i xx m# , where:
#DeltaT_f = -iK_fm#
#DeltaT_b = iK_bm#
#i# is the van't Hoff factor, i.e. the effective number of solute particles per dissolved solute particle.
#m# is the molality in#"mol solute/kg solvent"# .
#K_f# is the freezing point depression constant, and#K_b# is the boiling point elevation constant.Urea is a nonelectrolyte, and scandium(III) nitrate is a strong electrolyte. We expect
#i = 1# for the former and#i = 4# for the latter.Thus, the mols of solute dissolved in the same mass of solvent can't be the same, or else their
#i xx m# products wouldn't be the same.If the mols are not the same, and we know that their molar masses are not the same, then having the same mass would be a coincidence.
As we mentioned, these solutes dissociate to different extents. Somewhat of a tricky choice, but urea effectively does NOT dissociate into ions, so that nullifies this choice.
NOTE: If urea was replaced with a strong electrolyte, then this choice would be true.
As we mentioned in
#(b)# , the mols cannot be the same.Their values of
#i# are different, so if the mols were the same, their values of#i xx m# would be different, and (with the same#K_f# ) thus they would not have the same freezing point.
