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Ch.20 - Electrochemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.20 - ElectrochemistryProblem 111b
Chapter 20, Problem 111b

The Haber process is the principal industrial route for converting nitrogen into ammonia: N2(g) + 3 H2(g) → 2 NH3(g) (b) Using the thermodynamic data in Appendix C, calculate the equilibrium constant for the process at room temperature.

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1
Identify the relevant thermodynamic data needed for the calculation, such as the standard enthalpy change (\( \Delta H^\circ \)) and the standard entropy change (\( \Delta S^\circ \)) for the reaction.
Use the Gibbs free energy equation \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \) to calculate the standard Gibbs free energy change (\( \Delta G^\circ \)) for the reaction at room temperature (298 K).
Convert the calculated \( \Delta G^\circ \) from joules to kilojoules if necessary, to maintain consistency with the units typically used in thermodynamic tables.
Use the relationship between Gibbs free energy and the equilibrium constant \( K \), given by \( \Delta G^\circ = -RT \ln K \), where \( R \) is the universal gas constant (8.314 J/mol·K), to solve for \( K \).
Rearrange the equation to solve for the equilibrium constant \( K \): \( K = e^{-\Delta G^\circ / RT} \), and substitute the values to find \( K \).

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Key Concepts

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

Haber Process

The Haber process is a chemical reaction that synthesizes ammonia from nitrogen and hydrogen gases. It is represented by the equation N₂(g) + 3 H₂(g) → 2 NH₃(g). This process is crucial for producing fertilizers and has significant implications for agriculture and food production.
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Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It provides insight into the extent of a reaction and whether it favors products or reactants. For the Haber process, K can be calculated using the concentrations of NH₃, N₂, and H₂ at equilibrium.
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Thermodynamic Data

Thermodynamic data includes information such as enthalpy, entropy, and Gibbs free energy, which are essential for calculating the equilibrium constant. These values help predict the direction of a reaction and its spontaneity. In the context of the Haber process, thermodynamic data allows for the determination of K at room temperature, facilitating the understanding of the reaction's behavior under standard conditions.
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Related Practice
Textbook Question

Aqueous solutions of ammonia (NH3) and bleach (active ingredient NaOCl) are sold as cleaning fluids, but bottles of both of them warn: 'Never mix ammonia and bleach, as toxic gases may be produced.' One of the toxic gases that can be produced is chloroamine, NH2Cl. (a) What is the oxidation number of chlorine in bleach? (active ingredient NaOCl) are sold as cleaning fluids, but bottles of both of them warn: “Never mix ammonia and bleach, as toxic gases may be produced.” One of the toxic gases that can be produced is chloroamine, NH2Cl. (b) What is the oxidation number of chlorine in chloramine? (d) Another toxic gas that can be produced is nitrogen trichloride, NCl3. What is the oxidation number of N in nitrogen trichloride?

Textbook Question

Aqueous solutions of ammonia 1NH32 and bleach (active ingredient NaOCl) are sold as cleaning fluids, but bottles of both of them warn: 'Never mix ammonia and bleach, as toxic gases may be produced.' One of the toxic gases that can be produced is chloroamine, NH2Cl. (e) Is N oxidized, reduced, or neither, upon the conversion of ammonia to nitrogen trichloride?

Textbook Question

Calculate the number of kilowatt-hours of electricity required to produce 1.0 * 103 kg (1 metric ton) of aluminum by electrolysis of Al3+ if the applied voltage is 4.50 V and the process is 45% efficient.