Find the formula of halide of a metal whose successive ionization enthalpies are x, 2x, 5x, 100 x kJ `"mol"^(-1)` respectively

Options

A. MX
B. `MX_(2)`
C. `MX_(3)`
D. `M_(2)X`

Answer

To find the formula of the halide of a metal based on the given successive ionization enthalpies, we can follow these steps:

### Step 1: Understand Ionization Enthalpy
Ionization enthalpy is the energy required to remove an electron from an isolated gaseous atom. Successive ionization enthalpies refer to the energy required to remove additional electrons after the first one.

### Step 2: Analyze the Given Ionization Enthalpies
We are given the following successive ionization enthalpies:
- First ionization enthalpy (I1) = x
- Second ionization enthalpy (I2) = 2x
- Third ionization enthalpy (I3) = 5x
- Fourth ionization enthalpy (I4) = 100x

### Step 3: Identify the Trend in Ionization Enthalpies
Notice that the first three ionization enthalpies (x, 2x, and 5x) show a gradual increase, but there is a significant jump from I3 (5x) to I4 (100x). This large increase indicates that removing the fourth electron is much more difficult than removing the first three.

### Step 4: Determine the Number of Valence Electrons
The large jump in ionization enthalpy suggests that after removing three electrons, the metal achieves a stable electronic configuration. This implies that the metal has three valence electrons in its outermost shell.

### Step 5: Write the Formula of the Halide
Since the metal can lose three electrons, it will form a cation with a +3 charge (M^3+). Halogens (X) typically form anions with a -1 charge (X^-). Therefore, to balance the charges, the formula of the metal halide will be:

\[ \text{Metal Halide} = \text{MX}_3 \]

Where M is the metal and X is the halogen.

### Conclusion
The formula of the halide of the metal is \( \text{MX}_3 \).

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