In: Chemistry
. In a mixture of acetone and trichlormethane at 298 K, Ktrichloromethane = 22.0 kPa, whereas p*trichloromethane = 36.4 kPa. What is the relation between the standard chemical potential and that of the pure liquid?
If a solute of a solution follows henry's law with the vapour pressure pa, then pa=Kaxa
So, the chemical potential of the solute will be,a =a* + RT(lnpa/pa*) =a* + RT(lnKa/pa*) + RTlnxa
Where, R= gas constant = 8.314 4621 J K-1 mol-1
So, the new standard chemical potential, 'a = a* + RT(lnKa/pa*)
from the above data, Ktrichloromethane = 22.0 kPa and p*trichloromethane = 36.4 kPa
the temperature of the mixture is 298 K
So, the relation between the standard chemical potential and that of the pure liquid,
'trichloromethane = *trichloromethane + RT(lnKtrichloromethane/p*trichloromethane)
= *trichloromethane + 8.3144621J K-1 mol-1298 K(ln 22.0 kPa/ 36.4 kpa)
= *trichloromethane -1247.59 Jmol-1
Here,
'trichloromethane = standard chemical potential of trichloromethane
*trichloromethane = chemical potential of pure trichloromethane