Animated Solution for Chemistry - Chemical Thermodynamics: For the reaction, $C_2{H}_6⟶C_2{H}_4+H_2$ the reaction enthalpy ${\Delta }_{r}H=\dots \dots \dots {\text{ kJ mol}}^{-1}$ (Round off to the nearest integer). [Given : Bond enthalpies in ${\text{kJ mol}}^{-1}$ : $C-C=347,C=C=611;C-H=414;H-H=436$]

Decoding Reaction Enthalpy

Imagine you are a molecular architect. Your job is to dismantle an ethane molecule ($C_2{H}_6$) and use its parts to build an ethene molecule ($C_2{H}_4$) and a hydrogen molecule ($H_2$). This process isn't free; it requires an exchange of energy. Breaking the existing bonds costs energy, while forming new bonds releases energy. The net difference between these two is what we call the Enthalpy of Reaction (${\Delta }_{r}H$).

Let's break down the math behind this molecular construction project.

To find the total enthalpy change, we use a very logical principle:

Why this order? Because breaking bonds is an endothermic process (it absorbs energy, hence positive), and forming bonds is an exothermic process (it releases energy, hence negative). By subtracting the product energies from the reactant energies, we find the net energy flow.

The Reactants

Let's look at our starting material, ethane ($C_2{H}_6$). If you draw its structure, you will see a central carbon-carbon single bond surrounded by six carbon-hydrogen single bonds. To completely atomize this molecule, we must break all of them.

Substituting the given values:

We need to invest $2831\text{ kJ}$ of energy for every mole of ethane we break apart.

The Products

Now, let's assemble our products. We are forming ethene ($C_2{H}_4$) and hydrogen gas ($H_2$). Ethene features a strong carbon-carbon double bond and four carbon-hydrogen single bonds. The hydrogen molecule is simply one hydrogen-hydrogen single bond.

Substituting the values:

When these new bonds form, the system releases $2703\text{ kJ}$ of energy per mole.

We know how much energy we put in, and we know how much we got back. The net enthalpy change is simply the difference:

Because the result is positive, the overall reaction is endothermic. We had to supply a net amount of $128\text{ kJ}$ of energy per mole to make this reaction happen.

If you look closely at the structures, you'll notice that four $C-H$ bonds exist in both the reactants and the products. Instead of breaking them all and reforming four of them, we can just calculate the net change.

What actually happens? One $C-C$ single bond and two $C-H$ bonds break. In return, one $C=C$ double bond and one $H-H$ bond form.

This method is faster and less prone to calculation errors. Whether you take the long road or the shortcut, the physics remains beautifully consistent!