Hess's law can be used to calculate reaction enthalpies for hypothetical processes that can't be carried out in the labo- ratory. Set up a Hess's law cycle that will let you calculate ∆H° for the conversion of methane to ethylene: 2 CH4(g) → C2H4(g) + 2 H2(g) You can use the following information: 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(l) ∆H° = -3120.8 kJ CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) ∆H° = -890.3 kJ C2H4(g) + H2(g) → C2H6(g) ∆H° = -136.3 kJ H2O(l) ∆H°f = -285.8 kJ/mol

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Identify the target reaction: 2 CH4(g) → C2H4(g) + 2 H2(g).

Write the given reactions and their enthalpies: (1) 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(l), ΔH° = -3120.8 kJ; (2) CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l), ΔH° = -890.3 kJ; (3) C2H4(g) + H2(g) → C2H6(g), ΔH° = -136.3 kJ.

Reverse reaction (3) to get C2H6(g) → C2H4(g) + H2(g), changing the sign of ΔH° to +136.3 kJ.

Use reaction (2) twice to represent the combustion of 2 CH4(g), resulting in 2 CO2(g) + 4 H2O(l) and a total ΔH° of 2(-890.3 kJ).

Combine the modified reactions to form a Hess's law cycle: 2 CH4(g) → 2 CO2(g) + 4 H2O(l) (from reaction 2), 2 C2H6(g) → 4 CO2(g) + 6 H2O(l) (from reaction 1), and C2H6(g) → C2H4(g) + H2(g) (reversed reaction 3). Calculate ΔH° for the target reaction by adding the enthalpies of these steps.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps taken to complete the reaction. This principle allows chemists to calculate the enthalpy change of a reaction by using the enthalpy changes of related reactions, making it particularly useful for reactions that are difficult to measure directly.

Enthalpy of Formation (∆H°f)

The enthalpy of formation (∆H°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. This value is crucial for calculating reaction enthalpies using Hess's Law, as it provides a reference point for the energy changes associated with the formation of compounds from their constituent elements.

Standard Enthalpy Change (∆H°)

The standard enthalpy change (∆H°) refers to the heat change that occurs at constant pressure when reactants are converted to products under standard conditions (1 atm pressure and a specified temperature, usually 25°C). This value is essential for understanding the energy dynamics of chemical reactions and is used in Hess's Law calculations to derive the enthalpy changes for complex reactions.

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What is Hess's law, and why does it 'work'?

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