Consider the followng changes:
`M(s) to M(g)` . . . (1)
`M(s) to M^(2+)(g) +2e^(-)` . . . (2)
`M(g)to M^(+)(g)+e^(-)` . . . (3)
`M^(+)(g) to M^(2+)(g)+e^(-)` . . (4)
`M(g) to M^(2+)(g)+2e^(-)` . . . (5)
The second ionization energy of M could be calculated from the enrg values associated with:

Options

A. 1+3+4
B. 2-1+3
C. 1+5
D. `5-3`

Explanation

To determine the second ionization energy of M, we need to analyze the provided changes and identify the correct equations that relate to the ionization process.

### Step-by-Step Solution:

1. **Identify the Ionization Energy**:
The first ionization energy (IE1) is the energy required to remove one electron from a neutral atom (M) to form a cation (M⁺). The second ionization energy (IE2) is the energy required to remove an electron from the cation (M⁺) to form a doubly charged cation (M²⁺).

2. **Write the Relevant Equations**:
- The first ionization can be represented as:
\[ M(g) \rightarrow M^+(g) + e^- \]
This corresponds to equation (3).
- The second ionization can be represented as:
\[ M^+(g) \rightarrow M^{2+}(g) + e^- \]
This corresponds to equation (4).

3. **Combine the Equations**:
To find the second ionization energy, we need to combine the equations in such a way that we can derive the second ionization process from the first ionization process.

4. **Use Equation (5)**:
The equation (5) is:
\[ M(g) \rightarrow M^{2+}(g) + 2e^- \]
This represents the process of removing two electrons from the neutral atom directly.

5. **Subtract Equation (3) from Equation (5)**:
We can rearrange equation (3) to represent the reverse process:
\[ M^+(g) + e^- \rightarrow M(g) \]
Now, if we subtract equation (3) from equation (5), we can eliminate the electron terms:
\[ (M(g) \rightarrow M^{2+}(g) + 2e^-) - (M^+(g) + e^- \rightarrow M(g)) \]
This results in:
\[ M^+(g) \rightarrow M^{2+}(g) + e^- \]
This is exactly the equation for the second ionization energy (IE2).

6. **Conclusion**:
Therefore, the second ionization energy of M can be calculated using the energy values associated with equations (3) and (5).

### Final Answer:
The second ionization energy of M could be calculated from the energy values associated with equation (4) (M⁺ to M²⁺ + e⁻) derived from subtracting equation (3) from equation (5).

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