One of the following species acts as both Bronsted acid and base

Options

A. ` H_2PO_2^(-)`
B. ` HPO_3^(2-) `
C. ` HPO_4^(2-)`
D. all of these

Explanation

To determine which species among the given options acts as both a Bronsted acid and a Bronsted base, we will analyze each option based on the definitions of Bronsted acids and bases.

### Step-by-Step Solution:

1. **Understanding Bronsted Acid and Base**:
- A Bronsted acid is a substance that donates a proton (H⁺ ion).
- A Bronsted base is a substance that accepts a proton (H⁺ ion).

2. **Analyzing Option 1: H₂PO₂⁻**:
- H₂PO₂⁻ is the conjugate base of H₃PO₂ (phosphorous acid).
- H₃PO₂ can donate one H⁺ ion, making it a monobasic acid.
- H₂PO₂⁻ cannot donate another H⁺ ion, so it cannot act as a Bronsted acid.
- Therefore, H₂PO₂⁻ is **not** both a Bronsted acid and base.

3. **Analyzing Option 2: HPO₃²⁻**:
- HPO₃²⁻ is the conjugate base of H₂PO₃⁻ (phosphorous acid).
- H₃PO₃ can donate two H⁺ ions, making it a dibasic acid.
- HPO₃²⁻ cannot donate another H⁺ ion, so it cannot act as a Bronsted acid.
- Therefore, HPO₃²⁻ is **not** both a Bronsted acid and base.

4. **Analyzing Option 3: HPO₄²⁻**:
- HPO₄²⁻ is derived from H₂PO₄⁻, which in turn is derived from H₃PO₄ (phosphoric acid).
- H₃PO₄ can donate three H⁺ ions, making it a tribasic acid.
- HPO₄²⁻ can donate one H⁺ ion to form PO₄³⁻, acting as a Bronsted acid.
- HPO₄²⁻ can also accept a proton to form H₂PO₄⁻, acting as a Bronsted base.
- Therefore, HPO₄²⁻ **is** both a Bronsted acid and base.

5. **Analyzing Option 4: All of These**:
- Since only HPO₄²⁻ acts as both a Bronsted acid and base, this option is incorrect.

### Conclusion:
The species that acts as both a Bronsted acid and base is **HPO₄²⁻** (Option 3).