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Chapter 9

Solutions

Partial Molar Quantities
Partial Molar Volumes * * * * V *  n1Vm,1  n2Vm, 2    nrVm,r   niVm,i
i

(9.4)

V

/cm3
100 99 98

75

V (H2O)/cm3
50 25

0The star indicates a property of a pure substance or a collection of pure substances.
Addition of 50.0 cm3 of water to 50.0 cm3 of ethanol at 20 oC and 1 atm gives a solution of 96.5 cm3 (Fig.9.1, left).

97 96
0 25 50 75 100 (ethanol)/cm3

V

V V*

Partial Molar Quantities
V V
*

(1) different intermolecular forces

V /cm3
100 99 98 97

75

(2) different packing ofmolecules V (H2O)/cm3 (different sizes and shapes of the 50 25 0 molecules being mixed)

V  V (T , P, n1 ,, nr ), U  U (T , P, n1 ,, nr )
The total differential of V
 V   V  dV    dT   dP T  P ,ni P T ,ni  

(9.5)

96
0 25

V

50 75 100 (ethanol)/cm3

 V   V   dn1      n   n  1 T , P ,ni1  r

  dnr  T , P ,nir

(9.6)

PartialMolar Quantities
 V   V  dV    dT    dP  T  P ,ni  P T ,ni  V   V  dn1      n    n  1 T , P ,ni1  r
The partial molar volume

  dnr  T , P ,nir

(9.6) V V j   n  j

   T , P ,ni j

one phase syst.

(9.7)*

nj: the amount of a substance j nij: the amount of all other substances present are constant

Partial Molar QuantitiesThe partial molar volume

 V V j   n  j

   T , P ,ni j

one phase syst.
V(a)
V

(9.7)*

The partial molar volume is the slope of the graph of the total volume as the amount ofj is changed, P, T, amount of other components being constant Equation (9.6) becomes

V(b)

 V   V  dV    dT    dP  V i dni  T  P,ni  P T ,ni i

x
(9.8)

Partial MolarQuantities
The partial molar volume  V   V j  one phase syst.  n   j T , P ,ni j

(9.7)* (9.9)

V i  V i (T , P, x1 , x2 ,)
 V   V j*  *      V m, j V    n   ...
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