The fuel in high-efficiency natural-gas vehicles consists primarily of methane (CH 4 ). (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

Hello everyone. So in this video we want to see the maximum amount of useful work that can be achieved by burning one mole of our ethanol under center conditions. So our key word here is going to be burning because burning is a combustion reaction. So first thing I'm gonna do is go ahead and route the combustion reaction for this problem. So that's going to be when again, starting off with our ethanol, the C two H five oh H. Which is a gas is gonna go ahead and react with three moles of our oxygen gas to give us two moles of our carbon dioxide. And that's going to also give us three moles of liquid water. So at constant temperature and pressure, the maximum work is equal to our delta G. And r delta G is going to equal to the delta G of my products, my sc delta G of my reactant. So just using this sort of table here, we're gonna go ahead and plug those values into this equation here, let's go ahead and do that. Then so again, our maximum work here is equal to, let's see here from my products, we have our carbon dioxide are two moles of carbon dioxide. So we have two moles and the corresponding delta G value for that is going to be negative 394.4 killer jules Permal. And then we also have our three moles of water. So three moles multiplied by negative 271.13 killer jewels per mole. And then we're gonna go ahead and subtract that of course with the delta G. Of my reactant putting the second role here. So we have one mole of our ethanol And the Delta G value for that is negative. 1 68.5 kill a jules Permal. And of course we're going to add that with the second starting reagents, which is going to be our oxygen gas. So we have three moles of that And the corresponding delta G is zero killer joules per mole. So once we put all that into the calculator, we get that. The maximum work is negative. 1331.69 kg joules. So we see here that the work is negative. This negative sign means that the work that's done by the system on the on the surroundings. So our answer then our final answer is that the maximum amount of work of useful work that the system can achieve is 133.1. Or let's see here. 1331.7 kg Joel's alright. And this right here is going to be my final answer for this problem. Thank you all so much for watching

Ch.19 - Chemical Thermodynamics

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Brown 15th Edition

Ch.19 - Chemical Thermodynamics

Problem 74b

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Chapter 19, Problem 74b

The fuel in high-efficiency natural-gas vehicles consists primarily of methane (CH₄). (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

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Identify the chemical reaction involved: The combustion of methane (CH4) in the presence of oxygen (O2) to produce carbon dioxide (CO2) and water (H2O). The balanced chemical equation is CH4 + 2O2 → CO2 + 2H2O.

Understand the concept of Gibbs free energy (ΔG), which is used to determine the maximum amount of non-expansion work that can be obtained from a chemical reaction at constant temperature and pressure. The equation for Gibbs free energy is ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

Look up standard enthalpy (ΔH°) and standard entropy (ΔS°) values for the reactants and products at 298 K (25°C). These values are typically found in thermodynamic tables.

Calculate the standard change in enthalpy (ΔH°) and the standard change in entropy (ΔS°) for the reaction using the formula: ΔH° = ΣH°(products) - ΣH°(reactants) and ΔS° = ΣS°(products) - ΣS°(reactants).

Substitute the values of ΔH°, ΔS°, and T (298 K) into the Gibbs free energy equation to find ΔG°, which represents the maximum amount of useful work under standard conditions.

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Key Concepts

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

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is crucial for determining the spontaneity of a reaction; a negative change in Gibbs Free Energy indicates that a process can perform useful work. In the context of methane combustion, calculating the Gibbs Free Energy change helps assess the maximum work output from the fuel.

Standard Conditions

Standard conditions refer to a set of specific conditions used as a reference point in thermodynamics, typically defined as 1 bar of pressure and a specified temperature, usually 25°C (298 K). These conditions allow for consistent comparisons of thermodynamic data, such as enthalpy and Gibbs Free Energy. Understanding standard conditions is essential for accurately calculating the maximum work from methane combustion.

Combustion Reaction

A combustion reaction is a chemical process in which a substance (usually a hydrocarbon like methane) reacts with oxygen to produce carbon dioxide, water, and energy. The stoichiometry of the reaction and the enthalpy change associated with it are vital for determining the energy released and the potential work that can be harnessed. In the case of methane, the complete combustion reaction is CH4 + 2O2 → CO2 + 2H2O, which releases significant energy.

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Combustion Apparatus

Related Practice

Methanol (CH₃OH) can be made by the controlled oxidation of methane: CH₄(g) + 12 O₂(g) → CH₃OH(g) (b) Will ΔG for the reaction increase, decrease, or stay unchanged with increasing temperature?

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Textbook Question

(a) Using data in Appendix C, estimate the temperature at which the free-energy change for the transformation from I₂(s) to I₂(g) is zero. (b) Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of I₂. (c) Which of the values in part (b) is closer to the value you obtained in part (a)?

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Textbook Question

The fuel in high-efficiency natural-gas vehicles consists primarily of methane (CH₄). (a) How much heat is produced in burning 1 mol of CH₄(g) under standard conditions if reactants and products are brought to 298 K and H₂O(l) is formed?

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Textbook Question

Consider the reaction 2 NO₂(g) → N₂O₄(g). (a) Using data from Appendix C, calculate ΔG° at 298 K. (b) Calculate ΔG at 298 K if the partial pressures of NO₂ and N₂O₄ are 0.40 atm and 1.60 atm, respectively.

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Textbook Question

Consider the reaction 3 CH₄(g) → C₃H₈(g) + 2 H₂(g). (a) Using data from Appendix C, calculate ΔG° at 298 K.

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Textbook Question

Consider the reaction 3 CH₄(g) → C₃H₈(g) + 2 H₂(g). (b) Calculate ΔG at 298 K if the reaction mixture consists of 40.0 atm of CH₄, 0.0100 atm of C₃H₈(g), and 0.0180 atm of H₂.

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The fuel in high-efficiency natural-gas vehicles consists primarily of methane (CH4). (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

Verified Solution

Key Concepts

Gibbs Free Energy

Standard Conditions

Combustion Reaction

The fuel in high-efficiency natural-gas vehicles consists primarily of methane (CH₄). (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?