Surface Tension of Solutions

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Surface Tension of Solutions

• Capillary Rise Method

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Surface Tension

• Molecules at surface are in an asymmetrical
  environment
• No intermolecular forces above the surface to
  balance those below
• Attractive intermolecular forces pull
  molecules to interior
• Work must be done to increase the surface area

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The mechanical work needed to increase the area
of a film may be equated to the Gibbs free
energy dG ?dA Where ? is the
surface tension, and therefore
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Separate the free energy into bulk and surface
terms GT Gono GSA GT total free energy
G0 molal free energy GS surface free
energy no - moles of liquid A
surface area Any heat associated with the
expansion of the film is dqrev T dSS
TSSdA Where SS is the surface entropy/area.
This leads to the temperature dependence of the
surface tension
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Effect of Composition on ?
At equilibrium the Gibbs-Duhem equation is
applicable for both bulk and surface phases n1
dµ1 n2 dµ2 0 n1 dµ1 n2 dµ2 A d?
0 ni moles of component i primes refer
to surface phase At equilibrium the µ for each
component must be the same in both phases
µ1 µ1 dµ1 dµ1
µ2 µ2 dµ2 dµ2
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Thus n1 dµ1 n2 dµ2 A d?
0 and with appropriate substitution n1(n2/
n1) dµ1 n2 dµ2 A d? 0 And
RHS number of moles of component 2 in excess in
the surface phase compared to the bulk. This
excess amount may be regarded as the amount
absorbed in the surface phase, G2.
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The chemical potential,at constant temperature,
is related to the activity µ2 µeo RT ln a2
dµ2 RT dln a2 Thus
Define G2 as the excess amount/unit surface area
of component 2 in the surface phase over the bulk.
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Thus G2
G2/A And

In dilute solutions a2 C2 So
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Electrolytes usually increase the surface tension
because of Coulombic attraction that draws the
ions together and away from the surface. In
dilute solution ? increases linearly with
concentration. model assumes a ionic
concentration of zero at the surface which
increases linearly until it reaches a distance,
xo, where bulk concentration, Co, is equaled.
This length is xo - G2/Co Taking the activity
to be equal to the concentration, the equation
for the length becomes - G2/2C for a 11
electrolyte with bulk concentration C. The
factor of two accounts for the fact that there
are two moles of particles produced in solution
for every one mole of NaCl.
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Capillary Rise Method
For a liquid that adheres to glass, the energy is
lowest when a thin film covers as much glass as
possible. This leads to curvature of the liquid
inside. Curvature means pressure beneath the
meniscus is less than atmospheric pressure by
about 2?/r where r is the radius of the tube.
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Pressure exerted by the liquid column of height,
h p ?gh 2?/r
Thus
Or
And for the case of a contact angle, ?
The amount of liquid above the meniscus can be
corrected for
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The contact angle arises from a balance of forces
at the line of contact between the liquid and the
solid. ?sg ?sl ?lg cos ? And so
Liquid wets the surface if 0 lt ?c lt 90o and
beads up if ?c 180o
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Procedure

• A clean capillary is essential to the success of
  the experiment. It kept in distilled water.
• Cleaning can be effected by soaking in hot nitric
  acid for several minutes and then thoroughly
  washing with distilled water.
• The apparatus should be assembled according to
  the following figure

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• Obtain the radius of the capillary by calibration
  with pure water.
• Calculate r from known surface tension
• Or use the equation
• h is the height of the column of liquid in the
  capillary, and ? is the density of the liquid.
  The reference liquid is designated by ref.

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• Measure the capillary rise. Assume a zero
  contact angle.
• Take at least four readings, alternately allowing
  meniscus to approach the final position from
  above and below.
• Be sure you have measured relative to the outside
  level.
• If agreement is poor, clean the apparatus and
  repeat the experiment.
• Repeat measurements using 0.8 M n-butanol
  solution.

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• Dilute to ¾ with distilled water and repeat.
• Continue ¾ dilutions until you have made eight
  sets of measurments. Your last concentration
  should be 0.11 M.
• Rinse the apparatus and capillary with fresh
  solution before beginning each new dilution
  measurement.
• Repeat the experiments with NaCl solutions of
  approximately 4, 3, 2 and 1 M.
• Thoroughly clean capillary and store under
  distilled water.

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Data Analysis

• There are several sources of error
• Major difficulty is absorption of surface active
  substances ( e.g. oil from skin ).
• A 1 Co change in temperature will alter the value
  of ? by about 0.5
• Capillary radius may not be uniform along its
  length and would be about 3 for an uncalibrated
  tube.

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• Calculate capillary radius or calibration factor.
  If calculating r then use the equation that
  accounts for the amount of liquid above the
  meniscus.
• Butanol solutions may be assumed to have the same
  density as water but the salt solutions densities
  should use Table XI-1.
• Plot ? of the solution(s) vs. log C and find
  slope.
• Calculate the surface concentration.
• Calculate the effective cross-sectional area of
  the molecule.

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• For the NaCl solutions plot ? vs. the bulk
  concentration in mol/cm3. The slope will give
  the value of G2/2C.
• Then calculate the empty layer thickness, x o.

Note on cathetometer