Question

The bond dissociation energies of H-H, C-C and C-H bonds respectively are 104.2, 83.1 and 98.9 kcal/mol. The electronegativity of carbon is:
A. 2.53
B. 2.51
C. 2.57
D. 2.52

Answer 1

Hint: We can solve this question by keeping the following formula in mind that relates the electronegativity of the elements to the bond energies between them:
\[{{X}_{C}}-{{X}_{H}}={{(eV)}^{1/2}}\sqrt{{{E}_{(C-H)}}-\dfrac{{{E}_{C-C}}+{{E}_{H-H}}}{2}}\]
where, \[{{X}_{C}}\]is the electronegativity of carbon, \[{{X}_{H}}\] is the electronegativity of hydrogen, eV denotes electron volt per molecule and \[{{E}_{H-H}}\], \[{{E}_{C-C}}\] and \[{{E}_{C-H}}\] are the bond energies of hydrogen-hydrogen, carbon-carbon, and carbon-hydrogen bonds respectively.

Complete Solution :
The bond dissociation energies of the following bonds are given as follows:
\[{{E}_{H-H}}=104.2\]kcal/mol
\[{{E}_{C-C}}=83.1\]kcal/mol
\[{{E}_{C-H}}=98.8\]kcal/mol
The difference in electronegativity of carbon and hydrogen can be given by the following equation:
\[{{X}_{C}}-{{X}_{H}}={{(eV)}^{1/2}}\sqrt{{{E}_{(C-H)}}-\dfrac{{{E}_{C-C}}+{{E}_{H-H}}}{2}}\]​​​
The standard value of hydrogen electronegativity, \[{{X}_{H}}\]​= 2.1 , and
eV = 0.04326 per molecule.

 Substituting these values in the given equation, we get:

\[\begin{align}
 & {{X}_{C}}-2.1=(0.208)\sqrt{98.8-\dfrac{104.2+83.1}{2}} \\
 & \Rightarrow {{X}_{C}}-2.1=(0.208)(2.2694) \\
 & \Rightarrow {{X}_{C}}=2.572 \\
\end{align}\]
 So, the correct answer is “Option C”.

Note: Bond dissociation energy is defined as “the amount of energy required to break one mole of bond of a particular type between the atoms in the gaseous state under standard conditions”.
- Electronegativity is defined as a measure of the tendency of an atom to attract a bonding pair of electrons. The Pauling scale is the most commonly used to measure electronegativity of the elements.
- Linus Pauling related the electronegativity difference between two atoms forming a bond to the bond energies of molecules. The larger the difference in the electronegativities of the bonded atoms, the greater is the bond dissociation energy.