# Find the partial pressure in a solution containing ethanol and 1-propanol with a total vapor pressure of #"56.3 torr"#? The pure vapor pressures are #"100.0 torr"# and #"37.6 torr"#, respectively, and the solution has a mol fraction of #0.300# of ethanol.

##### 1 Answer

Consider **Raoult's law** compared with **Dalton's law** of partial pressures:

#P_i = overbrace(chi_(i(l))P_i^"*")^"Raoult's Law" = underbrace(chi_(i(v))P_"tot")_"Dalton's Law"# ,where:

#P_i# is thepartial vapor pressureof component#i# , i.e.in a mixture.#P_i^"*"# is thepure vapor pressureof component#i# , i.e.by itself.#chi_(i(l))= n_i/(sum_k^N n_k)# is themol fractionof component#i# in the.liquid phase#chi_(i(v))# is the mol fraction in the.vapor phase#P_"tot"# is thetotalpressure.

As these are assumed to produce *ideal-gas vapors*, and to form ideal solutions, **designate ethanol as** **1-propanol as**

*Since you have not designated whether the mol fraction is in the liquid phase or the vapor phase, I will straight up assume that it is the liquid phase... you will have to verify whether it is the vapor phase or not...*

Note that mol fractions for all components in a mixture must add up to

#chi_(1(l)) + chi_(2(l)) = 1# ,

#chi_(1(v)) + chi_(2(v)) = 1# ,

#chi_(1(l)) ne chi_(1(v))# ,

#chi_(2(l)) ne chi_(2(v))# ,

for a binary mixture. Thus...

#color(blue)(P_1) = overbrace(underbrace(0.300)_(chi_(1(l))) cdot "100 torr")^"Ethanol" = color(blue)(ul"30.0 torr")#

#color(blue)(P_2) = overbrace(underbrace((1 - 0.300))_(chi_(2(l))) cdot "37.6 torr")^"1-propanol" = color(blue)(ul"26.3 torr")#

What is the total pressure when they are mixed together? Well...

#P_"tot" = P_1 + P_2 = ul"56.3 torr"#

#"30.0 torr" = chi_(1(v))P_"tot"# #" "" "" "" "" "" "" "" "bb((1))#

#"26.3 torr" = chi_(2(v))P_"tot" = (1 - chi_(1(v)))P_"tot"# #" "bb((2))#

What then is the mol fraction of ethanol