Enthalpy of sublimation of a substance is equal to :

Options

A. enthalpy of fusion `+` enthalpy of vaporisation
B. enthalpy of fusion
C. enthalpy of vaporisation
D. twice the enthalpy of vaporisation

Explanation

To determine the enthalpy of sublimation of a substance, we need to understand the process of sublimation and how it relates to other thermodynamic processes.

### Step-by-Step Solution:

1. **Define Sublimation**:
- Sublimation is the process in which a solid directly converts into a vapor without passing through the liquid phase.
- This can be represented as:
\[ \text{Solid} \rightarrow \text{Vapor} \]

2. **Identify the Steps Involved**:
- Sublimation can be broken down into two distinct steps:
- **Step 1: Fusion** (Solid to Liquid)
\[ \text{Solid} \rightarrow \text{Liquid} \]
- **Step 2: Vaporization** (Liquid to Vapor)
\[ \text{Liquid} \rightarrow \text{Vapor} \]

3. **Assign Enthalpy Changes**:
- Let’s denote the enthalpy change for the fusion process as \( \Delta H_1 \) and for the vaporization process as \( \Delta H_2 \).
- \( \Delta H_1 \) = Enthalpy of fusion
- \( \Delta H_2 \) = Enthalpy of vaporization

4. **Apply Hess's Law**:
- According to Hess's Law, the total enthalpy change for a process is the sum of the enthalpy changes for the individual steps.
- Therefore, the enthalpy of sublimation \( \Delta H \) can be expressed as:
\[ \Delta H = \Delta H_1 + \Delta H_2 \]

5. **Interpret the Result**:
- From the equation derived, we conclude that:
- The enthalpy of sublimation is equal to the sum of the enthalpy of fusion and the enthalpy of vaporization.
- Thus, we can write:
\[ \Delta H_{\text{sublimation}} = \Delta H_{\text{fusion}} + \Delta H_{\text{vaporization}} \]

6. **Select the Correct Option**:
- Based on the options provided:
- Option A: Enthalpy of fusion + Enthalpy of vaporization (Correct)
- Option B: Enthalpy of fusion (Incorrect)
- Option C: Enthalpy of vaporization (Incorrect)
- Option D: Twice the enthalpy of vaporization (Incorrect)

### Final Conclusion:
- The enthalpy of sublimation of a substance is equal to the enthalpy of fusion plus the enthalpy of vaporization.