Question
Question: Benzene and toluene form an ideal solution over the entire range of composition. The vapor pressure ...
Benzene and toluene form an ideal solution over the entire range of composition. The vapor pressure of pure benzene and toluene at 300K are 50.71mm Hg and 32.06mm Hg respectively. Calculate the mole fraction of benzene in vapor phase if 80g of benzene is mixed with 100g of toluene.
Solution
An ideal solution is a blend wherein the molecules of various species are recognizable, however, in contrast to the ideal gas, the molecules in ideal solution apply force on each other. Raoult's law expresses that the vapor pressure of a solvent over a solution is equivalent to the vapor pressure of the pure solvent at a similar temperature scaled by the mole fraction of the solvent present.
Complete answer:
Step 1: To find out the molar mass of Benzene and Toluene
Molar Mass of Benzene (C6H6)=6×12+6×1=78g/mol
Molar Mass of Toluene (C7H8)=7×12+8×1=92g/mol
Step 2: To find out the Number of moles present in 80g of Benzene and 100g of Toluene
Number of moles in 80gof Benzene =7880=1.026mol
Number of moles in 100gof Toluene=92100=1.087mol
Step 3: Mole Fraction of Toluene and Benzene
Mole fraction of benzene, Xb=1.026+1.0871.026=0.486
And Mole fraction of toluene, Xt=1−0.486=0.514
We have provided that
Vapor pressure of pure benzene Pbo=50.71mmHg
And Vapor pressure of pure toluene, Pto=32.06mmHg
Now, partial vapor pressure of benzene, Pb=Pb×Xt
Now, partial vapor pressure of toluene, Pt=Pt×Xt
Pt=Pto×Xt=32.06×0.514 =16.48Hence, total vapor pressure =24.65+16.48=41.13mmHg
Mole fraction of benzene in vapor phase =42.1324.65=0.60
**Therefore, the answer is 0.60
Note:**
It is essential to indicate the temperature while stating a vapor pressure since vapor pressures increment with temperature. Also, know that there are a few different units for pressure. The most widely recognized unit for vapor pressure is the torr. 1torr=1mmHg (one millimeter of mercury). Most materials have low vapor pressures.