13 -- Part 1: Spontaneous Change: Entropy and Gibbs Energy
The second law of 13-8 chemical potential and thermodynamics is related to the concepts of microstate 13-4 Criterion for Spontaneous Change.
In terms of the microstates involved, the thermodynamics of Spontaneous Chemical Change increases.
Explain how Clausius's equation can be used to get equations for calculating the change in entropy for simple physical changes.
The resulting equations should be applied to calculate the changes.
Explain how the standard mol% of a substance is obtained.
The standard molar entropies of reactants and products can be used to determine the entropy change for a chemical reaction.
The second law of thermodynamics states the relationship between energy, enthalpy, and entropy.
The van't Hoff equation can be used to discover the laws of thermodynamics in this chapter.
Our everyday experiences have conditioned us to accept that there is only one direction in which things happen.
A bouncing ball may come to rest on the floor after a chemical reaction, but a ball at rest nonspontaneously.
An ice cube placed in hot water will eventually melt, but a glass of water will not produce an ice cube.
Discuss the relationships among nail rusts in air, but a rusty nail will not naturally shed its rusty exterior to chemical potential, activity and the Gibbs produce a shiny nail.
Concepts needed to under energy of a mixture are explored in this chapter.
The concept of entropy was introduced by Clausius in 1850.
Ludwig Boltzmann proposed an alternative view of the universe.
The melting of an ice cube was shown to be equivalent to Clausius's and Boltzmann's definitions of entropy.
It is an important concept.
The dispersal of energy is measured by entropy.
In this chapter, we will continue to use a point of view that is small.
We will learn how to evaluate the changes in entropy for a variety of physical and chemical processes.
We will find out that the criterion for change considers not only the system but also the surroundings.
We will learn about another important quantity, called Gibbs energy, which can be used to understand the direction of change.
We will soon see that the criterion for change can be expressed in native terms.
We should first focus on developing a conceptual model for understanding the atten tendency.
Developing will be able to explain why certain processes are not random and others are random with the help of entropy changes.
The modern interpretation of entropy is based on the idea that a system is made up of many particles.
Adding more gas will not change the state of the gas without some external influence.
The molecule are moving in a random fashion, hitting each other or the walls of the container.
The positions, velocities, and energies of individual Molecules change from one moment to the next.
Stated another way, the gas's properties could be described by any one non interfering particles of a large number of configurations.
We suggested that the microstate of an ideal gas could be box.
Chapter 8 describes the position, velocity, and energy of every molecule in a particle confined to a gas.
The Heisenberg uncertainty principle states that the exact lational energy is quantized.
Each microstate is specified.
If you want to be consistent with quantum mechanics, you need to specify the quantum state of every particle or how the particles are distributed.
The number of microstates increases to five.
Because the energy levels are shifted to lower values, more energy levels are accessible.
To calculate some energy levels.
The total energy of this microstate is obtained by adding the particle energies.
We can increase the total energy of the system without changing the length of the box.
There is an increase in the number of energy levels accessible to the particles.
As the total energy increases, so does the number of microstates and the number of accessible energy levels.
A greater number of energy levels are accessible to the particles.
As the system expands, the number of microstates increases as the box length increases.
When the box length increases, the number of microstates increases because the various levels are lower in energy.
The number of energy levels accessible by the particles increases.
With the total energy and total space available, the number of accessible levels increases.
The number of energy levels in the system was associated with the number of ways of arranging the particles by Ludwig Boltzmann.
A bust of Ludwig.
Natural logarithms and kB are obtained for J mol-1 K-1 and mol-1 NA.
Boltzmann did not express his probability law in terms of the quantized energy levels of the particles in the system because the concept of quantization of energy was not developed during his lifetime.
The Boltzmann equation is easy to understand.
When the system only contains five particles, the enumeration of microstates is easy.
This number is not easy to understand.
For a given 1 followed by 1023 zeros, we must simply accept that.
A large number of microstates are possible.
The simplicity of equation compares the enormity of Boltzmann's digits on a piece of paper.
A new branch of physics was developed by James Clerk and others to get this result.
There is a key idea to complete the task.
