Unformatted text preview: the volume occupied by one mole of A, in a mixture of A and B, is the partial molar volume of A and generally depends Marand’s Notes: Chapter 5  The Properties of Simple Mixtures 157 on the composition of the mixture. To describe composition, we use the mole fraction (defined by the symbol x). The mole fraction of a substance J is simply: xJ = € nJ
nA which for a binary (A, B) mixture leads to: x A = n A + nB
nJ
∑ Experimentally, we can measure the total volume of a mixture as a function €
of the composition. Mix nA moles of A with nB moles of B, measure the volume and divide by the total number of moles (nA + nB). This gives us v, the average molar volume of the A/B solution. Repeat this procedure for different solutions made up with different numbers of moles of A and B and we can plot v vs xA (see figure below for an arbitrary solution) v T’
H H’
P
VA T
v = f(xA) VB S’ O
0 S 1 Marand’s Notes: Chapter 5  The Properties of Simple Mixtures xA 158 We want to express the partial molar volume of A and B in terms of v and xA. First, we start with the definition of partial molar volumes: # ∂ (n + n )v
# ∂V &
A
B
VA = %
=%
(
∂n A
$ ∂n A 'P,T,nB %
$ [
&
( (
'P,T,nB # ∂[n + n ] &
# ∂v &
A
B
(
VA = (n A + nB )%
+ v%
(
% ∂n
(
∂n A 'P,T,n
$
A
$
'P,T,nB B
# ∂v &
VA = (n A + nB )%
+v
(
$ ∂n A 'P,T,nB
# ∂v &
# ∂v &
# ∂x A &
=%
%
(
(
%
(
$ ∂n A 'P,T,nB $ ∂x A 'P,T,nB $ ∂n A 'P,T,nB € The partial derivative of xA with respect to nA at constant nB is given by: # ∂x A &
(1− x A ) nB
xB
=
=
=
%
(
$ ∂n A 'P,T...
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 Spring '07
 AREsker
 Physical chemistry, pH, Chemical substance, Simple Mixtures

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