Detailed kinetic explanation for vapor pressure reduction by dissolved solute?

Question

The following problem was asked in JEE Mains 2020 (Sept 2, Shift 1),

An open beaker of water in equilibrium with water vapor is in a sealed container. When a few grams of glucose are added to the beaker of water, the rate at which water molecules:

(A) leaves the solution increases
(B) leaves the solution decreases
(C) leaves the vapor increases
(D) leaves the vapor decreases

According to the NCERT for Class XII, Part I, pg. 46, para 3,

In a pure liquid the entire surface is occupied by the molecules of the liquid. If anon-volatile solute is added to a solvent to give a solution [Fig. 2.4.(b)], the vapor pressure of the solution is solely from the solvent alone. This vapor pressure of the solution at a given temperature is found to be lower than the vapor pressure of the pure solvent at the same temperature. In the solution, the surface has both solute and solvent molecules; thereby the fraction of the surface covered by the solvent molecules gets reduced. Consequently, the number of solvent molecules escaping from the surface is correspondingly reduced, thus, the vapor pressure is also reduced.

So, after reading the last lines of above quoted text, I think that the vapor pressure is reduced, because the rate at which solvent molecules leaves the solution decreases, due to a decrease in exposed surface area. So, acc. to me option (B) should be correct. But, it was incorrect, acc. to the key.

Is there anything else, I'm missing?

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The answer given is,

(C) leaves the vapor increases

Answer 1

I'd like to specifically commment on this:

According to the NCERT for Class XII, Part I, [pg. 46, para 3][1],

In a pure liquid the entire surface is occupied by the molecules of the liquid. If a non-volatile solute is added to a solvent to give a solution [Fig. 2.4.(b)], the vapor pressure of the solution is solely from the solvent alone. This vapor pressure of the solution at a given temperature is found to be lower than the vapor pressure of the pure solvent at the same temperature. In the solution, the surface has both solute and solvent molecules; thereby the fraction of the surface covered by the solvent molecules gets reduced. Consequently, the number of solvent molecules escaping from the surface is correspondingly reduced, thus, the vapor pressure is also reduced. [emphasis mine]

NCERT's explanation for why vapor pressure is lowered due to the presence of a dissolved solute is incorrect, because vapor pressure is independent of the surface area accesible to the solvent (assuming it's non-zero). Consider these two examples:

1. You have two sealed containers, both of which contain an open beaker of identical solvent. In container A, the beaker is low and wide. In container B, the beaker is tall and narrow. The surface area of solvent in container B is thus smaller. Yet, assuming the conditions in the respective containers are identical, the equilibrium vapor pressures will be the same.

2. You have two sealed containers, both of which contain an open beaker of identical solvent. The beakers are identical, so the surface area of liquid is the same. The conditions in the containers are also identical. Glucose is dissolved into the solvent in container A, while sucrose is dissolved into the solvent in container B. The final concentrations are the same. Sucrose is larger than glucose. Consequently, the fraction of the surface area covered by solvent in container A is larger than in container B. Yet, ignoring non-ideality, the vapor pressures are the same; they depend only on the concentration of solute, not its nature.

The surface area only matters for kinetics, i.e., for how quickly the solvent can escape the container to reach equilibrium. Clearly, with a larger surface area, the equilibrium vapor pressure will be reached more rapidly.

Feel free to send an email to NCERT with a link to this comment.

Here's the thermodynamic explanation: The addition of solute lowers the chemical potential of the solvent, due to the entropy of mixing. [There can also be energetic effects, in either direction, but with a soluble solute the entropy term is dominant.]

At equilibrium, the chemical potential of the solvent in the liquid and vapor phases must be equal. Thus, since the chemical potential of the solvent in the liquid phase has lowered, that of the the solvent in the vapor phase must lower as well.

And since the chemical potential of a gas increases with its partial pressure, the vapor pressure of the solvent in the gas phase will decrease until its chemical potential reaches the new (lowered) chemical potential of the solvent in the liquid phase.