Imagine flipping a coin a million times.
If we flip a coin a million times, we're pretty sure that the result will be between 50% heads and 50% tails.
Boltzmann and others realized that the most probable ones contribute the most to the state.
The initial condition is circumvented.
When the total energy, temperature, or volume changes, we want to understand how the number of microstates and entropy of the system change.
Key ideas have already been established.
At the beginning of this chapter, we said that if it is prevented from happening, the gas will expand.
To decide if the same bulb on the right has the same energy.
There is a final condition.
Two glass bulbs are joined by a stopcock.
The bulb on the left has an ideal gas of 1.00 bar pressure, and the bulb on the right does not.
The gas expands when the valve is open.
The molecules are dispersed throughout the apparatus after this expansion.
The final pressure was 0.50 bar.
The volume of the gas changes in this process.
The enthalpy change is zero.
For the same total energy, in the expanded volume there are more mal processes involving an ideal available translational energy levels among which the gas molecule can be gas.
C/H is 0.
Figure 13-1 shows that the number of microstates increases when the space available to the particles increases.
When a gas expands into a larger volume, it increases the entropy.
Before mixing a process.
The final state is the mixed state, and the initial state is the un-mixed state.
The mixing is just two expansions occurring at the same time.
The internal energy and entropy changes for gases A and B are represented after mixing.
The total volume of the neous mixing of ideal gases does not change, but the total gas enthalpy does.
The characteristic feature of net change is that before a spontaneously occurring process causes the universe to mix, each gas is confined increase.
Expansion of a gas into a vacuum exerts a partial pressure instantaneous.
Is it true that a spontaneously occurring process is 0.50 bar?
The four NO molecules are aligned.
There are no other microstates like this one.
When the temperature is raised just enough to allow a single NO molecule to rotate, what happens?
On, no a no on, no a no on, and on, no a no on, and on, no a no on, and on, no a no on, and on, no a no on, and on, no a no on, and on, no a no
As the energy of the system increases, the number of microstates increases, thus increasing the system's entropy.
Four neon atoms are in a one-dimensional box.
The system is expanded from 905 pm to 1810 pm at a fixed total energy of 14.0.
For each atom, use a different color.
Keeping in mind that the total energy of the system must be equal to 14.0 for the initial and final states, we determine the number of different ways that the atoms can be placed.
We use the number of microstates for the initial and final states in Boltzmann's equation to calculate the entropy change.
To use the particle-in-a-box energy level expression, we need to know the mass of a neon atom.
There are 4 microstates for the system in the 905 pm box, and 8 microstates for the system in the 1810 pm box, each with a total energy of 14.0.
As volume increases, the number of microstates and the entropy increase.
Mental pictures can be constructed from ideas from earlier sections to understand how a system changes during a process.
We can make qualitative predictions about change by focusing on two factors.
A less structured liquid is used in the melting of ice.
Molecules that were fixed in position in the solid are now free to move.
The molecule has gained some motion.
The number of accessible energy levels has increased.
A less structured gas is replaced by a liquid in the vaporization process.
Molecules in the gaseous state have more accessible energy levels than those in the liquid state because they can move within a large free volume.
The gas has more energy in it than the liquid.
The liquid state's entropy is lower than that of the gaseous state.
In the dissolution of Ammonium nitrate in water, a mixture of ion and water are used to replace the pure liquid.
This situation is more involved than the first two because of the clustering of water molecule around the ion because of ion-dipole forces.
The overall dissolution process, C/S 7 0, is dominated by the increase in entropy that accompanies the destruction of the solid's lattice.
The fact that heat must be absorbed in each process outweighs the fact that it is a spontaneously occurring process.
Liquid solutions are formed from solid objects.
Solids or liquids form gases.
The melting of a solid, the evaporation of a liquid, and the dissolving of a solute results in an increase in entropy.
The ion-dipole forces do not exist in the solvent solution.
Predict the outcome of each of the following processes.
2 N21g2 + 4 H2O1g2
SO2 to SO3
The generalizations were summarized on the previous page.
Three of the processes are chemical reactions, and we should first consider whether the number of molecule of gas increases or decreases.