Alkaline water has a higher pH level than pure water and so is more basic. Does that make it better for your health or not? Here are a few points that might help elucidate what these "ionized" alkaline water can do to our body.
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E.g. it is perfectly fine to say hydronium/hydroxide ions have an extra/missing hydrogen atom. The term atom doesn't imply neutral, and so in chemistry a proton is still referred to as a hydrogen atom (hence why some push to call it a hydron instead of a proton... not that I've heard anyone actually use that term used outside of work with deuterated chemicals). Saying the "pH is inversely proportional to the concentration of hydronium ion" will draw ire from some math crowds as "inversely proportional" has a very meaning (1/x) that doesn't apply to pH vs OH concentration. Equal numbers of hydronium and hydroxide ions is what is called neutral as neither dominates, so effectively they do "cancel", just cancel is a horribly imprecise word (I knew several profs, especially in math, that would call out a student using the word cancel in nearly any context as it was often too vague and misleading). Since self-ionization of water depends on temperature and mass, neutral pH being 7 only happens for light water near 25 C. "they exist in a state of natural equilibrium at pH 7" seems kind of meaningless as there will be a natural equilibrium for just about any pH once reactions have settled... ad nauseum.
In general any discussion of acids and bases in popsci is going to be a minefield, as the Arrhenius definition of acids and bases is quite narrow and effectively now almost a century out of date. But it is also way more straightforward to laymen than the Brønsted–Lowry definition and effective for common situations. There are a lot of subject like this where things are left fuzzy, vague or possibly sloppy to avoid going too far down the rabbithole.
Where to draw the line with technical correctness in popsci writing is a massive source of debate among scientists trying to write for outreach. Most discussion panels I've seen on the topic breaks down into two camps: those who say, "you have to lie a little" to effectively teach intro science and those that insist you have to do a very careful dance to be technically correct while sticking to the point. (Personally, the latter approach fails once anyone edits your writing...). Regardless of approach, a lot of people who know the science are just bad at writing anyway...
_Acids release hydronium ions (basically a positively charged water molecule with an extra hydrogen atom); the lower an acid's pH, the more ions it releases. Because the pH scale is logarithmic, an acid with pH 4 produces 10 times as many hydrogen ions in water than an acid with pH 5, and 100 times more than an acid with pH 6.
Meanwhile, bases release hydroxide ions (a negatively charged water molecule with a missing hydrogen atom) when dissolved in water. Despite the fact that pure water actually contains hydronium and hydroxide ions itself, they cancel each other out. As a result, it has a perfectly neutral pH of 7._
1. Hydronium ions do not contain an extra hydrogen atom; they contain the proton from hydrogen dissociation, which is why it carries a positive charge.
2. "The lower an acid's pH, the more ions it releases" is nonsense. It should read, "pH is inversely proportional to the concentration of hydronium ions. The greater the concentration, the lower the pH".
3. Hydroxide ions are a negatively-charged water molecule missing a proton, not missing a hydrogen atom.
4. "Despite the fact that pure water actually contains hydronium and hydroxide ions itself, they cancel each other out. As a result, it has a perfectly neutral pH of 7". More nonsense. The ions do not cancel each other out; they exist in a state of natural equilibrium at pH 7, meaning that the concentration of both hydronium and hydroxide ions is 10^-7. Look at the pH chart in the link; this is exactly what it illustrates.
Anyway, most alkaline water contains alkalinity, which raises the pH. Again, from my article, "Hard water has a high pH mainly due to the presence of carbonates and phosphates (hydroxides do not occur naturally) but chlorides and sulfates also contribute when in the presence of calcium and magnesium. Depending on the vendor, supermarket alkaline water may contain hydroxides, carbonates, phosphates, and chlorides, all in varying quantity. A brand called Crazy Water is naturally occurring hard water, available in 4 degrees of hardness. Others are formulated from pure water, typically that produced by reverse osmosis, with the addition of alkaline food-grade additives.
There is also available ‘ionic’ alkaline water that contains no added chemicals such as those described previously but rather is the product of induced dissociation with stabilizers. A commercial brand available in supermarkets is “Essentia” and it boasts a pH ≥ 9.5. One can even purchase a home water ionizer but they are costly."
To the layman, the linked article is misleading and it contains technical errors. 'Nuff said.