As far as the question itself goes, I'm uncertain, because the question is asking for a kinetic, rather than a thermodynamic, explanation. But I can offer two alternative pictures:

Let's represent the movement between the liquid and vapor phases of the solvent ("X"), as follows:

$$\ce{X_{(l)}<=>X_{(g)}}$$

Picture (I): Both "B" and "C" are correct.

Let's start with the vapor in equilibrium with pure solvent. At equilibrium, the rates of the forward and backward reactions are equal.

Now suppose we add solute to the liquid phase. This shifts the reaction to the left, which means that the rate of the forward reaction initially decreases (which is answer "B") and the rate of the backward reaction initially increases (which is answer "C"). Eventually the system reaches its new equilibrium point, at which point the rates of the forward and reverse reactions are again equal.

Picture (II): "B" is correct.

Again, let's start with the vapor in equilibrium with pure solvent. At equilibrium, the rates of the forward and backward reactions are equal.

Now suppose we add solute to the liquid phase. The rate at which gas enters the liquid phase depends only on the concentration of gas, so the backwards reaction will be unaffected by the presence of the solute in the liquid. However, the rate of the forward reaction will be reduced, since it is now more favorable to for the solvent to remain in the liquid state. Hence the answer is "B".

As I mention in the Comments:

In Picture (I), the change in relative chemical potentials would raise the energetic barrier in the forward direction and lower it in the reverse direction, which would in turn increase the % of collisions that are succesful in the rev. direction, thus increasing the rate of the rev. reaction even though the collision frequency of the vapor with the liquid woudn't be changed by the presence of the dissolved solute.

But: If there isn't any barrier in the rev. direction, such that 100% of vapor molecules that collide with the liquid phase become liquid, then Picture (I) would not apply.

I'm afraid I don't know enough about the microscopic kinetics to have certainty on this. Perhaps someone that has done simulation work on this could provide an answer. [But to get this, you would want to vote to reopen the question.]

Answer 2

Water is in equilibrium with vapor. The simple interpretation is that rates of condensation and evaporation are equal, but that is not really true in the description of an open beaker in a closed space with respect to the beaker eventually the liquid would be dispersed thruout the container droplets here, there, and everywhere. Addition of a solute to the liquid definitely lowers the vapor pressure of that liquid . It does NOTHING to the vapor at the moment of dissolution. A simple experiment to show this would be to have two identical beakers in the enclosed space one with pure water the other with the solution; a careful observation will show that water will leave the pure water and accumulate in the solution. the rate of condensation is not affected by the solution. It is affected by the partial pressure of the water vapor in the container.

If the only source of water vapor is the beaker with the solute[!] the rate of evaporation will decrease; the initial rate of condensation will be the same and the partial pressure of water vapor will then slowly decrease and the rate of condensation will slowly decrease until equilibrium at the new vapor pressure is established. The question is simply inane.

Answer 3

I am also a JEE Aspirant and this question intrigued me. This is also my first answer on Stack Exchange :)

First of all we need to understand that Vapour Pressure decreases when any solute is added to a solvent, i.e $$VP_solution < VP_solvent$$ A very simple explanation for this is that the solute particles introduce new forces of attraction between themselves and solvent molecules and these forces help to prevent vaporisation of solvent.

Another thing to know that Vapour Pressure is an equilibrium phenomenon. In the question as soon as the glucose is added, the already existing equilibrium was disturbed.

There was already an equilibrium stage attained where as many molecules were leaving the solution, were also leaving the vapour state.

Now the addition of glucose has lowered the amount of molecules leaving the solution. So when the new equilibrium is attained, the Vapour Pressure will be less than what it was when no glucose was added.

Now it is understood that Vapour Pressure must decrease, i.e, more molecules should leave the vapour state. Just lowering the amount of molecules leaving the solution wouldn't decrease the Vapour Pressure. So, the rate at which the molecules leave the vapour must increase and this is why Vapour Pressure decreases.

Mind you, when the new equilibrium is attained the amount and rate of molecules leaving and entering the solution become equal but they are less than what they were initially.

I hope this helped!