`X_((g)) to X_((g))^(+) +e^(-), " "DeltaH=+720kJ" "mol^(-1)`
Calculate the amoung of energy required to convert 110 mg 'X' atom in gaseous state into `X^(+)` ion. (Atoic wt. for X=7 g /mol)

Options

A. 10.4 kJ
B. 12.3 kJ
C. 11.3 kJ
D. 14.5 kJ

Explanation

To calculate the amount of energy required to convert 110 mg of atom 'X' in gaseous state into \( X^+ \) ion, we will follow these steps:

### Step 1: Convert mass from milligrams to grams
Given:
- Mass of 'X' = 110 mg

To convert milligrams to grams:
\[ \text{Mass in grams} = \frac{110 \, \text{mg}}{1000} = 0.110 \, \text{g} \]

### Step 2: Calculate the number of moles of 'X'
We know the atomic weight of 'X' is 7 g/mol.

Using the formula for moles:
\[ \text{Moles of } X = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Moles of } X = \frac{0.110 \, \text{g}}{7 \, \text{g/mol}} \approx 0.01571 \, \text{mol} \]

### Step 3: Calculate the energy required for the conversion
The enthalpy change (\( \Delta H \)) for the reaction is given as +720 kJ/mol. This means that to convert 1 mole of 'X' to \( X^+ \), 720 kJ of energy is required.

Now, we can find the energy required for 0.01571 moles:
\[ \text{Energy required} = \text{Moles of } X \times \Delta H \]
Substituting the values:
\[ \text{Energy required} = 0.01571 \, \text{mol} \times 720 \, \text{kJ/mol} \approx 11.3 \, \text{kJ} \]

### Final Answer
The amount of energy required to convert 110 mg of 'X' atom in gaseous state into \( X^+ \) ion is approximately **11.3 kJ**.

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