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Chapter 17: Problem 2

Assess the validity of the statement, "In all spontaneous processes, the system moves toward a state of lowest energy." Correct any errors you identify.

Short Answer

Expert verified
The statement is inaccurate; spontaneity depends on minimizing Gibbs Free Energy, not just energy.

Step by step solution

01

Understand Spontaneity in Thermodynamics

Spontaneity in a thermodynamic process refers to the tendency of a system to undergo changes that lead to a particular state naturally, without the need for external work. Spontaneous processes are often associated with an increase in entropy, rather than necessarily a decrease in energy.
02

Identify Gibbs Free Energy Role

The Gibbs Free Energy (G) is a useful criterion for determining the spontaneity of processes at constant temperature and pressure. The change in Gibbs Free Energy, represented by \( \Delta G \), determines spontaneity:- \( \Delta G < 0 \): Process is spontaneous.- \( \Delta G > 0 \): Process is non-spontaneous.- \( \Delta G = 0 \): System is in equilibrium.
03

Decompose Gibbs Free Energy Formula

The formula for Gibbs Free Energy: \[\Delta G = \Delta H - T\Delta S\]Where:- \( \Delta H \) is the change in enthalpy (energy change of the system).- \( \Delta S \) is the change in entropy.- \( T \) is the absolute temperature.Spontaneity depends on both entropy and enthalpy changes, not just energy.
04

Analyze the Given Statement

The statement claims that spontaneity moves the system toward a state of lowest energy. While processes often tend toward lower energy states, they also include entropy considerations which are equally important.Hence, the statement is not entirely correct; spontaneity corresponds to minimizing \( \Delta G \), not only energy.
05

Correct the Statement

A more accurate statement would be: "In all spontaneous processes, the system moves toward minimizing Gibbs Free Energy, considering both enthalpy and entropy changes."

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gibbs Free Energy
Gibbs Free Energy provides a way to predict whether a process will occur spontaneously under constant temperature and pressure. It is represented by the letter \( G \), and it's a crucial concept in thermodynamics. The change in Gibbs Free Energy, \( \Delta G \), helps us understand the spontaneity of a system:
  • \( \Delta G < 0 \): The process is spontaneous.
  • \( \Delta G > 0 \): The process is non-spontaneous.
  • \( \Delta G = 0\): The system is at equilibrium.
The formula for calculating Gibbs Free Energy change is \[ \Delta G = \Delta H - T\Delta S \]. Here, \( \Delta H \) is the change in enthalpy, \( \Delta S \) is the change in entropy, and \( T \) is the temperature in Kelvin. Gibbs Free Energy serves as a bridge between energy and entropy, balancing both to determine if a process will progress on its own.
Spontaneous Processes
In thermodynamics, a spontaneous process is one that occurs naturally without any external energy input. Generally, these processes lead a system to a more favorable state in terms of energy and entropy. A common misconception is that a process lowers energy, but it's also about increasing entropy. The key factors driving spontaneity include:
  • An increase in entropy (disorder of the system).
  • A decrease in Gibbs Free Energy.
Spontaneous processes can vary from simple chemical reactions to more complex phenomena like rusting or ice melting. They move systems toward equilibrium, minimizing free energy, not just lowering energy alone.
Entropy
Entropy measures the degree of disorder or randomness in a system. It's a central concept that strongly impacts spontaneity. Higher entropy usually means greater disorder.The Second Law of Thermodynamics states that for any spontaneous process, the total entropy of a system and its surroundings always increases.Some key points about entropy include:
  • It's represented by \( S \).
  • Spontaneous processes often increase entropy.
  • It explains why certain reactions favor the formation of products over reactants.
Understanding entropy helps in grasping why spontaneous processes may proceed seemingly towards more "chaotic" states.
Enthalpy
Enthalpy is a measure of the total energy within a system, including internal energy and the energy required to displace its environment. Represented by \( H \), it plays a vital role in determining the spontaneity of processes, alongside entropy.While spontaneity involves minimizing Gibbs Free Energy rather than solely focusing on decreasing energy (enthalpy), the latter still plays a crucial part. Here are some important aspects of enthalpy:
  • It's involved in the calculation of Gibbs Free Energy as \( \Delta G = \Delta H - T\Delta S \).
  • Positive \( \Delta H \) implies an endothermic process (absorbing heat), while negative \( \Delta H \) indicates an exothermic process (releasing heat).
  • Enthalpy helps predict whether a process will release or absorb energy.
Balancing enthalpy with entropy changes allows a better understanding of the thermodynamic behavior of systems.

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Most popular questions from this chapter

Predict the sign of the entropy for the reaction $$ 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ Give an explanation, based on entropy and the Second Law, of why this reaction occurs spontaneously.

Using thermodynamic equilibrium arg uments, explain why a substance with weaker intermolecular forces has a greater vapor pressure than one with stronger intermolecular forces.

Why does the entropy of a gas increase as the volume of the gas increases? Why does the entropy decrease as the pressure increases?

For the reaction \(\mathrm{H}_{2}(g) \rightarrow 2 \mathrm{H}(g)\), predict the sign of both \(\Delta\left(\mathrm{H}^{\circ}\right)\) and \(\Delta\left(S^{\circ}\right)\). Should this reaction be spontaneous at high temperature or at low temperature? Explain.

Each possible sequence of the 52 cards in a deck is equally probable. However, when you shuffle a deck and then examine the sequence, the deck is never ordered. Explain why in terms of microstates, macrostates, and entropy.
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