Name: entropy in matter and energy changes
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 39 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Chemistry

CH.7

CH.7.d

Entropy

Entropy, or S, is a measure of the randomness or disorder of a thermodynamic system, such as the randomness in the arrangement of atoms, molecules, or ions. The greater the disorder in a system, the higher the entropy.
Entropy is a state function, which means that the change in entropy of a process can be calculated by finding the difference between the final state and the initial state, regardless of the path taken.
The entropy of a system can be expressed by Boltzmann&#8217;s equation, in which S is equal to Boltzmann&#8217;s constant, k, multiplied by the natural log of the number of microstates, W. 
Microstates are the distinct energetically equivalent configurations that are possible for the atoms and molecules in a given system.
Consider a system that contains two atoms with a total of two units of energy. This energy can be distributed between the two atoms in three different ways: both units with the first atom, both units with the second atom, or one unit with each atom. Thus, this system has three potential microstates, all of which are energetically equivalent.
It follows that entropy increases in proportion to the number of atoms in a molecule and its molecular weight. For example, under standard conditions of 25 &#176;C and 1 atm, the entropy of 1 mole of sulfuric acid is greater than the entropy of 1 mole of water.
Additionally, the entropy of a mixture is greater than the entropy of its pure components, as increased complexity results in a higher number of possible microstates.
The entropy of a system also increases with temperature. As the temperature increases, so does the kinetic energy resulting in an increase in the number of possible microstates. 
The physical state of matter is an indicator of a substance&#8217;s relative entropy. The entropy of a given solid is always less than the liquid form of the same substance, and the entropy of the liquid form is always less than that of the gas.
The molecules in a gas are far apart from each other and have many more possible microstates compared to molecules in a liquid or solid. Solids, on the other hand, are much more organized with fewer microstates, thereby resulting in lower entropy.

entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a thermodynamic system. The entropy may either increase (&#916;S &#62; 0, disorder increases) or decrease (&#916;S &#60; 0, disorder decreases) as a result of physical or chemical changes to the system. The change in entropy is the difference between the entropies of the final and initial states: &#916;S = Sf - Si.
Boltzmann&#8217;s Theory of Microstates
A microstate is a specific configuration of all the locations and energies of the atoms or molecules that make up a system. The relation between a system&#8217;s entropy and the number of possible microstates (W) is S = k ln W, where k is the Boltzmann constant, 1.38 &#215; 10&#8722;23 J/K.
The change in entropy is
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A system that has a greater number of possible microstates is more disordered (higher entropy) than an ordered system (lower entropy) with a fewer number of microstates. For processes involving an increase in the number of microstates, Wf &#62; Wi, the entropy of the system increases and &#916;S &#62; 0. Conversely, processes that reduce the number of microstates, Wf &#60; Wi, yield a decrease in system entropy, &#916;S &#60; 0.
Consider the distribution of an ideal gas between two connected flasks. Initially, the gas molecules are confined to just one of the two flasks. Opening the valve between the flasks increases the volume available to the gas molecules (energy is more dispersed through a larger domain) and, correspondingly, the number of microstates possible for the system. Since Wf &#62; Wi, the expansion process involves an increase in entropy (&#916;S &#62; 0) and is spontaneous.
A similar approach may be used to describe the spontaneous flow of heat. A hot cup of tea evenly disperses its energy over a larger number of air particles in the cooler room, resulting in a larger number of microstates.
Generalizations Concerning Entropy
The relationships between entropy, microstates, and matter/energy dispersal allow generalizations to be made regarding the relative entropies of substances and to predict the sign of entropy changes for chemical and physical processes.
In the solid phase, the atoms or molecules are restricted to nearly fixed positions with respect to each other and are capable of only modest oscillations about these positions. Thus, the number of microstates is relatively small. In the liquid phase, the atoms or molecules are free to move over and around each other, though they remain in relatively close proximity to one another. Thus, the number of microstates is correspondingly greater than for the solid. As a result, Sliquid &#62; Ssolid and the process of converting a substance from solid to liquid (melting) is characterized by an increase in entropy, &#916;S &#62; 0. By the same logic, the reciprocal process (freezing) exhibits a decrease in entropy, &#916;S &#60; 0.
 In the gaseous phase, a given number of atoms or molecules occupy a much greater volume than the liquid phase, corresponding to a much greater number of microstates. Consequently, for any substance, Sgas &#62; Sliquid &#62; Ssolid and the processes of vaporization and sublimation likewise involve increases in entropy, &#916;S &#62; 0. Likewise, the reciprocal phase transitions&#8212;condensation and deposition&#8212;involve decreases in entropy, &#916;S &#60; 0.
According to kinetic-molecular theory, the temperature of a substance is proportional to the average kinetic energy of its particles. Raising the temperature of a substance will result in more extensive vibrations of the particles in solids and more rapid translations of the particles in liquids and gases. At higher temperatures, the distribution of kinetic energies among the atoms or molecules of the substance is also more dispersed than at lower temperatures. Thus, the entropy for any substance increases with temperature.
The entropy of a substance is influenced by the structure of the particles (atoms or molecules) that comprise the substance. With regard to atomic substances, heavier atoms possess greater entropy at a given temperature than lighter atoms, which is a consequence of the relation between a particle&#8217;s mass and the spacing of quantized translational energy levels. For molecules, greater numbers of atoms increase the number of ways in which the molecules can vibrate and thus the number of possible microstates and the entropy of the system.
Finally, variations in the types of particles affect the entropy of a system. Compared to a pure substance, in which all particles are identical, the entropy of a mixture of two or more different particle types is greater. This is because of the additional orientations and interactions that are possible in a system composed of non-identical components. For example, when a solid dissolves in a liquid, the particles of the solid experience greater freedom of motion and additional interactions with the solvent particles. This corresponds to a more uniform dispersal of matter and energy and a greater number of microstates. The process of dissolution, therefore, involves an increase in entropy, &#916;S &#62; 0.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/16-2-entropy">Openstax, Chemistry 2e, Chapter 16.2: </a><a href="https://openstax.org/books/chemistry-2e/pages/16-2-entropy">Entropy</a>.

