Question

From the enthalpies of reaction calculate \(\Delta H\) for the reaction of ethylene with \(\mathrm{F}_{2}\) $$ \mathrm{C}_{2} \mathrm{H}_{4}(g)+6 \mathrm{~F}_{2}(g)-\cdots 2 \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g) $$

Short answer

The short version of the answer to the given problem is to use Hess's Law to calculate the change in enthalpy, \(\Delta H\), for the reaction of ethylene with fluorine gas. Break the overall reaction into simpler intermediate reactions: 1. Formation of carbon tetrafluoride: \(C(s) + 2F_2(g) \rightarrow CF_4(g);\, \Delta H_1\) 2. Formation of hydrogen fluoride: \(H_2(g) + F_2(g) \rightarrow 2HF(g);\, \Delta H_2\) 3. Formation of ethylene: \(2C(s) + 2H_2(g) \rightarrow C_2H_4(g);\, \Delta H_3\) Combine the intermediate reactions to match the overall reaction equation by multiplying them by the necessary coefficients and then add the balanced reactions together. Finally, calculate the overall enthalpy change using the enthalpy changes of each intermediate reaction: $$ \Delta H = 2\Delta H_1 + 4\Delta H_2 - \Delta H_3 $$

Step-by-step solution

Identify the intermediate reactions

To apply Hess's Law, we need to identify intermediate reactions that, when combined, will result in the overall reaction. We consider the following reactions: 1. Formation of carbon tetrafluoride from carbon and fluorine: $$ C(s) + 2F_2(g) \rightarrow CF_4(g);\, \Delta H_1 $$ 2. Formation of hydrogen fluoride from hydrogen and fluorine: $$ H_2(g) + F_2(g) \rightarrow 2HF(g);\, \Delta H_2 $$ 3. Formation of ethylene from carbon and hydrogen: $$ 2C(s) + 2H_2(g) \rightarrow C_2H_4(g);\, \Delta H_3 $$

Combine the intermediate reactions to obtain the overall reaction

Multiply the intermediate reactions by their necessary coefficients to match the overall reaction equation: 1. Multiply the first reaction by 2: $$ 2[C(s) + 2F_2(g) \rightarrow CF_4(g)];\, 2\Delta H_1 $$ 2. Multiply the second reaction by 4: $$ 4[H_2(g) + F_2(g) \rightarrow 2HF(g)];\, 4\Delta H_2 $$ 3. Reverse the third reaction and don't change the coefficients: $$ C_2H_4(g) \rightarrow 2C(s) + 2H_2(g);\, -\Delta H_3 $$ Now, add these balanced reactions together: $$ 2C_2H_4(g)+ 12F_2(g) \rightarrow 4C(s) + 2CF_4(g) + 8H_2(g) + 8HF(g) $$ The final reaction should now match the overall reaction given in the problem: $$ C_2H_4(g) + 6F_2(g) \rightarrow 2CF_4(g) + 4HF(g) $$

Calculate the overall enthalpy change

According to Hess's Law, the overall enthalpy change for the reaction is the sum of the enthalpy changes of the intermediate reactions multiplied by their coefficients: $$ \Delta H = 2\Delta H_1 + 4\Delta H_2 - \Delta H_3 $$ By substituting the given enthalpies of reaction for the intermediate reactions, we can calculate the value of \(\Delta H\).

Key concepts

Enthalpy Calculations

Enthalpy calculations are crucial when determining the heat change during a chemical reaction. Enthalpy, represented as \( \Delta H \), measures the heat absorbed or released at constant pressure.
To perform accurate enthalpy calculations:

• Use the known enthalpy changes of intermediate reactions involved.
• Apply Hess's Law, which states that the total enthalpy change is independent of the specific path, whether a reaction occurs in one step or multiple steps.
• Sum the enthalpy changes of each step, adjusting for the coefficients used in balancing the reactions.

By carefully combining enthalpy values, you determine the overall heat change for the entire reaction.

Reaction Enthalpy

Reaction enthalpy is the amount of energy absorbed or released during a chemical reaction. It provides insight into whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).
Key points about reaction enthalpy include:

• It is typically measured in kilojoules per mole (kJ/mol).
• An exothermic reaction has a negative \( \Delta H \) value, indicating energy release.
• An endothermic reaction has a positive \( \Delta H \) value, indicating energy absorption.

Understanding reaction enthalpy helps in predicting reaction behavior and energy requirements.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of bonds. This transformation is driven by changes in energy levels.
Here’s how chemical reactions are relevant in calculating enthalpy:

• Identify the reactants and products involved in the reaction.
• Use balanced chemical equations to ensure mass and energy are conserved.
• Apply Hess's Law by breaking down the overall reaction into intermediate steps, making it easier to calculate enthalpy changes.

A clear understanding of chemical reactions allows precise enthalpy calculations.

Intermediate Reactions

Intermediate reactions are steps that can be combined to replicate the overall chemical reaction. They are especially useful when applying Hess's Law.
Steps to using intermediate reactions:

• Identify each sub-reaction that, when summed, equals the overall reaction.
• Adjust the coefficients of these reactions to match the total balanced reaction.
• Reverse reactions if necessary by changing the sign of their enthalpy values.

Utilizing intermediate reactions simplifies the process of finding the total change in enthalpy for the main reaction.