Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problem 146

Chapter 18, Problem 146

For a process to be spontaneous, the total entropy of the system and its surroundings must increase; that isΔStotal = ΔSsystem + ΔSsurr 7 0 for a spontaneous processFurthermore, the entropy change in the surroundings, ΔSsurr, is related to the enthalpy change for the process by the equa- tion ΔSsurr = - ΔH>T.(b) What is the value of ΔSsurr for the photosynthesis of glu- cose from CO2 at 298 K?6 CO21g2 + 6 H2O1l2 S C6H12O61s2 + 6 O21g2ΔG° = 2879 kJΔS° = - 262 J>K

Verified step by step guidance

Identify the given values: ΔG° (change in Gibbs free energy) is 2879 kJ, ΔS° (change in entropy of the system) is -262 J/K, and the temperature T is 298 K.

Convert ΔG° from kJ to J for consistency in units. Recall that 1 kJ = 1000 J.

Use the Gibbs free energy equation ΔG = ΔH - TΔS to rearrange and solve for ΔH (change in enthalpy). The equation becomes ΔH = ΔG + TΔS.

Substitute the values of ΔG, T, and ΔS into the rearranged equation to calculate ΔH.

Calculate ΔSsurr (change in entropy of the surroundings) using the equation ΔSsurr = -ΔH/T. Substitute the calculated ΔH and the given temperature T into this equation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Entropy and Spontaneity

Entropy is a measure of the disorder or randomness in a system. For a process to be spontaneous, the total entropy change (ΔStotal) of the system and its surroundings must be positive. This means that the increase in disorder in the universe is favored, which is a fundamental principle of thermodynamics.

Enthalpy and Entropy Relationship

The relationship between enthalpy change (ΔH) and entropy change in the surroundings (ΔSsurr) is given by the equation ΔSsurr = -ΔH/T, where T is the temperature in Kelvin. This equation indicates that the entropy change in the surroundings is inversely related to the temperature and directly related to the enthalpy change of the process, which is crucial for determining spontaneity.

Gibbs Free Energy

Gibbs Free Energy (ΔG) is a thermodynamic potential that helps predict the spontaneity of a process at constant temperature and pressure. A negative ΔG indicates that a process is spontaneous, while a positive ΔG suggests it is non-spontaneous. The relationship ΔG = ΔH - TΔS connects enthalpy, temperature, and entropy, providing a comprehensive view of the thermodynamic favorability of reactions.

Recommended video:

Guided course

01:51

Gibbs Free Energy of Reactions

Related Practice

Textbook Question

Consider the unbalanced equation: I₂(s) → I^-(aq) + IO₃^-(aq) (d) What pH is required for the reaction to be at equilibrium at 25°C when [I^-] = 0.10M and [IO₃^-] = 0.50 M?

317

views

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. CH₃OH₁l₂ → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K

(k) Calculate an overall ΔG°, ΔH°, and ΔS° for the formation of CH₄ from CO and H₂.

365

views

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. CH₃OH₁l₂ → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K

(m) If you were designing a production facility, would you plan on carrying out the reactions in separate steps or together? Explain.

516

views