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Mechanism of operation of the glass membrane pH electrode

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Mimic:
Given that there is no matter exchange between the membrane and the bulk, when the book (Skoog, West, Holler, Crouch - Fundamentals of Analytical Chemistry) reports the reaction

[tex] \ce{Na^+Gl^- (glass) + H^+ (solution) } \rightleftharpoons \ce{H^+Gl^- (glass) + Na^+ (solution) } [/tex]

is refers to the ion exchange that occurs between the silica gel layer that wraps the glass membrane and the bulk, in the external wall, and the internal solution, in the internal wall.

I'm right?

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