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What textbook states about the formation of electric double layer:

When silver nitrate solution is added to potassium iodide solution the precipitated silver iodide adsorbs iodide ion from dispersion medium and negatively charged colloidal solution results. Having acquired a negative charge by selective adsorption on the surface of colloidal particles, this layer attracts counterion from the medium forming second layer. The combination of these two layers of opposite charge is called Helmholtz electrical double layer. The first layer of ions is firmly held and termed as fixed layer while second layer is mobile and termed as diffused layer.
Reference : chapter 5; page :141 http://ncertbooks.prashanthellina.com/class_12.Chemistry.ChemistryI/index.html

What I understand about electrical double layer by browsing various internet sources is:

An electric double layer consists:

  • Surface charge: charged ions adsorbed on the surface of the colloidal particles or intrinsic surface charge or through loss or gain of electrons as in case of electrodes.

  • Stern layer (fixed layer): counterion attracted to particle surface and closely attached to it by electrostatic forces.

  • Diffusion layer: a film of dispersions medium adjacent to the particle containing higher concentration of counterion due to the residual electrostatic forces from the charged colloidal particles.

Is my understanding correct? Does the textbook statement means something more or do I miss something? I like to have a almost clarified understanding about the electric double layer.

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    $\begingroup$ Please add a citation to the quote you are using. $\endgroup$ – Martin - マーチン Jan 27 at 8:48
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    $\begingroup$ NCERT textbook really is no proper citation; there should be an author (or editor), a title, a publisher, a year, an edition, and the chapter/page where the quote can be found on. This is to help identify which actual book we are talking about, and to see if changes to future editions make this question be perceived differently. $\endgroup$ – Martin - マーチン Jan 27 at 11:34
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If you are confused about the electrical double layer, it is completely fine because electrochemists spent several decades to understand it and yet the concept remains "grey" in the minds of most electrochemists. You will find different stories and versions on the web and of course different terminologies.

Your understanding is correct but I will call the surface charge not only due to permanently adsorbed ions but actually there are negatively or positively charged functional groups of the molecules making up the the material. For example, if we have a polystyrene bead, we sulfonate it to $covalently$ attach $\ce{-SO3H^-}$ groups. In that case, one should say the surface charge of the beads is negative. Surface charge is related to the zeta potential (an experimentally measurable quantity). The sign of the zeta potential tells us the sign of the surface charge. If we measure the zeta potential of the colloids particles, say, sulfonate polystrene, we see a negative zeta potential in water.

This diagram is basically a depiction of your explanation and a minor correction of surface charge.

enter image description here

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Your second and third explanation are good and not basically different from one another. On the other end the first sentence is not as good, as there is no gain or loss of electrons in or through the double layer.

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    $\begingroup$ Does that mean text explanation is not so correct. $\endgroup$ – Grace Jan 19 at 14:04

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