The correct order of increasing thermal stability of the given compound is
I. HF
II. HBr
III. HCl
IV. HI

Options

A. `I lt II lt III lt IV`
B. `IV lt II lt III lt I`
C. `IV lt II lt I lt III`
D. `II lt IV lt I lt III`

Answer

To determine the increasing order of thermal stability of the given compounds (HF, HCl, HBr, HI), we need to analyze the bond strengths of these hydrogen halides.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds we are considering are:
- HF (Hydrogen Fluoride)
- HCl (Hydrogen Chloride)
- HBr (Hydrogen Bromide)
- HI (Hydrogen Iodide)

2. **Understand Bond Strength**: The thermal stability of these compounds is related to the strength of the H-X bond (where X is the halogen). As we move down the group in the periodic table from fluorine to iodine, the size of the halogen increases, which affects the bond strength.

3. **Analyze Bond Strength Trend**:
- HF has a very strong bond due to the small size of fluorine, leading to high thermal stability.
- HCl has a weaker bond than HF but is still relatively strong.
- HBr has an even weaker bond than HCl.
- HI has the weakest bond due to the large size of iodine, resulting in the lowest thermal stability.

4. **Order of Thermal Stability**: Based on the bond strengths, we can arrange the compounds in order of increasing thermal stability:
- HI (weakest bond, least stable)
- HBr
- HCl
- HF (strongest bond, most stable)

5. **Final Order**: Therefore, the correct order of increasing thermal stability is:
- HI < HBr < HCl < HF

### Conclusion:
The increasing order of thermal stability of the given compounds is:
**HI < HBr < HCl < HF**