Calculate ΔH For The Reaction Of Ethene With F₂ Using Hess's Law

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Introduction

In the realm of chemical thermodynamics, understanding enthalpy changes (ΔH) during reactions is crucial for predicting reaction feasibility and energy requirements. Enthalpy, a thermodynamic property, represents the total heat content of a system at constant pressure. The change in enthalpy (ΔH) signifies the heat absorbed or released during a chemical reaction. Reactions that release heat are exothermic (ΔH < 0), while those that absorb heat are endothermic (ΔH > 0). In this comprehensive exploration, we will delve into the intricate process of calculating the enthalpy change (ΔH) for the reaction between ethene (C₂H₄) and fluorine (F₂), a reaction that yields carbon tetrafluoride (CF₄) and hydrogen fluoride (HF). This calculation will be performed using Hess's Law, a fundamental principle in thermochemistry.

The reaction we aim to analyze is:

C₂H₄(g) + 6 F₂(g) → 2 CF₄(g) + 4 HF(g)

To determine the enthalpy change (ΔH) for this reaction, we will leverage the provided enthalpies of formation for the following reactions:

  1. H₂(g) + F₂(g) → 2 HF(g) ΔH₁ = −537 kJ
  2. C(s) + 2 F₂(g) → CF₄(g) ΔH₂ = −680 kJ
  3. 2 C(s) + 2 H₂(g) → C₂H₄(g) ΔH₃ = +52.3 kJ

These reactions serve as stepping stones, allowing us to manipulate and combine them in a way that mirrors the target reaction. By applying Hess's Law, we can calculate the overall enthalpy change by summing the enthalpy changes of the manipulated reactions.

Hess's Law: A Cornerstone of Thermochemistry

Hess's Law, a cornerstone of thermochemistry, provides a powerful tool for calculating enthalpy changes in chemical reactions. Hess's Law states that the enthalpy change for a reaction is independent of the path taken, meaning that the overall enthalpy change is the same whether the reaction occurs in one step or in a series of steps. This principle allows us to determine the enthalpy change of a reaction by manipulating and combining the enthalpy changes of known reactions.

The essence of Hess's Law lies in the fact that enthalpy is a state function. A state function is a property that depends only on the initial and final states of the system, not on the path taken to reach those states. This characteristic of enthalpy makes Hess's Law a valuable tool for calculating enthalpy changes for reactions that are difficult or impossible to measure directly.

In essence, Hess's Law enables us to treat thermochemical equations as algebraic expressions, allowing us to add, subtract, multiply, and divide them to arrive at the desired reaction. By carefully manipulating the given reactions and their corresponding enthalpy changes, we can effectively construct a pathway to the target reaction and calculate its enthalpy change.

Step-by-Step Calculation Using Hess's Law

To calculate the enthalpy change (ΔH) for the reaction between ethene (C₂H₄) and fluorine (F₂), we will employ Hess's Law. This involves manipulating the given reactions to align with the target reaction, ensuring that when the reactions are combined, they yield the desired overall reaction. Each manipulation must be accompanied by a corresponding adjustment to the enthalpy change (ΔH).

1. Manipulating the Given Reactions

The target reaction is:

C₂H₄(g) + 6 F₂(g) → 2 CF₄(g) + 4 HF(g)

We need to manipulate the given reactions to match the stoichiometry and reactants/products of the target reaction.

Reaction 1: H₂(g) + F₂(g) → 2 HF(g) ΔH₁ = −537 kJ

This reaction produces HF, which is a product in our target reaction. We need 4 moles of HF in the target reaction, so we multiply this reaction by 2:

2 [H₂(g) + F₂(g) → 2 HF(g)] 2ΔH₁ = 2 × (−537 kJ) = −1074 kJ

2 H₂(g) + 2 F₂(g) → 4 HF(g) ΔH₁' = −1074 kJ

Reaction 2: C(s) + 2 F₂(g) → CF₄(g) ΔH₂ = −680 kJ

This reaction produces CF₄, another product in our target reaction. We need 2 moles of CF₄, so we multiply this reaction by 2:

2 [C(s) + 2 F₂(g) → CF₄(g)] 2ΔH₂ = 2 × (−680 kJ) = −1360 kJ

2 C(s) + 4 F₂(g) → 2 CF₄(g) ΔH₂' = −1360 kJ

Reaction 3: 2 C(s) + 2 H₂(g) → C₂H₄(g) ΔH₃ = +52.3 kJ

This reaction produces C₂H₄ as a product, but in our target reaction, C₂H₄ is a reactant. Therefore, we need to reverse this reaction and change the sign of ΔH₃:

C₂H₄(g) → 2 C(s) + 2 H₂(g) ΔH₃' = −52.3 kJ

2. Summing the Manipulated Reactions

Now, we add the manipulated reactions together:

  1. 2 H₂(g) + 2 F₂(g) → 4 HF(g) ΔH₁' = −1074 kJ
  2. 2 C(s) + 4 F₂(g) → 2 CF₄(g) ΔH₂' = −1360 kJ
  3. C₂H₄(g) → 2 C(s) + 2 H₂(g) ΔH₃' = −52.3 kJ

Adding these reactions, we get:

2 H₂(g) + 2 F₂(g) + 2 C(s) + 4 F₂(g) + C₂H₄(g) → 4 HF(g) + 2 CF₄(g) + 2 C(s) + 2 H₂(g)

3. Simplifying the Overall Reaction

We can cancel out the species that appear on both sides of the equation: 2 H₂(g) and 2 C(s).

This simplifies the reaction to:

C₂H₄(g) + 6 F₂(g) → 2 CF₄(g) + 4 HF(g)

This is our target reaction!

4. Calculating the Overall Enthalpy Change (ΔH)

Now, we sum the enthalpy changes of the manipulated reactions:

ΔH = ΔH₁' + ΔH₂' + ΔH₃'

ΔH = (−1074 kJ) + (−1360 kJ) + (−52.3 kJ)

ΔH = −2486.3 kJ

Final Result and Conclusion

Result

The enthalpy change (ΔH) for the reaction of ethene (C₂H₄) with fluorine (F₂) to produce carbon tetrafluoride (CF₄) and hydrogen fluoride (HF) is:

ΔH = -2486.3 kJ

Conclusion

This calculation, performed using Hess's Law, demonstrates the power of thermochemical principles in predicting the energy changes associated with chemical reactions. The negative value of ΔH indicates that the reaction is highly exothermic, meaning it releases a significant amount of heat. This information is crucial for understanding the reaction's feasibility, energy requirements, and potential applications. By understanding and applying concepts such as Hess's Law, we can gain valuable insights into the thermodynamics of chemical reactions.

The key takeaways from this calculation are:

  • Hess's Law is a valuable tool for calculating enthalpy changes for reactions that are difficult to measure directly.
  • By manipulating and combining known reactions, we can determine the enthalpy change for a target reaction.
  • The negative value of ΔH indicates that the reaction is exothermic and releases heat.
  • Understanding enthalpy changes is crucial for predicting reaction feasibility and energy requirements.

In summary, the reaction of ethene with fluorine is a highly exothermic process, releasing 2486.3 kJ of heat. This detailed calculation underscores the significance of thermochemistry in understanding and predicting chemical behavior.

Keywords for SEO

  • Enthalpy change (ΔH)
  • Hess's Law
  • Ethene reaction with fluorine
  • Carbon tetrafluoride
  • Hydrogen fluoride
  • Exothermic reaction
  • Thermochemistry
  • Heat of reaction
  • Chemical thermodynamics
  • Enthalpy calculation