If the ionisation 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
C. 4
D. 2.6

Explanation

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

### Step 1: Identify the Given Values
- Ionization Enthalpy (IE) = 275 kcal/mol
- Electron Gain Enthalpy (EGE) = 86 kcal/mol

### Step 2: Calculate the Difference Between Ionization Enthalpy and Electron Gain Enthalpy
We need to find the difference (ΔE) between the ionization enthalpy and the electron gain enthalpy:
\[ \Delta E = \text{Ionization Enthalpy} - \text{Electron Gain Enthalpy} \]
\[ \Delta E = 275 \, \text{kcal/mol} - 86 \, \text{kcal/mol} = 189 \, \text{kcal/mol} \]

### Step 3: Convert kcal/mol to kJ/mol
Since the Pauling scale formula uses kJ/mol, we need to convert kcal to kJ. The conversion factor is:
\[ 1 \, \text{kcal} = 4.18 \, \text{kJ} \]
Now, convert the difference:
\[ \Delta E = 189 \, \text{kcal/mol} \times 4.18 \, \text{kJ/kcal} = 790.82 \, \text{kJ/mol} \]

### Step 4: Use the Pauling Scale Formula
The electronegativity (χ) can be calculated using the formula:
\[ \chi = 0.102 \times (\Delta E)^{1/2} \]
Substituting the value of ΔE:
\[ \chi = 0.102 \times (790.82)^{1/2} \]

### Step 5: Calculate the Square Root
Calculate the square root of 790.82:
\[ (790.82)^{1/2} \approx 28.14 \]

### Step 6: Final Calculation
Now, substitute this value back into the electronegativity formula:
\[ \chi = 0.102 \times 28.14 \approx 2.87 \]

### Step 7: Round to Appropriate Significant Figures
Rounding 2.87 gives approximately 2.8.

### Conclusion
The electronegativity of the element on the Pauling scale is approximately **2.8**.