36.2.1 |
Gibb’s Adsorption Isotherm (contd..)
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When solution is very dilute, the activity a2 of solute could be replaced by its concentration.
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or, in general for any solute and liquid adsorbent, |
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In the above equation  is essentially surface energy per unit area, which may easily be replaced by surface tension (force/length).
The application of the above equation is as follows. If the detergent (solute or adsorbate) tends to accumulate at the interface its surface excess is positive, and so  is negative. This means surface tension decreases when a solute accumulates at the surface.
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Example 36.1: The surface tensions of the dilute solutions of phenol in water at  are the following: |
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| Mass % phenol |
0.024 |
0.05 |
0.125 |
0.25 |
0.40 |
| x 10 3/(Nm -1) |
72.7 |
72.2 |
71.3 |
70.3 |
69.3 |
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Calculate surface excess concentration ( Г ) at a concentration of 0.15 mass of phenol. Comment on the significance of the observed value of Г. |
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Solution : A plot of us mole of phenol gives a curvature with negative slope for 0.15 mol of phenol slope is  , putting values in equation, |
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Fig 36.2 Surface tension of phenol vs mass %. |
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We get, 
= 5.45 x 10-4 mol m-2
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The positive value of
 signifies that phenol is surface active and accumulates at the interface. |
