Enthalpy of sublimation of iodine is `"24 cal g"^(-1)" at " 200^(@)C`. If specific heat of `l_(2)(s) and l_(2)` (vap) are 0.055 and 0.031 respectively, then enthalpy of sublimation of iodine at `250^(@)C` in `"cal g"^(-1)` is:

Options

A. 5.7
B. 22.8
C. 11.4
D. 2.85

Explanation

To determine the enthalpy of sublimation of iodine at 250°C, we can use the concept of heat capacity and the relationship between temperature and enthalpy. The enthalpy of sublimation at a given temperature can be adjusted from a known value at a different temperature using the specific heat capacities of the solid and gaseous states.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Enthalpy of sublimation at 200°C, \( \Delta H_{sub} (200°C) = 24 \, \text{cal/g} \)
- Specific heat of solid iodine, \( C_{p(s)} = 0.055 \, \text{cal/g°C} \)
- Specific heat of gaseous iodine, \( C_{p(g)} = 0.031 \, \text{cal/g°C} \)
- Temperature change, \( \Delta T = 250°C - 200°C = 50°C \)

2. **Calculate the Heat Required to Raise the Temperature of Solid Iodine:**
- The heat required to raise the temperature of solid iodine from 200°C to 250°C is calculated using the formula:
\[ q_{solid} = m \cdot C_{p(s)} \cdot \Delta T \]
- Since we are interested in per gram, we can set \( m = 1 \, \text{g} \):
\[ q_{solid} = 1 \cdot 0.055 \cdot 50 = 2.75 \, \text{cal} \]

3. **Calculate the Heat Required to Raise the Temperature of Gaseous Iodine:**
- The heat required to raise the temperature of gaseous iodine from 200°C to 250°C is calculated similarly:
\[ q_{gas} = m \cdot C_{p(g)} \cdot \Delta T \]
- Again, setting \( m = 1 \, \text{g} \):
\[ q_{gas} = 1 \cdot 0.031 \cdot 50 = 1.55 \, \text{cal} \]

4. **Adjust the Enthalpy of Sublimation:**
- The total enthalpy of sublimation at 250°C can be calculated by adding the heat required to raise the temperature of the solid and subtracting the heat required to raise the temperature of the gas from the initial enthalpy:
\[ \Delta H_{sub} (250°C) = \Delta H_{sub} (200°C) + q_{solid} - q_{gas} \]
\[ \Delta H_{sub} (250°C) = 24 + 2.75 - 1.55 = 25.20 \, \text{cal/g} \]

### Final Answer:
The enthalpy of sublimation of iodine at 250°C is \( \Delta H_{sub} (250°C) = 25.20 \, \text{cal/g} \).