To find the enthalpy of sublimation of iodine at 250°C, we can use the given data and the formula for the change in enthalpy based on specific heat capacities. Here’s a step-by-step breakdown of the solution:
### Step 1: Understand the Concept of Enthalpy of Sublimation
The enthalpy of sublimation is the amount of energy required to convert a substance from solid to vapor without passing through the liquid phase. For iodine, this is represented as:
\[ \text{I}_2 (s) \rightarrow \text{I}_2 (g) \]
### Step 2: Identify Given Values
- Enthalpy of sublimation at 200°C, \( \Delta H_1 = 24 \, \text{cal g}^{-1} \)
- Specific heat of solid iodine, \( C_{p(s)} = 0.055 \, \text{cal g}^{-1} \text{K}^{-1} \)
- Specific heat of iodine vapor, \( C_{p(v)} = 0.031 \, \text{cal g}^{-1} \text{K}^{-1} \)
- Initial temperature, \( T_1 = 200°C = 473 \, \text{K} \)
- Final temperature, \( T_2 = 250°C = 523 \, \text{K} \)
### Step 3: Calculate the Change in Specific Heat Capacity
The change in specific heat capacity (\( \Delta C_p \)) is calculated as:
\[
\Delta C_p = C_{p(v)} - C_{p(s)} = 0.031 - 0.055 = -0.024 \, \text{cal g}^{-1} \text{K}^{-1}
\]
### Step 4: Calculate the Change in Temperature
The change in temperature (\( \Delta T \)) is:
\[
\Delta T = T_2 - T_1 = 523 \, \text{K} - 473 \, \text{K} = 50 \, \text{K}
\]
### Step 5: Calculate the Change in Enthalpy
Using the formula for the change in enthalpy (\( \Delta H \)):
\[
\Delta H = \Delta C_p \cdot \Delta T
\]
Substituting the values:
\[
\Delta H = (-0.024 \, \text{cal g}^{-1} \text{K}^{-1}) \cdot (50 \, \text{K}) = -1.2 \, \text{cal g}^{-1}
\]
### Step 6: Calculate the New Enthalpy of Sublimation at 250°C
Now we can find the enthalpy of sublimation at 250°C (\( \Delta H_2 \)):
\[
\Delta H_2 = \Delta H_1 + \Delta H = 24 \, \text{cal g}^{-1} - 1.2 \, \text{cal g}^{-1} = 22.8 \, \text{cal g}^{-1}
\]
### Final Answer
The enthalpy of sublimation of iodine at 250°C is:
\[
\Delta H_2 = 22.8 \, \text{cal g}^{-1}
\]
