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Ch.5 - Thermochemistry
All textbooksBrown 15th EditionCh.5 - ThermochemistryProblem 78
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Chapter 5, Problem 78

Calcium carbide (CaC2) reacts with water to form acetylene (C2H2) and Ca(OH)2. From the following enthalpy of reaction data and data in Appendix C, calculate H°f for CaC2(s): CaC2(s) + 2 H2O(l) → Ca(OH2)(s) + C2H2(g) ΔH° = -127.2 kJ

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Identify the given chemical reaction: \( \text{CaC}_2(s) + 2 \text{H}_2\text{O}(l) \rightarrow \text{Ca(OH)}_2(s) + \text{C}_2\text{H}_2(g) \) with \( \Delta H^\circ = -127.2 \text{ kJ} \).
Use the formula for the standard enthalpy change of reaction: \( \Delta H^\circ = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants}) \).
Look up the standard enthalpy of formation values for \( \text{Ca(OH)}_2(s) \) and \( \text{C}_2\text{H}_2(g) \) in Appendix C.
Set up the equation: \( -127.2 \text{ kJ} = [\Delta H^\circ_f(\text{Ca(OH)}_2) + \Delta H^\circ_f(\text{C}_2\text{H}_2)] - [\Delta H^\circ_f(\text{CaC}_2) + 2 \times \Delta H^\circ_f(\text{H}_2\text{O})] \).
Solve for \( \Delta H^\circ_f(\text{CaC}_2) \) using the known values from Appendix C and the given \( \Delta H^\circ \).

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Key Concepts

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

Enthalpy of Reaction

Enthalpy of reaction, denoted as ΔH, is the heat change associated with a chemical reaction at constant pressure. It indicates whether a reaction is exothermic (releases heat, ΔH < 0) or endothermic (absorbs heat, ΔH > 0). In the given reaction, the negative ΔH value of -127.2 kJ signifies that the reaction releases energy, which is crucial for calculating the standard enthalpy of formation.
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Standard Enthalpy of Formation (H°f)

The standard 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. It is a key concept in thermodynamics and is used to calculate the enthalpy changes in reactions. To find H°f for CaC2(s), one must apply Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.
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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 or the pathway taken. This principle allows chemists to calculate the enthalpy change of a reaction indirectly by using known enthalpy changes of other reactions. In this case, it can be applied to derive the standard enthalpy of formation for CaC2(s) by combining the enthalpy of the given reaction with the enthalpies of formation of the products and reactants.
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