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has ...

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Thermodynamics

KEY TERMS AND CONCEPTS

entropy in matter and energy changes

Entropy describes how energy and matter are spread through a system. It is a thermodynamic state function, so it can change when a physical or chemical change occurs. When entropy increases, disorder increases. When entropy decreases, disorder decreases.

A change in entropy is written as ΔS = Sf - Si. The concept is also linked to microstates, which are the specific arrangements of the locations and energies of all atoms or molecules in a system. Boltzmann’s relation, S = k ln W, connects entropy to the number of possible microstates, where k is the Boltzmann constant. A system with more microstates is more disordered and has higher entropy.

This idea helps explain why some processes happen on their own. For example, when a gas expands into a vacuum, the gas spreads into a larger volume and the number of possible microstates increases. The same logic explains heat flow. A hot cup of tea transfers energy to the cooler air in the room, so the energy becomes more dispersed.

Entropy also helps compare the phases of matter. In a solid, particles stay near fixed positions and only vibrate a little, so the number of microstates is small. In a liquid, particles can move around one another, so entropy is higher than in the solid. In a gas, particles occupy much more volume, so the number of microstates is even greater. As a result, Sgas &gt; Sliquid &gt; Ssolid. Melting, vaporization, and sublimation increase entropy. Freezing, condensation, and deposition decrease entropy.

Temperature also affects entropy. According to kinetic-molecular theory, temperature is proportional to the average kinetic energy of particles. When temperature rises, particles vibrate more in solids and move faster in liquids and gases. The energy distribution becomes more spread out, so entropy increases.

The structure of the particles matters too. Heavier atoms have greater entropy than lighter atoms at the same temperature. Molecules with more atoms also have higher entropy because they can vibrate in more ways. A mixture of different particle types has greater entropy than a pure substance, since non-identical components allow more orientations and interactions. This is why dissolving a solid in a liquid increases entropy, because the particles gain more freedom of motion and interact with the solvent more widely.

Entropy in Matter and Energy Changes

spontaneity

Spontaneous Change in Matter and Energy

Spontaneous change in matter and energy happens naturally under certain conditions. A nonspontaneous process will not occur unless it is driven by a continual input of energy from an outside source. Under a given set of conditions, processes also tend to move in one direction rather than the other. Water flows downhill on its own, so that is a spontaneous process. Water flowing uphill needs a pump, so that is nonspontaneous. Iron in the earth’s atmosphere will corrode, but rust does not turn...

