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The bond dissociation energies of gaseous ${{H}_{2}}$, $C{{l}_{2}}$ and HCl are 104 ,58 and 103 kcal respectively. The enthalpy of formation of HCl gas would be,
(A) 44kcal
(B) 44kcal
(C) 22kcal
(D) 22kcal

Answer Verified Verified
Hint: Values of Bond energy are taken according to the balanced chemical equation of the reaction, also the coefficients of reactants and products are multiplied with the bond energy.
Complete step by step answer:
Bond energy is defined as the amount of energy required to break apart a mole of molecules into its component atoms. It is a measure of the strength of a chemical bond. Bond energy is also known as bond enthalpy or simply as bond strength.
The standard enthalpy of formation refers to the enthalpy change when one mole of a compound is formed from its elements. The standard enthalpy of formation, or standard heat of formation, of a compound is the change in enthalpy that accompanies the formation of one mole of the compound from its elements in their standard states.
\[\frac{1}{2}{{H}_{2}}+\frac{1}{2}C{{l}_{2}}\to HCl\]
Given bond energies of ${{H}_{2}}$is 104kcal, $C{{l}_{2}}$is 58kcal , and HCl is 103 kcal.
According to the reaction, Enthalpy of formation HCl will be calculated using the bond energy of reactant and bond energy of product.
By the formula of enthalpy of formation, we get,
\[\begin{align}
& \Delta {{H}_{f}}=(Bond\text{ }energy\text{ }of\text{ }reactant)-(Bond\text{ }energy\text{ }of\text{ }Product) \\
& \Rightarrow \Delta {{H}_{f}}=\left( \frac{1}{2}\Delta {{H}_{BE({{H}_{2}})}}+\frac{1}{2}\Delta {{H}_{BE(C{{l}_{2}})}} \right)-\left( \Delta {{H}_{BE(HCl)}} \right) \\
& \Rightarrow \Delta {{H}_{f}}=\left( \frac{1}{2}(104)+\frac{1}{2}(58) \right)-\left( 103 \right) \\
& \Rightarrow \Delta {{H}_{f}}=52+29-103 \\
& \Rightarrow \Delta {{H}_{f}}=-22kcal \\
\end{align}\]

Hence, the correct answer is (C) option.

 Note: When a bond is strong, there is a higher bond energy because it takes more energy to break a strong bond. This correlates with bond order and bond length. When the Bond order is higher, bond length is shorter, and the shorter the bond length means a greater the Bond Energy because of increased electric attraction. In general, the shorter the bond length, the greater the bond energy.