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During the lecture in my chemistry class, my teacher posed the following problem:

Arrange in terms of increasing vapor pressure:

a) $\pu{0.5m}$ sugar

b) $\pu{0.5m} ~ \ce{NaCl}$

c) $\pu{2m}$ ethylene glycol

d) $ \pu{2m} ~\ce{ LiBr}$

The answer turned out to be: d, c, b, a. However, I do not understand why this is the case. I know the formula for vapor pressure is:

$$ \Delta P = -XP^\circ $$

which means that the pressure of the solvent is proportional to the mole fraction of the solute. I'm still not grasping why the aforementioned answer is correct though. Can anyone provide me with an explanation?

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To solve this problem, use Raoult's law. In Raoult's law, the vapor pressure of a fluid is lowered proportionally with the mole fraction of solute particles in the fluid.

You know the formula, but you only need it if you want to calculate the actual resulting vapor pressure. We can know which is bigger like this:

A. $\pu{0.5M }$ sugar. Sugar does not ionize, thus there are $\pu{0.5 M }$ particles in the solvent.

B. $\pu{0.5M \ce{NaCl}}$. Sodium chloride dissociates to two ions. Thus there are $0.5 \times \pu{2 M}$ particles in the solvent.

C. $\pu{2M}$ ethylene glycol. Again, this doesn't dissociate, so there are $\pu{2M}$ particles.

D. $\pu{2M \ce{LiBr}}$. Dissociates, resulting in $2 \times \pu{2 M}$ particles.

Thus, listing the concentration of particles in the solvent, you see where the answer comes from:

D: $\pu{4 M}$

C: $\pu{2 M}$

B: $\pu{1 M}$

A: $\pu{0.5 M}$

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