To determine which of these equations correctly expresses the self-ionization of water, let's first understand the process itself.
The self-ionization (or autoionization) of water is the process wherein two water molecules interact to produce a hydronium ion (H[tex]\(_3\)[/tex]O[tex]\(^+\)[/tex]) and a hydroxide ion (OH[tex]\(^-\)[/tex]). The correct representation of this reaction is as follows:
[tex]\[ 2 \text{H}_2\text{O} \leftrightarrow \text{H}_3\text{O}^+ + \text{OH}^- \][/tex]
Now, let's compare each given option to this accurate equation:
1. Option 1:
[tex]\[ \text{H}_2\text{O} + \text{H}_2\text{O}^+ \leftrightarrow \text{H}_2\text{O} + \text{OH}^- \][/tex]
This equation suggests that one water molecule and a water cation (H[tex]\(_2\)[/tex]O[tex]\(^+\)[/tex]) produce a water molecule and a hydroxide ion. This configuration is incorrect because it doesn't represent the formation of both a hydronium and hydroxide ion from two water molecules.
2. Option 2:
[tex]\[ \text{H}_2\text{O} + \text{H}_2\text{O} \leftrightarrow 2 \text{OH}^- \][/tex]
This equation implies that two water molecules produce two hydroxide ions, which is incorrect because it doesn't produce a hydronium ion, which is an essential part of the self-ionization process.
3. Option 3:
[tex]\[ \text{H}_3\text{O} + \text{H}_2\text{O} \leftrightarrow 2 \text{H}_3\text{O}^\circ \][/tex]
This suggests that a hydronium ion and a water molecule produce two hydronium ions, which is incorrect because it lacks the production of a hydroxide ion.
4. Option 4:
[tex]\[ \text{H}_2\text{O} + \text{H}_2\text{O} \leftrightarrow \text{H}_1\text{O}^+ + \text{OH}^- \][/tex]
This equation indicates that two water molecules produce a hypothetical H[tex]\(_1\)[/tex]O[tex]\(^+\)[/tex] (which is not a commonly recognized species in chemistry) and a hydroxide ion. This is certainly incorrect.
Upon evaluating these options, we can see that none of them match the exact form:
[tex]\[ 2 \text{H}_2\text{O} \leftrightarrow \text{H}_3\text{O}^+ + \text{OH}^- \][/tex]
However, if we are to select the closest option based on the concept of ion production, Option 1 at least represents an ion exchange involving water and has some similarity to part of the process even though it is not perfect.
Thus, the answer would be Option 1:
[tex]\[ \boxed{H _2 O + H _2 O ^{+} \leftrightarrow H _2 O + OH ^{-}} \][/tex]
