In
chemistry, the standard molar entropy is the
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
content of one
mole
Mole (or Molé) may refer to:
Animals
* Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America
* Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
of pure substance at a
standard state of pressure and any temperature of interest. These are often (but not necessarily) chosen to be the
standard temperature and pressure.
The standard molar entropy at pressure =
is usually given the symbol , and has units of
joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applie ...
s per
mole
Mole (or Molé) may refer to:
Animals
* Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America
* Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
per
kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
(J⋅mol
−1⋅K
−1). Unlike
standard enthalpies of formation, the value of is absolute. That is, an element in its standard state has a definite, nonzero value of at
room temperature. The entropy of a pure
crystalline
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
structure can be 0J⋅mol
−1⋅K
−1 only at 0K, according to the
third law of thermodynamics
The third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: This constant value cannot depend on any other parameters characterizing the closed system, such as pressure or applied magnetic fiel ...
. However, this assumes that the material forms a '
perfect crystal' without any
residual entropy. This can be due to
crystallographic defect
A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell para ...
s,
dislocations
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
, and/or incomplete rotational quenching within the solid, as originally pointed out by
Linus Pauling. These contributions to the entropy are always present, because crystals always grow at a finite rate and at temperature. However, the residual entropy is often quite negligible and can be accounted for when it occurs using
statistical mechanics.
Thermodynamics
If a
mole
Mole (or Molé) may refer to:
Animals
* Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America
* Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would be the sum of a series of stepwise and reversible entropy changes. The limit of this sum as
becomes an integral:
:
In this example,
and
is the
molar heat capacity
The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of ...
at a constant pressure of the substance in the
reversible process . The molar heat capacity is not constant during the experiment because it changes depending on the (increasing) temperature of the substance. Therefore, a table of values for
is required to find the total molar entropy. The quantity
represents the ratio of a very small exchange of heat energy to the temperature . The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process.
Chemistry
The standard molar entropy of a gas at
STP
STP may refer to:
Places
* São Tomé and Príncipe (ISO 3166-1 alpha-3 code, IOC country code, and FIFA country code STP)
* St Pancras railway station, London St Pancras (Domestic) railway station (National Rail code STP)
* St. Paul Downtown Air ...
includes contributions from:
* The
heat capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity ...
of one mole of the solid from 0K to the
melting point
The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depen ...
(including heat absorbed in any changes between different
crystal structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns ...
s).
* The
latent heat of fusion of the solid.
* The heat capacity of the liquid from the melting point to the
boiling point.
* The
latent heat of vaporization
The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. T ...
of the liquid.
* The heat capacity of the gas from the boiling point to room temperature.
Changes in entropy are associated with
phase transitions
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
and
chemical reactions.
Chemical equations
A chemical equation is the symbolic representation of a chemical reaction in the form of symbols and chemical formulas. The reactant entities are given on the left-hand side and the product entities on the right-hand side with a plus sign between t ...
make use of the standard molar entropy of
reactants
In chemistry, a reagent ( ) or analytical reagent is a substance or compound added to a system to cause a chemical reaction, or test if one occurs. The terms ''reactant'' and ''reagent'' are often used interchangeably, but reactant specifies a ...
and
products
Product may refer to:
Business
* Product (business), an item that serves as a solution to a specific consumer problem.
* Product (project management), a deliverable or set of deliverables that contribute to a business solution
Mathematics
* Produ ...
to find the standard entropy of reaction:
:
The standard entropy of reaction helps determine whether the reaction will take place
spontaneously. According to the
second law of thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings:
:
Molar entropy is not the same for all gases. Under identical conditions, it is greater for a heavier gas.
See also
*
Entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
*
Heat
In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
*
Gibbs free energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and ...
*
Helmholtz free energy
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz ener ...
*
Standard state
*
Third law of thermodynamics
The third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: This constant value cannot depend on any other parameters characterizing the closed system, such as pressure or applied magnetic fiel ...
References
{{reflist
External links
Standard Thermodynamic Properties of Chemical Substances Table
Chemical properties
Thermodynamic entropy