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It depends on the molecule of course.

some molecules have a soft hydroxide group, that is a OH sticking out somewhere that isn't all that closely held. Increasing the pH in the environment of such a molecule can result in a free hydrogen ion latching onto the hydroxide group and forming a water molecule - in effect removing the hydroxide group from the molecule. This is a process known as dehydration - the removal of water. Dehydration is both an important and detrimental process in making Urea, a nitrogen rich fertilizer.

Some slightly complex molecules we 'bend into a new shape' in the presence/absence of hydrogen ion. The electro-presence of hydrogen ions affecting the arrangement of certain hydrogen bonds with in the molecule. This is the case with some pH indicators. This bending and refolding can occur countless times as there is no net change to the molecule.

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