Question

Use average bond enthalpies from the given data to estimate the change in enthalpy $\Delta H^{\circ }$for the reaction:${\mathit{C}}_{\mathbf{2}}{\mathit{H}}_{\mathbf{4}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\to }{\mathit{C}}_{\mathbf{2}}{\mathit{H}}_{\mathbf{6}}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

Short answer

The answer is $\Delta H=492kJ$.

Step-by-step solution

Given data

Bond	Enthalpy
C=C	615
H-H	436
C-H	413
C-C	348

Concept used

Enthalpy change is the amount of heat absorbed or evolved in a reaction when carried out at a constant pressure. It is generally calculated as the difference in energy required for bond breaking in a chemical reaction and energy gained in forming new bonds in the chemical reaction.

It is represented by $\Delta H$.

By the use bond enthalpies the change in enthalpy has been calculated.

The structures of the participants of this reaction are given below.

The reactants:

C₂H₂: 6C-H Bonds, 4C-H bonds and H₂:1H-H bond.

The product:

$C_2{H}_6:6C-HBonds,andoneC-Cbond.$

Calculate the enthalpy change of the products

By the use of bond enthalpies, the product enthalpy change has been calculated.

$$\begin{gathered} C_2{H}_6:6C-HBondsandoneC-Cbond. \\ \Delta BEproduct=\Delta BE(C-C)+6\times \Delta BE(C-H) \\ \Delta BEproduct=348+6\times 413 \\ \Delta BEproducts=2826kJ \end{gathered}$$

Calculate the enthalpy change of the reactants

By the use of bond enthalpies, the product enthalpy change has been calculated.

$$\begin{gathered} C_2{H}_4:2C=CBonds,4C-Hbondsand{H}_2:1H-Hbond. \\ \Delta B{E}_{reac\tan ts}=2\times \Delta BE(C=C)+4\times \Delta BE(C-H)+\Delta BE(H-H) \\ \Delta B{E}_{reac\tan ts}=2\times 615+4\times 413+436 \\ \Delta B{E}_{reac\tan ts}=3318kJ \end{gathered}$$

Calculate the overall energy change

Overall energy:

$$\begin{gathered} \Delta B{E}_{reac\tan ts}=3318kJ \\ \Delta B{E}_{Products}=2826kJ \end{gathered}$$

Apply these values to calculate the overall energy change.

$$\begin{gathered} \Delta H=\Delta B{E}_{reac\tan ts}-\Delta B{E}_{products} \\ \Delta H=3381-2826 \\ \Delta H=492kJ \end{gathered}$$