For which of the following reaction `DeltaH^(@)` vlaue is equal to the first ionization energy of Ca is?

Options

A. `Ca^(+)(g) to Ca^(2+)(g) +e`
B. `Ca(g)to Ca^(+)(g)+e`
C. `Ca(s) to Ca^(+) (g)+e`
D. `Ca(g) to Ca^(2+)(g)+2e`

Answer

To determine which reaction has a ΔH° value equal to the first ionization energy of calcium (Ca), we need to understand what the first ionization energy is. The first ionization energy is defined as the energy required to remove the outermost electron from a gaseous atom.

### Step-by-Step Solution:

1. **Define Ionization Energy**:
- The first ionization energy is the energy needed to remove one electron from a neutral gaseous atom. For calcium, this can be represented as:
\[ \text{Ca (g)} \rightarrow \text{Ca}^+ (g) + e^- \]
- Here, the ΔH° for this reaction is equal to the first ionization energy of calcium.

2. **Examine the Given Reactions**:
- We need to analyze the provided options to find which one matches the above reaction.

3. **Identify the Correct Reaction**:
- **Option 1**: Does not represent the removal of a single electron from a gaseous calcium atom.
- **Option 2**:
\[ \text{Ca (g)} \rightarrow \text{Ca}^+ (g) + e^- \]
- This matches the definition of the first ionization energy.
- **Option 3**: Involves solid calcium, which is not relevant since we need a gaseous state.
- **Option 4**: Involves removing two electrons at once, which does not correspond to the first ionization energy.

4. **Conclusion**:
- The correct reaction that corresponds to the first ionization energy of calcium is **Option 2**.

### Final Answer:
The reaction for which ΔH° value is equal to the first ionization energy of Ca is **Option 2**:
\[ \text{Ca (g)} \rightarrow \text{Ca}^+ (g) + e^- \]