The hydronium ion is a key species in many acid-base reactions and is essential for the characterization of acidic solutions in chemistry. Let's go through the given answer choices to identify the correct formula for the hydronium ion:
1. [tex]$NH_4^+$[/tex]: This is the ammonium ion, which forms from the protonation of ammonia ([tex]$NH_3$[/tex]). It does not represent the hydronium ion.
2. [tex]$OH^-$[/tex]: This is the hydroxide ion, commonly associated with basic or alkaline solutions. It is not the hydronium ion.
3. [tex]$H_2O$[/tex]: This is water, a neutral molecule that can act as both an acid and a base in various reactions. However, it is not the hydronium ion either.
4. [tex]$H_3O^+$[/tex]: This is indeed the formula for the hydronium ion. It forms when a water molecule ([tex]$H_2O$[/tex]) gains an additional hydrogen ion ([tex]$H^+$[/tex]), resulting in the [tex]$H_3O^+$[/tex] species. This ion is prevalent in acidic solutions and plays a crucial role in the definition and measurement of pH.
Therefore, the correct formula for the hydronium ion is [tex]$H_3O^+$[/tex]. Hence, the correct choice is:
[tex]$H_3O^+$[/tex]
