# Does equality of molarity or molality determine constancy of boiling (or freezing) points of different solutions?

I encountered a question among papers for JEE (2005) that demands completing a statement:

Equimolar solutions in the same solvent have _______

There are four options and the correct answers are

same boiling point

and

same freezing point

I don't think this is correct as the change in boiling and freezing point depends on molality and not molarity. Hence, according to the options, the one saying different boiling and freezing points seems to be correct to me.

However, such exams very rarely have mistakes which are not corrected later. Please clarify.

• Is this in a question block about ideal solutions? Because at higher concentrations, both answers would even be wrong if you ignored the "lality"/"larity" mistake.
– Karl
Jul 28, 2019 at 20:03
• @Karl it's about ideal solutions. I forgot to mention it
– user78585
Jul 28, 2019 at 20:16
• Equimolar solutions are also equimolal ! Jun 25, 2021 at 16:34
• @Maurice not at all! Molarity is a volumetric property, therefore depends on density. Jun 26, 2021 at 6:07
• @Buck Thorn. Equimolar solutions do not have the same molality. But compared to one another, their molalities are equal. Jun 26, 2021 at 9:08

## 1 Answer

At low concentrations for which the ideal bp elevation/fp depression expressions usually apply, molarity is linearly proportional to molality, therefore the statements are equivalent.

This webpage explains nicely why low concentrations are important:

Raoult's law only works for low concentration solutions. Why? Well, in order for our approximation to work, the interactions between the solute and solvent molecules must be nearly identical. If the interactions are stronger, then the heat of vaporization of the solvent will change and thus our whole approximation falls apart. Since we know that intermolecular forces vary greatly between molecules, the affect of those forces must be kept at a minimum by keeping the solute concentration real low.

In any case (as explained by additional statements in the abovementioned website, which discusses dissociation of ionic solutes), the statement made in the answer to your exam would not be true generally even if molality instead of molarity was mentioned.

The point of the question seems to be that a student should associate a universal response of the solvent that is independent of solute with colligative properties as described using Raoult's law, which is behavior most often approximated by dilute solutions (the statement that Raoult's law only applies to dilute solutions happens to be false, btw), and that in this realm of application molarity is approx linearly proportional to molality.

• Hm, the question never says that the cocentration is low.
– Karl
Jul 28, 2019 at 19:51
• @Karl No, some details seem implicit - or at the very least, the point seems to be that a student should associate a universal response that is independent of solute with colligative properties as described using Raoult's law, which as my answer explains, is behavior most often approximated by dilute solutions (the statement that Raoult's law only applies to dilute solutions happens to be false, but then the point is not to write an essay on solution chemistry, just to clarify the confusion), and that in this realm of application molarity is approx linearly proportional to molality. Jul 28, 2019 at 20:27
• @BuckThorn Very well said
– user78585
Aug 11, 2019 at 17:22