# Does vapor pressure vary with the number of particles in solution? What if you have "1 M" of "NaCl", vs. "1 M" "KCl", vs. "1 M" "CaCl"_2?

May 5, 2017

Maybe the following concept map will make things clearer. These electrolytes generate approximately two, two, and three ions, respectively, in solution for each formula unit of the solute.

${\text{NaCl"(aq) -> "Na"^(+)(aq) + "Cl}}^{-} \left(a q\right)$

${\text{KCl"(aq) -> "K"^(+)(aq) + "Cl}}^{-} \left(a q\right)$

${\text{CaCl"_2(aq) -> "CaCl"^(+)(aq) + "Cl}}^{-} \left(a q\right)$
${\text{CaCl"^(+)(aq) -> "Ca"^(2+)(aq) + "Cl}}^{-} \left(a q\right)$

Hence, the molar and molal concentration, and thus the NONIDEAL "mol fraction" (will be discussed below), of electrolyte particles originating from $\boldsymbol{{\text{CaCl}}_{2}}$ will be higher from analogous solutions of $\text{NaCl}$ and $\text{KCl}$.

The approximate concentrations of the above solutions are $\text{2 M}$, $\text{2 M}$, and $\text{3 M}$ simply by counting the electrolyte particles and assuming 100% dissociation.

Refer to this answer for more on osmotic pressure, vapor pressure, and freezing point. All of these depend on the effective concentration of electrolytes in the solution.

RAOULT'S LAW IS ONLY FOR IDEAL SOLUTIONS

The decrease in vapor pressure, $\Delta {P}_{j} = {P}_{j} - {P}_{j}^{\text{*}}$, can be determined based on Raoult's law,

${P}_{j} = {\chi}_{j \left(l\right)} {P}_{j}^{\text{*}}$

in terms of mol fractions of solute $j$ in the liquid phase, but the problem is that it is only for ideal solutions. Equations such as

$\Delta {T}_{f} = {T}_{f} - {T}_{f}^{\text{*}} = - i {K}_{f} m$

already account for nonideality using the van't Hoff factor $i$. Sometimes we assume what $i$ is by looking at the number of particles are in solution per formula unit of solute, but in general $i$ accounts for nonideality. For example, $i = 1.9$ for $\text{NaCl}$, but $2.7$ for ${\text{MgCl}}_{2}$.

Raoult's law can be rewritten in another way that does account for nonideality:

${P}_{j} = {a}_{j \left(l\right)} {P}_{j}^{\text{*}}$

where:

• ${a}_{j \left(l\right)} = {\gamma}_{j} {\chi}_{j}$ is the activity of the solute $j$ in the liquid phase.
• ${\gamma}_{j}$ is the activity coefficient of the solute $j$.
• ${\chi}_{j \left(l\right)}$ is the mol fraction of the solute $j$ in the liquid phase.

The activity coefficient ${\gamma}_{j}$ can be considered as a weighting factor to account for nonideality, and the activity ${a}_{j \left(l\right)}$ can be considered the "nonideal" version of the mol fraction.

Since mol fraction, molality, and molarity are approximately interconvertible (see the above concept map), we can indirectly say that the "true mol fraction" (the activity) of solute in solution is not simply due to the original solute, such as ${\text{CaCl}}_{2}$, but due to ALL the electrolytes that it generates, namely ${\text{Ca}}^{+}$, ${\text{Cl}}^{-}$, AND ${\text{CaCl}}^{+}$!

So, no, we cannot say that the vapor pressure decrease is to the same extent for solutions of nonvolatile solutes, even if they have the same face-value concentrations.

We must look at their effective concentrations instead, which is not readily-seen trend and might have to be inferred indirectly when it comes to vapor pressure.