The homonuclear bond dissociation energies and are and respectively. The heteronuclear bond energy i — Periodic Table and Periodicity Chemistry Question
Question
The homonuclear bond dissociation energies $E_{H-H}$ and $E_{X-X}$ are $104 \text{ kcal/mol}$ and $60 \text{ kcal/mol}$ respectively. The heteronuclear bond energy $E_{H-X}$ is $101 \text{ kcal/mol}$. Assuming the Pauling electronegativity of Hydrogen ($X_H$) is $2.1$ and using Pauling's arithmetic mean approximation, what is the exact calculated electronegativity of the unknown halogen $X$ ($X_X$)?
💡 Solution & Explanation
Using the Pauling equation: $X_A - X_B = 0.208 \times \sqrt{\Delta}$, where $\Delta = E_{H-X} - \frac{E_{H-H} + E_{X-X}}{2}$ (using arithmetic mean). $\Delta = 101 - \frac{104 + 60}{2} = 101 - 82 = 19$. Taking the square root of 19 gives roughly $4.36$. Substituting: $X_X - 2.1 = 0.208 \times 4.36 \approx 0.906$. Therefore, $X_X = 2.1 + 0.906 = 3.006 \approx 3$.