Ch.9 - Thermochemistry: Chemical Energy

Problem 143f

Chapter 9, Problem 143f

Methanol (CH₃OH) is made industrially in two steps from CO and H₂. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane (CH₄):
Step 1. CO(g) + 2 H₂(g) → CH₃OH(l) ΔS° = –332 J/K
Step 2. CH₃OH(l) → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K
(f) Calculate ΔH° for step 2.

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Identify the given values and the required value. Here, the given value is the standard entropy change (ΔS°) for step 2, which is 162 J/K. The required value is the standard enthalpy change (ΔH°) for step 2.

Recall the Gibbs free energy equation: ΔG° = ΔH° - TΔS°. To find ΔH°, rearrange the equation to ΔH° = ΔG° + TΔS°.

Determine the temperature (T) at which the reaction occurs. If not specified, assume standard conditions (298 K).

Calculate ΔG° for step 2 using the standard free energy change equation for the reaction. If ΔG° is not provided, it may need to be calculated or approximated based on other given data or standard free energy values.

Substitute the values of ΔG°, T, and ΔS° into the rearranged Gibbs free energy equation to solve for ΔH°.

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Key Concepts

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

Enthalpy Change (ΔH°)

Enthalpy change, denoted as ΔH°, refers to the heat content change of a system at constant pressure during a chemical reaction. It indicates whether a reaction is exothermic (releases heat, ΔH° < 0) or endothermic (absorbs heat, ΔH° > 0). Understanding ΔH° is crucial for predicting the energy requirements and feasibility of reactions, especially in industrial processes.

Gibbs Free Energy and Entropy (ΔS°)

Gibbs free energy combines enthalpy and entropy to determine the spontaneity of a reaction. The change in entropy (ΔS°) reflects the disorder of a system; a positive ΔS° indicates increased disorder. In the context of the given reactions, ΔS° values help assess the thermodynamic favorability of the steps involved in methanol production and its conversion to hydrocarbons.

Thermodynamic Relationships

Thermodynamic relationships, such as the Gibbs-Helmholtz equation, connect ΔH°, ΔS°, and the temperature of a reaction to predict its spontaneity. For reactions, the relationship ΔG° = ΔH° - TΔS° is fundamental, where ΔG° is the change in Gibbs free energy. This relationship is essential for calculating ΔH° for step 2, as it allows the integration of entropy changes into the enthalpy calculations.

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Related Practice

Textbook Question

Methanol (CH₃OH) is made industrially in two steps from CO and H₂. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane (CH₄):

Step 1. CO(g) + 2 H₂(g) → CH₃OH(l) ΔS° = –332 J/K

Step 2. CH₃OH(l) → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K

(a) Calculate ΔH° in kilojoules for step 1.

463

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Textbook Question

Methanol (CH₃OH) is made industrially in two steps from CO and H₂. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane (CH₄):

Step 1. CO(g) + 2 H₂(g) S CH₃OH(l) ΔS° = - 332 J/K

Step 2. CH₃OH(l) → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K

(e) In what temperature range is step 1 spontaneous?

391

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Textbook Question

Ethyl chloride 1C2H5Cl2, a substance used as a topical anes-thetic, is prepared by reaction of ethylene with hydrogen chloride: C2H41g2 + HCl1g2 ¡ C2H5Cl1g2 ΔH° = - 72.3 kJ How much PV work is done in kilojoules, and what is the value of ΔE in kilojoules if 89.5 g of ethylene and 125 g of HCl are allowed to react at atmospheric pressure and the volume change is - 71.5 L?

904

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Textbook Question

We said in Section 9.1 that the potential energy of water at the top of a dam or waterfall is converted into heat when the water dashes against rocks at the bottom. The potential energy of the water at the top is equal to EP = mgh, where m is the mass of the water, g is the acceleration of the falling water due to gravity 1g = 9.81 m>s22, and h is the height of the water. Assuming that all the energy is converted to heat, calculate the temperature rise of the water in degrees Celsius after falling over California's Yosemite Falls, a distance of 739 m. The specific heat of water is 4.18 J/(g·K).

2019

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Textbook Question

When a gaseous compound X containing only C, H, and Ois burned in O2, 1 volume of the unknown gas reacts with3 volumes of O2 to give 2 volumes of CO2 and 3 volumesof gaseous H2O. Assume all volumes are measured at thesame temperature and pressure.(d) Combustion of 5.000 g of X releases 144.2 kJ heat.Look up ΔH°f values for CO21g2 and H2O1g2 inAppendix B, and calculate ΔH°f for compound X.

497

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