The second ionisation potential of an element M is the energy required to

Options

A. Remove one mole of electron from one mole of gaseous anion
B. Remove one mole of electron from one mole of gaseous cation of the element
C. Remove one mole of electron from one mole of monovalent gaseous cation of the element
D. Remove 2 moles of electrons from one mole of gaseous atoms

Answer

To solve the question regarding the second ionization potential of an element M, we need to understand what ionization potential (or ionization energy) is and how it applies to the removal of electrons from an atom.

### Step-by-Step Solution:

1. **Definition of Ionization Potential**:
The ionization potential (IP) is the energy required to remove an electron from an atom or ion in the gaseous state. The first ionization potential (IE1) refers to the energy required to remove the first electron, while the second ionization potential (IE2) refers to the energy required to remove a second electron after the first has already been removed.

2. **Understanding the Process**:
For an element M, the first ionization can be represented as:
\[ M(g) \rightarrow M^+(g) + e^- \]
This reaction shows that one mole of electrons is removed from one mole of gaseous atoms of element M, resulting in a cation (M^+).

3. **Second Ionization Potential**:
The second ionization potential involves removing an electron from the already formed cation (M^+). This can be represented as:
\[ M^+(g) \rightarrow M^{2+}(g) + e^- \]
Here, we are removing one mole of electrons from one mole of gaseous cations of the element M.

4. **Conclusion**:
Therefore, the second ionization potential of element M is defined as the energy required to remove one mole of electrons from one mole of gaseous cations of the element M.

5. **Final Answer**:
The correct option is:
- Remove one mole of electron from one mole of gaseous cation of the element (this is the essence of the second ionization potential).