If the ionization enthalpy and electron gain enthalpy of an element are 275 and 86 kcal `mol^(-1)` respectively, then the electronegativity of the element on the Pauling scale is

Options

A. 2.8
B. `0.0`
C. `4.0`
D. `2.6`

Answer

To find the electronegativity of the element on the Pauling scale using the given ionization enthalpy and electron gain enthalpy, we can follow these steps:

### Step 1: Write down the given values
- Ionization enthalpy (I.E) = 275 kcal/mol
- Electron gain enthalpy (E.G.E) = 86 kcal/mol

### Step 2: Use the formula for electronegativity
The formula to calculate electronegativity (χ) on the Pauling scale is:
\[ \chi = 0.102 \sqrt{I.E - E.G.E} \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ \chi = 0.102 \sqrt{275 \text{ kcal/mol} - 86 \text{ kcal/mol}} \]

### Step 4: Calculate the difference
Calculate the difference between the ionization enthalpy and electron gain enthalpy:
\[ 275 - 86 = 189 \text{ kcal/mol} \]

### Step 5: Substitute the difference into the formula
Now substitute this value back into the electronegativity formula:
\[ \chi = 0.102 \sqrt{189} \]

### Step 6: Calculate the square root
Calculate the square root of 189:
\[ \sqrt{189} \approx 13.75 \]

### Step 7: Multiply by 0.102
Now multiply by 0.102:
\[ \chi \approx 0.102 \times 13.75 \approx 1.4 \]

### Step 8: Convert kcal to kJ
Since the values are in kcal, we need to convert them to kJ for the final calculation. The conversion factor is:
\[ 1 \text{ kcal} = 4.18 \text{ kJ} \]
Thus, we convert the values:
- Ionization enthalpy: \( 275 \text{ kcal/mol} \times 4.18 \text{ kJ/kcal} = 1145 \text{ kJ/mol} \)
- Electron gain enthalpy: \( 86 \text{ kcal/mol} \times 4.18 \text{ kJ/kcal} = 359.48 \text{ kJ/mol} \)

### Step 9: Substitute the converted values into the formula
Now we substitute these values into the electronegativity formula:
\[ \chi = 0.102 \sqrt{1145 - 359.48} = 0.102 \sqrt{785.52} \]

### Step 10: Calculate the square root and finalize
Calculate the square root:
\[ \sqrt{785.52} \approx 28.03 \]
Now multiply:
\[ \chi \approx 0.102 \times 28.03 \approx 2.86 \]

### Step 11: Round to the nearest value
Rounding this value gives us approximately \( 2.8 \).

### Final Answer
Thus, the electronegativity of the element on the Pauling scale is approximately **2.8**.

---