Name: entropy at absolute zero
Uploaded: 2020-09-24T15:06:52.000Z
Duration: 2 min 38 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Chemistry

CH.7

CH.7.d

Third Law of Thermodynamics

The components of a substance have kinetic energy, which appears as different types of molecular motion, including translational, rotational, and vibrational motion.
With greater molecular motion, a substance has more ways to distribute the kinetic energy among its components; that is, it has a greater number of possible microstates.
The third law of thermodynamics states that at zero Kelvin, also known as absolute zero, the entropy of a pure, perfectly crystalline substance is zero.
At zero Kelvin, the components of a crystal have no kinetic energy and no molecular motion, meaning that they can only occupy one fixed position.
Thus, these components have a singular microstate, and W is equal to 1. Solving Boltzmann&#8217;s equation, the entropy is equal to zero.
There are two major consequences of the third law of thermodynamics.
First, at temperatures greater than absolute zero, the entropy of all substances must be positive. Second, all entropy values can be measured against a fixed reference point&#8212;the entropy at absolute zero.
Using this reference, the standard molar entropy, S&#176;, is the entropy of 1 mole of a substance under standard state conditions. Values for the standard molar entropy, in J/mol&#183;K, can be found in reference tables.
Whether a substance will have a high or low standard molar entropy depends on several factors, including the physical state of the substance, its molar mass, and the specific form of the substance.
As a substance transitions from a solid to a liquid to a gaseous state, its entropy increases because there are more possible microstates due to increasing molecular motion.
Allotropes, which are different structural forms of an element, have different standard molar entropies, and the less rigid form has a higher standard molar entropy.
For example, diamond and graphite are allotropes of solid carbon. In diamond, the carbon atoms are fixed in a crystal structure.
Conversely, in graphite, the carbon atoms are arranged in layers that can slide over each other. Thus, the graphite carbon atoms have more mobility, which means graphite has more microstates and a higher standard molar entropy.

third law of thermodynamics

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
<img alt="Chemical equilibrium, reversible reaction equations; diagram shows equilibrium constants and dynamic balance." src="/files/ftp_upload/11425/11425_Equation_1.png" style="text-align: center; height: 50px;" data-altupdatedat="1761830439000" data-alt="Eq1" />
This limiting condition for a system&#8217;s entropy represents the third law of thermodynamics: the entropy of a pure, perfect crystalline substance at 0 K is zero.
Careful calorimetric measurements can be made to determine the temperature dependence of a substance&#8217;s entropy and to derive absolute entropy values under specific conditions. Standard entropies (S&#176;) are for one mole of a substance under standard conditions. Different substances have different standard molar entropy values depending on the substance's physical state, molar mass, allotropic forms, molecular complexity, and extent of dissolution.
Due to the greater energy dispersal among the scattered particles in the gas phase, gaseous forms of substances tend to have much larger standard molar enthalpies than their liquid forms. For similar reasons, liquid forms of substances tend to have larger values than their solid forms. For example, S&#176;H2O (l) = 70 J/mol&#183;K and S&#176;H2O (g) = 188.8 J/mol&#183;K.
Among elements in the same state, the heavier element (larger molar mass) has a higher standard molar entropy value than the lighter element. For example, S&#176;Ar (g) = 154.8 J/mol&#183;K and S&#176;Xe (g) = 159.4 J/mol&#183;K.
Similarly, among substances in the same state, more complex molecules have higher standard molar enthalpy values than simpler ones. There are more possible arrangements of atoms in larger, more complex molecules, which increases the number of possible microstates. For example, S&#176;Ar (g) = 154.8 J/mol&#183;K and S&#176;NO (g) = 210.8 J/mol&#183;K despite the higher molar mass of argon. This is because in gaseous argon, energy takes the form of translational motion of the atoms, whereas in gaseous nitric oxide (NO), energy takes the form of translational motion, rotational motion, and (at high enough temperatures) vibrational motions of the molecules.
The standard molar entropy of any substance increases with increasing temperature. At phase transitions, such as from solid to liquid and liquid to gas, large jumps in entropy occur, which is due to the sudden increased molecular mobility and larger available volumes associated with phase changes.
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/16-3-the-second-and-third-laws-of-thermodynamics">Openstax, Chemistry 2e, Chapter 16.2: The Second and Third Law of Thermodynamics</a>.

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single ...

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Thermodynamics

KEY TERMS AND CONCEPTS

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 entropies, written as S° , describe one mole of a substance under standard conditions.

Standard molar entropy depends on several factors. A substance’s physical state, molar mass, allotropic form, molecular complexity, and extent of dissolution can all affect its value. Gases usually have much larger standard molar entropy than liquids, and liquids usually have larger values than solids. For example, S° for H2O(l) is 70 J/mol·K, while S° for H2O(g) is 188.8 J/mol·K.

Within the same state, heavier elements often have higher standard molar entropy than lighter ones. For example, S° for Ar(g) is 154.8 J/mol·K and S° for Xe(g) is 159.4 J/mol·K. More complex molecules can also have higher values because they have more possible microstates. That is why NO(g), with S° = 210.8 J/mol·K, has a higher value than Ar(g), even though argon has the higher molar mass.

The difference comes from motion and available arrangements. In gaseous argon, energy is mainly translational motion of the atoms. In gaseous nitric oxide, energy can include translational motion, rotational motion, and, at high enough temperatures, vibrational motion.

Entropy also increases as temperature rises. Large jumps in entropy occur at phase changes such as solid to liquid and liquid to gas. These jumps happen because particles gain more freedom of motion and more available space. The third law helps explain why entropy has a zero point and why it changes across different states of matter.

Entropy at Absolute Zero

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

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...

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,...

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...

effects of temperature on free energy

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 the third law sets entropy to zero at 0 K, and see why entropy changes with temperature, phase, molar mass, and molecular complexity.

Entropy at Absolute Zero | JoVE K12

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CHEM.13

CHEM.13.A

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CH.7.a

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CH.7.b

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CH.7.c

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CH.7.f

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CH.7.g

Entropy at Absolute Zero

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