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In adsorption, the concentration of adsorbate is greater on the surface. So, how is it possible that the solvent will be more on the surface and the solute (adsorbate) in the bulk… or does solute not always mean adsorbate?

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Solute does not mean adsorbate always.An Adsorbate is a substance that is adsorbed on a surface of another substance. In a dilute solution, negative adsorption occurs as solvent is adsorbed by the adsorbent and not solute. In positive adsorption, solute is adsorbed.

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Per a source:

If the concentration of the adsorbate is less than its concentration in the bulk then it is called negative adsorption. Example: When a dilute solution of KCl is shaken with blood charcoal, it shows negative adsorption.

The reference link also provides an educational video discussing also positive adsorption and related topics.

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