To determine which pair represents an acid-conjugate base pair in the given reaction:
[tex]\[
HI + H_2O \rightarrow H_3O^+ + I^-
\][/tex]
we will analyze the species involved:
1. Identify the roles:
- [tex]\( HI \)[/tex] donates a proton ([tex]\( H^+ \)[/tex]) and becomes [tex]\( I^- \)[/tex].
- [tex]\( H_2O \)[/tex] accepts a proton ([tex]\( H^+ \)[/tex]) and becomes [tex]\( H_3O^+ \)[/tex].
2. Definition check:
- An acid is a species that donates a proton ([tex]\( H^+ \)[/tex]).
- A conjugate base is the species that remains after the acid has donated a proton.
- Therefore, an acid and its conjugate base are related to each other by the loss of a single proton.
3. Identify pairs:
- [tex]\( HI \)[/tex] is an acid since it donates a proton to form [tex]\( I^- \)[/tex]. Therefore, [tex]\( HI \)[/tex] and [tex]\( I^- \)[/tex] form an acid-conjugate base pair.
- [tex]\( H_2O \)[/tex] accepts a proton to become [tex]\( H_3O^+ \)[/tex]. So, [tex]\( H_2O \)[/tex] and [tex]\( H_3O^+ \)[/tex] also form an acid-conjugate base pair.
Now, we carefully match these identified pairs with the given options:
1. [tex]\( HI \)[/tex] and [tex]\( H_2O \)[/tex]
- This is not an acid-conjugate base pair.
2. [tex]\( H_2O \)[/tex] and [tex]\( H_3O^+ \)[/tex]
- This is a correct acid-conjugate base pair.
3. [tex]\( H_3O^+ \)[/tex] and [tex]\( I^- \)[/tex]
- These do not form an acid-conjugate base pair.
4. [tex]\( HI \)[/tex] and [tex]\( I^- \)[/tex]
- This is a correct acid-conjugate base pair.
Among the options, we are looking for the pair involving [tex]\( HI \)[/tex] and [tex]\( I^- \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{HI \text{ and } I^{-}}
\][/tex]
