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-1
298 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