Question

Bond energy of \[{{H - H,F -F}}\] and \[{{H - F}}\] bonds are \[{{104, 38}}\] and \[{{135 kcal mol}}{{{1}}^{{{ - 1}}}}\] respectively. Resonance energy \[\left( {{{kcalmo}}{{{1}}^{{{ - 1}}}}} \right)\] in the \[{{H - F}}\] molecule is :
A. $72.14$
B. \[42.44\]
C. \[78.34\]
D. None of these

Answer 1

Hint: The amount of energy needed to break a bond between a covalently bound gas is called the bond energy. The measure of the extra stability of the conjugated system as compared to the number of isolated double bonds is the resonance energy of a compound.

Complete step by step answer:
It is given that the bond energy of ${{H - H}}$ bond, ${{B}}{{{E}}_{{{H}} - {{H}}}} = {{144kcalmo}}{{{1}}^{{{ - 1}}}}$
Bond energy of ${{F - F}}$ bond, ${{B}}{{{E}}_{{{F - F}}}} = {{38kcalmo}}{{{1}}^{{{ - 1}}}}$
Bond energy of ${{H - F}}$, ${{B}}{{{E}}_{{{H - F}}}} = {{135kcalmo}}{{{1}}^{{{ - 1}}}}$
Bond Energy is also called average bond enthalpy or bond enthalpy. It gives an information about the strength of a chemical bond. The IUPAC definition bond energy is, it is the average value obtained from the bond dissociation enthalpies of all the chemical bonds of a specific type. Bond energy of a chemical bond in a given compound can be seen as the average amount of energy that is required to break one such chemical bond. The bond energy of a chemical bond is directly proportional to the stability, i.e., the larger the bond energy of a given chemical bond between two atoms, the greater is the stability of that chemical bond.
Resonance energy can be calculated from experimental methods. It can be also calculated from the bond energies of the molecules.
Resonance Energy, \[{{{\Delta }}_{{{H - F}}}}{{ = }}{\left( {{{BE}}} \right)_{{{H - F}}}}{{ - }}\sqrt {{{\left( {{{BE}}} \right)}_{{{H - H}}}}{{\left( {{{BE}}} \right)}_{{{F - F}}}}{{\;}}} \], where ${{B}}{{{E}}_{{{H - F}}}}$ is the bond energy of ${{H - F}}$ bond, ${{B}}{{{E}}_{{{H}} - {{H}}}}$ is the bond energy of ${{H - H}}$ bond and ${{B}}{{{E}}_{{{F - F}}}}$ is the bond energy of ${{F - F}}$ bond.
Substituting the values of these bond energies, we get
\[{{{\Delta }}_{{{H - F}}}}{{ = 135 - }}\sqrt {{{104 \times 38}}} {{\; = 135 - 62}}{{.86\;}}\]
On simplification we get,
\[{{{\Delta }}_{{{H - F}}}}{{\; = 72}}{{.14kcalmo}}{{{l}}^{{{ - 1}}}}\]
Hence, the answer is \[{{72}}{{.14kcalmo}}{{{l}}^{{{ - 1}}}}\]

So, the correct answer is Option A.

Additional information:
When a single chemical structure is insufficient to express all the properties of a compound, a hybrid of structures are drawn. These are called resonance structures. Each contributing structure is called a canonical structure.

Note: The standard change in enthalpy when a bond is broken through a homolytic fission is the bond dissociation enthalpy. Radicals are the products formed from the homolysis of the bond. Bond dissociation enthalpy can also be used to measure the strength of the chemical bond.