Entropy describes how energy and matter are spread through a system. It is a thermodynamic state function, so it can change when a physical or chemical change occurs. When entropy increases, disorder increases. When entropy decreases, disorder decreases. A change in entropy is written as ΔS = Sf - Si. The concept is also linked to microstates, which are the specific arrangements of the locations and energies of all atoms or molecules in a system. Boltzmann’s relation, S = k ln W, connects...

second law of thermodynamics

Entropy and Spontaneous Change

Entropy and spontaneous change are linked through the entropy of the universe. Entropy is a thermodynamic property that helps predict whether a process will happen on its own. Processes with an increase in system entropy, or ΔS &gt; 0, are often spontaneous, but there are many exceptions. To make a better prediction, entropy changes must include both the system and the surroundings. In thermodynamics, the system plus the surroundings make up the universe. When heat moves between two objects,...

third law of thermodynamics

Entropy at Absolute Zero

The third law of thermodynamics links entropy to absolute zero. A pure, perfectly crystalline solid with no kinetic energy at 0 K has only one microstate. Because there is only one possible arrangement for its identical atoms or molecules, its entropy is zero. This limiting case sets the entropy scale for real substances. Careful calorimetric measurements can be used to find how entropy changes with temperature and to calculate absolute entropy values under specific conditions. Standard...

standard entropy change for a reaction

Calculating Entropy Change from Tables

Entropy is a state function, so the standard entropy change of a chemical reaction can be found from standard molar entropy values in a table. The reaction entropy, written as ΔS°rxn, is calculated by subtracting the total entropy of the reactants from the total entropy of the products. The balanced equation matters because the stoichiometric coefficients set how many moles of each substance are included. A table of standard entropies gives values in J/mol·K for substances such as graphite,...

gibbs free energy

Predicting Spontaneity with Gibbs Energy

Gibbs free energy helps predict whether a process is spontaneous under constant temperature and pressure. It is a thermodynamic property based on the system’s enthalpy and entropy. Chemists also call it free energy, and it is a state function. The idea was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. Unlike the second law approach, it uses system properties only. That makes it a useful shortcut when tracking both the system and the surroundings is...

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Temperature and Spontaneous Processes

Temperature can change whether a process is spontaneous. In chemistry, spontaneity means a process can happen on its own under a given set of conditions. Phase changes are one clear example, and some chemical reactions also change spontaneity as temperature changes. The relationship uses free energy change, enthalpy change, and entropy change. Entropy is a measure of disorder in the system. The key equation shows that the sign of free energy depends on the signs of enthalpy and entropy, and in...

calculating standard free energy changes

Using Formation Data to Find Free Energy

Standard free energy change is the free energy change for a reaction under standard conditions of 1 bar pressure and 298 K. Free energy is a state function, so its value depends only on the starting and ending states of the system. That makes it possible to calculate standard free energy changes from tabulated thermodynamic data. One common method uses standard enthalpy and entropy values to find standard free energy change, ΔG°. Another method uses standard free energies of formation, ΔGf°,...

free energy changes for nonstandard states

free-energy-changes-for-nonstandard-states

Predicting Spontaneity with Reaction Quotient Q

Free energy under nonstandard conditions depends on the reaction quotient, Q, and the standard free energy change. Nonstandard conditions mean that concentrations are not 1 M or pressures are not 1 bar. The relation links the gas constant R, the absolute temperature T in kelvin, and Q. It can be used to predict whether a process is spontaneous under a given set of conditions. The reaction quotient, Q, helps show the status of a reversible reaction. It is based directly on the balanced chemical...

free energy and equilibrium

Predicting Reaction Direction with Free Energy

Free energy and equilibrium help predict which way a chemical reaction will move. A negative value of ΔG means the forward reaction is favored. A positive value means the reverse reaction is favored. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the system is at equilibrium. The reaction quotient, Q, helps show whether a reaction must move forward or backward to reach equilibrium. Q is the numerical value of the mass action expression for the system. If Q is less...

key terms and concepts

Explore how entropy tracks energy dispersal, microstates, phase changes, temperature, and dissolution in high school chemistry.

Entropy in Matter and Energy Changes | JoVE K12

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CH.7.g

Texas Essential Knowledge and Skills

High School

CHEM.13

CHEM.13.A

Florida Department of Education

Earth and Space Science

SC.912.E.5

SC.912.E.5.2

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CH.7.c

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CH.7.f

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Entropy in Matter and Energy Changes

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