To identify the correct conjugate relationships in the given chemical entities, let's break it down step-by-step:
1. Understand the conjugate relationships:
- A conjugate acid is formed when a base gains a proton (H⁺).
- A conjugate base is formed when an acid loses a proton.
2. Identify the species in question:
- [tex]\(H₂PO₄^{-}\)[/tex]: Dihydrogen phosphate ion
- [tex]\(HPO₄^{2-}\)[/tex]: Hydrogen phosphate ion
- [tex]\(PO₄^{3-}\)[/tex]: Phosphate ion
3. Determine the conjugate relationships:
- When [tex]\(H₂PO₄^{-}\)[/tex] loses a proton (H⁺), it forms [tex]\(HPO₄^{2-}\)[/tex]. This means [tex]\(HPO₄^{2-}\)[/tex] is the conjugate base of [tex]\(H₂PO₄^{-}\)[/tex].
- Conversely, if [tex]\(HPO₄^{2-}\)[/tex] gains a proton (H⁺), it forms [tex]\(H₂PO₄^{-}\)[/tex]. This confirms that [tex]\(HPO₄^{2-}\)[/tex] is the conjugate base of [tex]\(H₂PO₄^{-}\)[/tex].
- When [tex]\(HPO₄^{2-}\)[/tex] loses a proton (H⁺), it forms [tex]\(PO₄^{3-}\)[/tex]. This means [tex]\(PO₄^{3-}\)[/tex] is the conjugate base of [tex]\(HPO₄^{2-}\)[/tex].
- Conversely, if [tex]\(PO₄^{3-}\)[/tex] gains a proton (H⁺), it forms [tex]\(HPO₄^{2-}\)[/tex]. This confirms that [tex]\(HPO₄^{2-}\)[/tex] is the conjugate acid of [tex]\(PO₄^{3-}\)[/tex].
4. Conclusion:
- [tex]\(HPO₄^{2-}\)[/tex] acts as:
- The conjugate base of [tex]\(H₂PO₄^{-}\)[/tex] (since it results from loss of a proton by [tex]\(H₂PO₄^{-}\)[/tex])
- The conjugate acid of [tex]\(PO₄^{3-}\)[/tex] (since it results from gain of a proton by [tex]\(PO₄^{3-}\)[/tex])
So, the correct answer is:
[tex]\(HPO₄^{2-}\)[/tex] is the conjugate base of [tex]\(H₂PO₄^{-}\)[/tex] and the conjugate acid of [tex]\(PO₄^{3-}\)[/tex].
