`M_((g)) rarr M_((g))^(+) +e^(-), DeltaH = 100eV`
`M_((g)) rarr M_((g))^(2+) +2e^(-), DeltaH = 250 eV` which is incorrect statement?

Options

A. `I_(1)` of `M_((g))` is `100eV`
B. `I_(1)` of `M_((g))^(+)` is `150eV`
C. `I_(2)` of `M_((g))` is `250eV`
D. `I_(2)` of `M_((g))` is `150eV`

Answer

To determine which statement is incorrect based on the given ionization energies, we can analyze the provided equations step by step.

### Step 1: Understand the Ionization Energies
We have two ionization equations:
1. \( M_{(g)} \rightarrow M_{(g)}^{+} + e^{-}, \Delta H = 100 \, \text{eV} \) (First ionization energy)
2. \( M_{(g)} \rightarrow M_{(g)}^{2+} + 2e^{-}, \Delta H = 250 \, \text{eV} \) (Second ionization energy)

### Step 2: Identify the Ionization Energies
- The first ionization energy (IE1) is the energy required to remove one electron from a neutral atom in the gas phase, which is given as 100 eV.
- The second ionization energy (IE2) is the energy required to remove a second electron from the singly charged ion \( M^{+} \), which is given as 250 eV.

### Step 3: Calculate the Energy for the Second Ionization
To find the energy required to remove the second electron (IE2) from the neutral atom, we can use the relationship:
\[ \text{IE2} = \text{IE1} + \text{Energy to remove the second electron from } M^{+} \]
From the equations, we can see that:
\[ \text{Energy to remove the second electron from } M^{+} = \Delta H_{2} - \Delta H_{1} = 250 \, \text{eV} - 100 \, \text{eV} = 150 \, \text{eV} \]

### Step 4: Analyze the Statements
Now, we need to analyze the statements based on the calculated energies:
- The first ionization energy is 100 eV (Correct).
- The second ionization energy is 250 eV (Correct).
- The energy required to remove the second electron from \( M^{+} \) should be 150 eV, not 100 eV.

### Conclusion
Based on the calculations, the incorrect statement is that the second ionization energy is equal to the first ionization energy, which is not true. Therefore, the incorrect statement is option C.

### Final Answer
The incorrect statement is option C.

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