The energy required to convert all atoms present in 1.2 g. magnesium to `Mg^(2+)` ions if IE and `IE_(2)` of magnesium are 120 kJ `"mol"^(-1)` and 240 kJ `"mol"^(-1)` respectively

Options

A. 18 kJ
B. 36 kJ
C. 360 kJ
D. 24 kJ

Answer

To find the energy required to convert all atoms present in 1.2 g of magnesium to Mg²⁺ ions, we will follow these steps:

### Step 1: Determine the number of moles of magnesium
First, we need to calculate the number of moles of magnesium in 1.2 g. The molar mass of magnesium (Mg) is approximately 24 g/mol.

\[ \text{Number of moles of Mg} = \frac{\text{mass of Mg}}{\text{molar mass of Mg}} = \frac{1.2 \, \text{g}}{24 \, \text{g/mol}} = 0.05 \, \text{mol} \]

### Step 2: Calculate the total ionization energy for Mg to Mg²⁺
The total energy required to convert magnesium to Mg²⁺ involves two ionization energies:
- First ionization energy (IE₁) = 120 kJ/mol
- Second ionization energy (IE₂) = 240 kJ/mol

The total ionization energy (IE_total) is the sum of the first and second ionization energies:

\[ \text{IE}_{\text{total}} = \text{IE}_1 + \text{IE}_2 = 120 \, \text{kJ/mol} + 240 \, \text{kJ/mol} = 360 \, \text{kJ/mol} \]

### Step 3: Calculate the energy required for 0.05 moles of Mg
Now, we will calculate the energy required to convert 0.05 moles of magnesium to Mg²⁺ ions using the total ionization energy calculated in Step 2.

\[ \text{Energy required} = \text{Number of moles} \times \text{IE}_{\text{total}} = 0.05 \, \text{mol} \times 360 \, \text{kJ/mol} = 18 \, \text{kJ} \]

### Final Answer
The energy required to convert all atoms present in 1.2 g of magnesium to Mg²⁺ ions is **18 kJ**.

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