Which of the following equlibria would have highest and lowest value of `K_(p)` at a commone temperature?

Options

A. `BeCO_(3) to BeO+CO_(2)`
B. `CaCO_(3) to CaO+CO_(2)`
C. `SrCO_(3) to SrO+CO_(2)`
D. `BaCO_(3) to BaO+CO_(2)`

Answer

To determine which of the given equilibria has the highest and lowest value of \( K_p \) at a common temperature, we need to analyze the stability of the carbonates of alkaline earth metals involved in the reactions. The reactions given are:

1. Beryllium carbonate (\( BeCO_3 \)) decomposing to beryllium oxide (\( BeO \)) and carbon dioxide (\( CO_2 \)).
2. Calcium carbonate (\( CaCO_3 \)) decomposing to calcium oxide (\( CaO \)) and carbon dioxide (\( CO_2 \)).
3. Strontium carbonate (\( SrCO_3 \)) decomposing to strontium oxide (\( SrO \)) and carbon dioxide (\( CO_2 \)).
4. Barium carbonate (\( BaCO_3 \)) decomposing to barium oxide (\( BaO \)) and carbon dioxide (\( CO_2 \)).

### Step 1: Understand Stability of Carbonates
The stability of alkaline earth metal carbonates (\( MCO_3 \)) increases down the group in the periodic table. This means that:

- \( BeCO_3 \) is the least stable.
- \( BaCO_3 \) is the most stable.

### Step 2: Relate Stability to \( K_p \)
The equilibrium constant \( K_p \) is inversely related to the stability of the compound. This means:

- The less stable the compound, the higher the value of \( K_p \) because it decomposes more readily.
- The more stable the compound, the lower the value of \( K_p \) because it does not decompose easily.

### Step 3: Analyze Each Compound
- **Beryllium Carbonate (\( BeCO_3 \))**: Least stable → Highest \( K_p \)
- **Calcium Carbonate (\( CaCO_3 \))**: More stable than \( BeCO_3 \) → Lower \( K_p \) than \( BeCO_3 \)
- **Strontium Carbonate (\( SrCO_3 \))**: More stable than \( CaCO_3 \) → Lower \( K_p \) than \( CaCO_3 \)
- **Barium Carbonate (\( BaCO_3 \))**: Most stable → Lowest \( K_p \)

### Conclusion
From the analysis:
- **Highest \( K_p \)**: Beryllium carbonate (\( BeCO_3 \))
- **Lowest \( K_p \)**: Barium carbonate (\( BaCO_3 \))

### Final Answer
- Highest \( K_p \): Beryllium carbonate (\( BeCO_3 \))
- Lowest \( K_p \): Barium carbonate (\( BaCO_3 \))

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