To determine which compounds form a conjugate acid-base pair, we need to understand the concept of conjugate acids and bases. A conjugate acid-base pair consists of two species that differ by a single proton ([tex]\(\text{H}^+\)[/tex]). One species can be transformed into the other by the gain or loss of one proton.
Let's analyze each option provided:
Option A: [tex]\(H_2PO_4^-\)[/tex] and [tex]\(HPO_4^{2-}\)[/tex]
Here, we can observe that:
- [tex]\(H_2PO_4^-\)[/tex] (dihydrogen phosphate) can lose one proton to become [tex]\(HPO_4^{2-}\)[/tex] (hydrogen phosphate).
[tex]\[
H_2PO_4^- \rightarrow H^+ + HPO_4^{2-}
\][/tex]
They differ by a single proton.
Option B: [tex]\(H_3PO_4\)[/tex] and [tex]\(HPO_4^{2-}\)[/tex]
Here, we can see that:
- [tex]\(H_3PO_4\)[/tex] (phosphoric acid) can lose two protons to become [tex]\(HPO_4^{2-}\)[/tex] (hydrogen phosphate), as shown in the following steps:
[tex]\[
H_3PO_4 \rightarrow H^+ + H_2PO_4^- \rightarrow 2H^+ + HPO_4^{2-}
\][/tex]
They differ by two protons, not one.
Option C: [tex]\(H_2PO_4^-\)[/tex] and [tex]\(PO_4^{3-}\)[/tex]
In this case:
- [tex]\(H_2PO_4^-\)[/tex] (dihydrogen phosphate) can lose two protons to become [tex]\(PO_4^{3-}\)[/tex] (phosphate), as shown in the following steps:
[tex]\[
H_2PO_4^- \rightarrow H^+ + HPO_4^{2-} \rightarrow 2H^+ + PO_4^{3-}
\][/tex]
They differ by two protons, not one.
Option D: [tex]\(H_3PO_4\)[/tex] and [tex]\(PO_4^{3-}\)[/tex]
For this pair:
- [tex]\(H_3PO_4\)[/tex] (phosphoric acid) can lose three protons to become [tex]\(PO_4^{3-}\)[/tex] (phosphate), as shown in the following steps:
[tex]\[
H_3PO_4 \rightarrow H^+ + H_2PO_4^- \rightarrow 2H^+ + HPO_4^{2-} \rightarrow 3H^+ + PO_4^{3-}
\][/tex]
They differ by three protons, not one.
From the analysis, we see that only Option A [tex]\(H_2PO_4^-\)[/tex] and [tex]\(HPO_4^{2-}\)[/tex] are indeed a conjugate acid-base pair since they differ by one proton.
Therefore, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
Option A: [tex]\(H_2PO_4^-\)[/tex] and [tex]\(HPO_4^{2-}\)[/tex].
