APPENDIX A: EFFECT OF CONCENTRATION SCALES ON ACTIVITIES
The value of an activity of a solute depends on the concentration scale that is
chosen. This is because the standard-state chemical potentials for different refer-
ence functions are themselves different (Mills 1988). For a molality reference func-
tion, the standard-state chemical potential for solute B is
∞
mB
(
)
O
O
m,B (T ) = T , p , mB,L RT ln O
(60)
mB
and the standard-state chemical potential for solute B for a mole-fraction reference
function is
[(T , p
]
)
∞
, mB,L RT ln(xB ) .
O,B (T ) =
O
(61)
x
Subtracting eq 60 from eq 61 yields
∞
mB
x,B (T ) m,B (T ) = RT ln(xB ) ln O .
O
O
(62)
mB
This is equivalent to
∞
mB
mB
ln O
ln
O
O
x,B (T ) m,B (T ) = RT
mB
1
(63)
+ mB
MA
and
∞
mB
mB
O
ln O
x,B (T ) m,B (T ) = RT ln
mB
O
O
mB
1 +m
(64)
B
MA
O
mB
which results in
(
)
O,B (T ) = m,B (T ) RT ln MAmB .
O
O
(65)
x
The molality-based activity of solute B is
B m,B
O
am,B = exp
(66)
RT
and its mole-fraction-based activity is
B O,B
x
ax,B = exp
.
(67)
RT
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