`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

Answer

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

### Step 1: Convert the mass of 'X' 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'
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Molar mass of 'X' = 7 g/mol

Substituting the values:
\[ \text{Number of moles} = \frac{0.110 \text{ g}}{7 \text{ g/mol}} \approx 0.01571 \text{ mol} \]

### Step 3: Calculate the energy required for the conversion
We know that the energy required to convert 1 mole of 'X' to \( X^+ \) is \( \Delta H = +720 \text{ kJ/mol} \).

To find the energy for the calculated number of moles:
\[ \text{Energy required} = \text{Number of moles} \times \Delta H \]
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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