Question

For the reaction: \[{C_2}{H_6}\xrightarrow{{}}{C_2}{H_4} + {H_2}\] : the reaction enthalpy \[\Delta {H_r} = \]__________ \[kJ\,mo{l^{ - 1}}\] . (Round off to the Nearest Integer).
[Given: Bond enthalpies in \[kJ\,mo{l^{ - 1}}\] : \[C - C:347\] , \[C = C:611\] , \[C - H:414\] , \[H - H:436\] ]

Answer 1

Hint: The average bond enthalpy or just bond enthalpy are other names for bond energy. It is a number that provides information about the strength of the chemical bonds. "Bond energy" is defined by the IUPAC as "the average value that is determined from the bond dissociation enthalpies (in the gaseous phase) of the whole chemical bonds of a specific type, which is given in a chemical compound."

Complete Step by Step Solution:
The given reaction is as follows:
\[{C_2}{H_6}\xrightarrow{{}}{C_2}{H_4} + {H_2}\]

The reaction enthalpy is the difference in enthalpy between products and reactants. It can be calculated as follows:
\[\Delta {H_r} = \left( {{\text{Bond}}\,{\text{enthalpy}}\,{\text{of}}\,{\text{reactants}}} \right) - \left( {{\text{Bond}}\,{\text{enthalpy}}\,{\text{of}}\,{\text{products}}} \right)\]
There are six carbon-hydrogen bonds and one carbon-carbon bond present in reactants. There are four carbon-hydrogen bonds, one carbon-carbon double bond, and one hydrogen-hydrogen bond present in products.

Let us calculate the reaction enthalpy as follows:
\[ \Delta {H_r} = \left[ {1\left( {C - C} \right) + 6\left( {C - H} \right)} \right] - \left[ {1\left( {C = C} \right) + 4\left( {C - H} \right) + 1\left( {H - H} \right)} \right] \\
   \Rightarrow \Delta {H_r} = \left[ {347 + 6\left( {414} \right)} \right] - \left[ {611 + 4\left( {414} \right) + 433} \right] \\
   \Rightarrow \Delta {H_r} = 2831 - 2700 \\ \]

Further solving,
\[\Delta {H_r} = 131\,kJ/mol\]
Therefore, the reaction enthalpy is \[131\,kJ/mol\] .

Additional Information: The enthalpy shift connected with breaking a chemical bond via homolytic cleavage is known as the bond dissociation energy of a chemical bond, or BDE for short. The energy required to assist the homolytic breakage of the bond between A and B, which subsequently results in the creation of two free radicals, is an example of bond dissociation energy in an A-B molecule.

Note: It is crucial to understand that the bond dissociation energy of a chemical bond is entirely reliant on the absolute temperature of the surrounding environment. Consequently, the bond dissociation energy is typically estimated under the normative circumstances (where the temperature is equal to 298 Kelvin, roughly). On the other hand, the average value of all bond dissociation enthalpies for the same bond in the molecule constitutes the bond energy of a chemical bond that exists in a compound.