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# Linus Pauling defined electronegativity as the power of an atom in a molecule to attract electrons. Given the bond disassociation enthalpies, $\varepsilon_{C-C} = 348\; \text{ kJ/mol}, \varepsilon_{C-H} = 412 \; \text{ kJ/mol}, \varepsilon_{H-H} = 436 \; \text{ kJ/mol}$, what is the Pauling elctronegativity of $C$? (Electronegativity of $H$ is $2.1$)

$\begin{array}{1 1} 2.41 \\ 1.82 \\ 3.45 \\ 2.58 \end{array}$

Linus Pauling took the geometrical mean and derived elctronegativity between $X$ and $Y$ as follows: $\chi_C - \chi_H = 0.102 \sqrt (\Delta D)$
$\Delta D$ is the geometric mean of $\varepsilon_{X-X}$ and $\varepsilon_{Y-Y}$ as follows: $\Delta D \;\text{kJ/mol} = \varepsilon_{XY} - \sqrt (\varepsilon_{XX}\varepsilon{XY})$
Given $\varepsilon_{C-C} = 348\; \text{ kJ/mol}, \varepsilon_{C-H} = 412 \; \text{ kJ/mol}, \varepsilon_{H-H} = 436 \; \text{ kJ/mol}$
$\Rightarrow \Delta D = 412 - \sqrt (348 \times 436) = 22.47$
$\chi_C - \chi_H = 0.102 \sqrt (\Delta D) \rightarrow \chi_C -2.1 = 0.102 \times \sqrt 22.47$ (It is given that $\chi_H = 2.1)$
$\Rightarrow \chi_C = 2.1 + 0.102 \times 4.74 \approx 2.58$

edited Mar 24, 2014