Question

The \(\Delta H\) for \(\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) is \(-44 \mathrm{~kJ}\). What is the \(\Delta H\) for this reaction? \(2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4}+2 \mathrm{H}_{2} \mathrm{O}\)

Short answer

\( \Delta H = +88 \mathrm{~kJ} \) for the reverse reaction.

Step-by-step solution

Understand the Given Reaction

We are given the enthalpy change (\( \Delta H \)) for the reaction \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) as -44 kJ. This means that forming one mole of \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) releases 44 kJ of heat.

Write the Reverse Reaction

The provided reaction \( 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \) is simply the reverse of twice the given reaction. Therefore, we must reverse the initial reaction and double its quantities.

Apply the Concept of Reversing a Reaction

Reversing a chemical reaction changes the sign of \( \Delta H \). Therefore, the enthalpy change for the reverse reaction \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{H}_{2} \mathrm{O} \) is +44 kJ.

Adjust for Reaction Coefficients

Since the reaction in question is \( 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \), we need to multiply the enthalpy change of the reverse reaction by 2: \( 2 \times 44 \mathrm{~kJ} = 88 \mathrm{~kJ} \).

Calculate the Final \( \Delta H \)

Thus, for the given reaction \( 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \), the enthalpy change, \( \Delta H \), is +88 kJ.

Key concepts

Reversing Chemical Reactions

Reversing a chemical reaction involves changing the direction of the reaction and adjusting the enthalpy change accordingly. In simple terms, if you start with products and go backward to the reactants, you are reversing the reaction.
When a reaction is reversed, the sign of its enthalpy change (\(\Delta H\)) is also reversed. This is because the energy absorbed or released during the forward reaction becomes the opposite in the reverse reaction.
For example, if a reaction has a \(\Delta H\) of \(-44 \text{ kJ}\) when moving forward, the reverse would have a \(\Delta H\) of \(+44 \text{ kJ}\).

• Forward Reaction: \(A \rightarrow B\) with \(\Delta H = -44 \text{ kJ}\) (exothermic: energy is released)
• Reverse Reaction: \(B \rightarrow A\) with \(\Delta H = +44 \text{ kJ}\) (endothermic: energy is absorbed)

Understanding this concept is crucial in thermodynamics as it helps predict how much energy is required or released when the reaction direction is changed.

Thermodynamics

Thermodynamics is the scientific study concerned with heat, energy, and their transformations. It dictates how energy flows in chemical systems and processes, particularly during chemical reactions.
In chemical reactions, thermodynamics allows us to understand how energy is transferred between reactants and products. This is primarily quantifiable through enthalpy (\(\Delta H\)), a measure of heat change at constant pressure.

• If \(\Delta H\) is negative, it indicates that the system releases energy (exothermic reaction).
• If \(\Delta H\) is positive, it signifies that the system absorbs energy (endothermic reaction).
• The understanding of these energy changes is vital for controlling processes, such as in industrial chemical reactions, to ensure safeness and efficiency.

Thermodynamics goes beyond just energy changes, also covering spontaneity of reactions and how to manipulate conditions to influence chemical behavior.

Chemical Reactions

Chemical reactions are processes where substances known as reactants transform into different substances, called products. These transformations involve breaking old bonds and forming new ones, which involves energy exchange.
The nature of a chemical reaction can be demonstrated through a balanced chemical equation, which shows the relative quantities of reactants and products. In terms of energy:

• Reactions can be classified as either exothermic, which release heat, or endothermic, which absorb heat.
• Each reaction has a unique enthalpy change (\(\Delta H\)), often determined experimentally or calculated using Hess's law.

An essential part of understanding chemical reactions is knowing the effect of different conditions like temperature and pressure on the reaction's direction and rate. Mastery of how these factors influence reactions helps in various fields, including chemistry, engineering, and environmental science. The balance of chemical equations not only ensures the law of conservation of mass is followed but also simplifies reactions for practical use.