All the following substances react with water. The pair that gives the same gaseous product is

Options

A. `K and CO_3`
B. `Na and Na_2O_2`
C. `Ca and CaH_2`
D. `Ba and BaO_2`

Explanation

To solve the problem of identifying the pair of substances that react with water to give the same gaseous product, we will analyze each option step by step.

### Step 1: Analyze Potassium (K)
- **Reaction with Water**:
\[ 2K + 2H_2O \rightarrow 2KOH + H_2 \]
- **Gaseous Product**: Hydrogen gas (H₂)

### Step 2: Analyze Sodium (Na)
- **Reaction with Water**:
\[ 2Na + 2H_2O \rightarrow 2NaOH + H_2 \]
- **Gaseous Product**: Hydrogen gas (H₂)

### Step 3: Analyze Calcium (Ca)
- **Reaction with Water**:
\[ Ca + 2H_2O \rightarrow Ca(OH)_2 + H_2 \]
- **Gaseous Product**: Hydrogen gas (H₂)

### Step 4: Analyze Barium (Ba)
- **Reaction with Water**:
\[ Ba + 2H_2O \rightarrow Ba(OH)_2 + H_2 \]
- **Gaseous Product**: Hydrogen gas (H₂)

### Step 5: Analyze Sodium Peroxide (Na₂O₂)
- **Reaction with Water**:
\[ Na_2O_2 + 2H_2O \rightarrow 2NaOH + H_2O_2 \]
- **Gaseous Product**: Oxygen gas (O₂)

### Step 6: Analyze Barium Oxide (BaO₂)
- **Reaction with Water**:
\[ BaO_2 + 2H_2O \rightarrow Ba(OH)_2 + O_2 \]
- **Gaseous Product**: Oxygen gas (O₂)

### Conclusion
From the analysis, we find that:
- Potassium, Sodium, Calcium, and Barium all produce hydrogen gas (H₂) when they react with water.
- Sodium Peroxide and Barium Oxide produce oxygen gas (O₂) when they react with water.

Thus, the pair that gives the same gaseous product is **Potassium (K) and Sodium (Na)**, as both produce hydrogen gas (H₂).

### Final Answer
The pair that gives the same gaseous product is **Potassium (K) and Sodium (Na)**.

---