Question

If the \(\Delta H\) for \(\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}\) is \(-65.6 \mathrm{~kJ}\), what is the \(\Delta H\) for this reaction? \(2 \mathrm{C}_{2} \mathrm{H}_{4}+2 \mathrm{H}_{2} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{6}\)

Short answer

The \( \Delta H \) for the reaction is \(-131.2 \text{ kJ}\).

Step-by-step solution

Understand the given reaction

We have the reaction \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{H}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{6} \) with a given \( \Delta H = -65.6 \text{ kJ} \) per mole of reaction.

Analyze the required reaction

The question asks for the \( \Delta H \) of the reaction \( 2 \mathrm{C}_{2} \mathrm{H}_{4} + 2 \mathrm{H}_{2} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{6} \). Notice that this reaction is exactly twice the given reaction.

Calculate \( \Delta H \) for two moles

Since the given \( \Delta H \) is for one mole of the initial reaction, and the new reaction involves two moles, multiply the given \( \Delta H \) by 2. Thus, \( \Delta H = 2 \times (-65.6 \text{ kJ}) = -131.2 \text{ kJ}. \)

Key concepts

Chemical Reactions

In chemistry, a chemical reaction occurs when substances, known as reactants, transform into different substances called products. This transformation often involves the breaking and forming of chemical bonds. In the exercise, we see a simple yet fundamental chemical reaction where ethylene (\(\mathrm{C}_{2}\mathrm{H}_{4}\)) reacts with hydrogen (\(\mathrm{H}_{2}\)) to produce ethane (\(\mathrm{C}_{2}\mathrm{H}_{6}\)).

• Each reactant and product in a chemical reaction can be represented by a chemical formula.
• Chemical reactions must be balanced, meaning the number of each type of atom is conserved.

When we balance a reaction, we ensure that we follow the law of conservation of mass. Understanding how reactions work helps us better grasp other concepts such as enthalpy change, which plays a key role in determining whether a reaction is exothermic or endothermic.

Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. It examines how heat transfer influences changes in the substances' energy states. In the exercise, understanding the enthalpy change (\(\Delta H\)) is central to grasping the energetics of the reaction.

• \(\Delta H\) denotes the change in enthalpy, which is the total energy absorbed or released during a reaction.
• A negative \(\Delta H\) indicates an exothermic reaction, where heat is released.
• A positive \(\Delta H\) suggests an endothermic reaction, where heat is absorbed.

In the given exercise, the reaction has an enthalpy change of -65.6 kJ, implying that this reaction releases 65.6 kJ of energy per mole of ethylene converted into ethane. Such knowledge is crucial for predicting how reactions behave under different conditions.

Reaction Energetics

Reaction energetics refers to the study of energy changes accompanying a chemical reaction. It is essential to understand why certain reactions release energy, and others absorb it. By analyzing the exercise, we can explore this concept further by focusing on the enthalpy changes when the quantities in the reaction are scaled.

• Energetics informs us about reaction feasibility and spontaneity.
• The magnitude of \(\Delta H\) gives insights into the energy profile of the reaction.
• In the exercise, doubling the moles of reactants leads to doubling the \(\Delta H\), from -65.6 kJ to -131.2 kJ.

The scaling of \(\Delta H\) according to the number of moles is a vital detail showing proportionality in reaction energetics, helping us predict the energy involved in any scaled chemical reaction.