Properties of solutions

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G M Madhu Department of Chemical Engineering R
V College of Engineering, Bangalore
Session-15
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Properties of solutions
The relationships for pure component are not
applicable to solutions. Which needs
modification because of the change in
thermodynamic properties of solution. The
pressure temperature and amount of various
constituents determines an extensive state. The
pressure, temperature and composition determine
intensive state of a system.
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Partial Molar properties
The properties of a solution are not additive
properties, it means volume of solution is not
the sum of pure components volume.
When a substance becomes a part of a solution it
looses its identity but it still contributes to
the property of the solution.
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The term partial molar property is used to
designate the component property when it is
admixture with one or more component solution.

• A mole of component i is a particular solution
  at specified temperature and pressure has got a
  set of properties associated with it like.

These properties are partially responsible for
the properties of solution and it is known as
partial molar property
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It is defined as
Partial molar property of component i.
M Any thermodynamic property of the solution n
Total number moles in a solution niNumber of
moles of component i in the solution
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• The above expression is applicable only for an
  extensive property  

We can write
xi Mole fraction of component i in the solution.
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Physical Significance of Partial Molar Properties
To understand the meaning of physical molar
properties consider a open beaker containing huge
volume of water, if one mole of water is added to
it, the volume increase is 18x 10-6m3 If the same
amount of water is added to pure ethanol the
volume increased is approximately 14 x 10-6m3
this is the partial molar volume of H2O in pure
ethanol.
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• Therefore Partial molar property change with
  composition. The intermolecular forces also
  changes with change in thermodynamic property.

Partial molar volume of the water in ethanol
water solution
Molar volume of pure water at same temperature
and pressure
Total volume of solution when water added to
ethanol water mixture and allowed for sufficient
time so that the temperature remains constant
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property of solution for all infinitely small
amount of water.
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• Temperature, pressure an number of moles of
  ethanol remains constant during addition of
  water.

nE- no of moles of ethanol
The partial molar volume of component i
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Partial molar properties and properties of the
solution
Let total property of the solution
1,2,3 represents number of constituents Thermodyn
amic property is a
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• For small change in the pressure and temperature
  and amount of various constituents can be
  written as

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At constant temperature and pressure dP and dT
are equal to zero.
The above equation reduces to  
dMt in terms of partial molar property
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is an extensive property depends on
composition and relative amount of constituents.
All constituent properties at constant
temperature and pressure are added to give the
property of the solution
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• Problem
• A 30 mole by methanol water solution is to be
  prepared. How many m3 of pure methanol (molar
  volume 40.7x10-3m3/mol) and pure water (molar
  volume 18.068x10-6m3/mol) are to be mixed to
  prepare 2m3 of desired solution. The partial
  molar volume of methanol and water in 30
  solution are 38.36x10-6 m3/mol and 17.765x10-6
  m3/mol respectively.

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Methanol 0.3 mole fraction Water0.7 mole
fraction  
Vt0.3 x38.36x10-60.7x17.765x10-6
24.025x10-6 m3/mol
For 2 m3 solution
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• Number of moles of methanol in 2m3solution
•  83.246x103x0.3 24.97x103mol

Number of moles of water in 2m3solution  83.246x1
03x07 58.272x103mol  
Volume of pure methanol to be taken 24.97x103 x
40.7x10-3 1.0717 m3  
Volume of pure water to be taken 58.272x103 x
18.068x10-6 1.0529 m3
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Estimation of Partial molar properties for a
binary mixture
Two methods for estimation  Analytical Method and
Graphical Method(Tangent Intercept method)  
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Analytical Method

• The general relation between partial molar
  property and molar property of the solution is
  given by

For binary mixture
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At constant Temperature and pressure
, ,
--(a)
---(b)
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Tangent -Intercept method

• If the partial molar property (M) is plotted
  against the composition we get the curve as shown
  in the figure.

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The intercept of the tangent with two axis x11
and x10 are I1 and I2.
Slope of the tangent
Comparing I2 with equation (b)  
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Comparing with equation(a)
The intercept of the tangent gives the partial
molar properties
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• Limiting cases For infinite dilution of
  component

when a tangent is drawn at x10, will give the
partial molar property of component 1 at
infinite dilution
Tangent is drawn at x20 or x11 will give
infinite dilution the partial molar property of
component 2
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Problem Find weather the equation given below is
thermodynamically consistent
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G D equation
  It satisfies the GD equation, the above
equation is consistent.