# If #"14 g"# of calcium nitrate is dissolved in #"200 g"# of water, and it experiences a #70%# dissociation, what is the solution's vapor pressure if the solvent began at the normal boiling point of water? Hint: the normal boiling point occurs at 760 torr.

##### 1 Answer

#"748 torr"# .(what is the answer in

#"mm Hg"# ?)

Vapor pressure of the solution *relative to the solvent* is given by **Raoult's law** for ideal solutions:

#P_A = chi_(A(l)) P_A^"*"# where:

#P_A# is thevapor pressureof the solvent in the context of the solution.#"*"# indicatespuresolvent.#chi_(A(l))# is the mol fraction of solvent in thesolutionphase.

When nonvolatile solute is added to a solvent, it decreases its vapor pressure. **Thus, the answer will be less** than

In this case, we have a strong electrolyte. Normally, we assume 100% dissociation of strong electrolytes, but in this case there is ion pairing to form

We ignore the

The salt **dissociates** into

#"Ca"("NO"_3)_2(aq) -> "Ca"^(2+)(aq) + 2"NO"_3^(-)(aq)#

To calculate the new vapor pressure, we'll need the mol fraction

#chi_("ions") = n_"ions"/(n_"ions" + n_(H_2O))#

#chi_"ions" + chi_(H_2O) = 1#

We would have ** three** mols of

*ions*,

**mol of calcium nitrate,**

*one*For

#n_(Ca(NO_3)_2) = 14 cancel("g Ca"("NO"_3)_2) xx ("1 mol Ca"("NO"_3)_2)/(164.088 cancel("g Ca"("NO"_3)_2))#

#=# #"0.08532 mols Ca"("NO"_3)_2#

Again, *three* times the mols of ions result from *100%* dissociation, so:

#n_"ions" = 3n_(Ca(NO_3)_2) = "0.2560 mols ions"#

With **70% dissociation**, we simply have *70% of the mols*, or

#0.7n_"ions" = n_"ions"' = "0.1792 mols"# .

Given

#200 cancel("g H"_2"O") xx ("1 mol H"_2"O")/(18.015 cancel("g H"_2"O")) = "11.10 mols H"_2"O"#

This gives us a mol fraction of:

#chi_("ions")' = (n_"ions"')/(n_"ions"' + n_(H_2O))#

#= "0.1792 mols"/("0.1792 mols" + "11.10 mols")#

#= 0.01588#

or since all mol fractions for a solution when added together equal

#chi_(H_2O) = 1 - chi_("ions")' = 0.9841#

Therefore, the **solution vapor pressure** is:

#color(blue)(P_A) = 0.9841 cdot "760 torr"#

#=# #color(blue)("748 torr")#