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: Calculate the change in enthalpy (ΔE)
The change in enthalpy (ΔE) can be calculated as:
\[ \Delta E = \text{Ionization Enthalpy} - \text{Electron Gain Enthalpy} \]
Substituting the values:
\[ \Delta E = 275 \text{ kcal/mol} - 86 \text{ kcal/mol} = 189 \text{ kcal/mol} \]

### Step 3: Convert ΔE from kcal to kJ
To convert kcal to kJ, we use the conversion factor \(1 \text{ kcal} = 4.184 \text{ kJ}\):
\[ \Delta E = 189 \text{ kcal/mol} \times 4.184 \text{ kJ/kcal} = 791.056 \text{ kJ/mol} \]

### Step 4: Calculate the electronegativity using the formula
The formula for electronegativity (χ) on the Pauling scale is given by:
\[ \chi = 0.102 \times \sqrt{\Delta E} \]
Substituting the value of ΔE:
\[ \chi = 0.102 \times \sqrt{791.056} \]

### Step 5: Calculate the square root
Calculating the square root:
\[ \sqrt{791.056} \approx 28.14 \]

### Step 6: Calculate electronegativity
Now substituting back into the electronegativity formula:
\[ \chi = 0.102 \times 28.14 \approx 2.87 \]

### Step 7: Round the answer
Rounding to two decimal places, we find:
\[ \chi \approx 2.9 \]

### Conclusion
The electronegativity of the element on the Pauling scale is approximately **2.9**.

---