Editing Enthalpy (section)

==Applications==
In thermodynamics, one can calculate enthalpy by determining the requirements for creating a system from "nothingness"; the mechanical work required, {{nobr|{{mvar|pV}},}} differs based upon the conditions that obtain during the creation of the [[thermodynamic system]].

[[Energy]] must be supplied to remove particles from the surroundings to make space for the creation of the system, assuming that the pressure {{mvar|p}} remains constant; this is the {{mvar|pV}} term. The supplied energy must also provide the change in internal energy {{mvar|U}}, which includes [[activation energy|activation energies]], ionization energies, mixing energies, vaporization energies, chemical bond energies, and so forth. Together, these constitute the change in the enthalpy {{nobr|{{mvar|U + pV}}.}} For systems at constant pressure, with no external work done other than the {{mvar|pV}} work, the change in enthalpy is the heat received by the system.

For a simple system with a constant number of particles at constant pressure, the difference in enthalpy is the maximum amount of thermal energy derivable from an isobaric thermodynamic process.<ref>
{{cite book
 |last=Rathakrishnan |date=2015
 |title=High Enthalpy Gas Dynamics
 |publisher=John Wiley and Sons Singapore Pte. Ltd.
 |isbn=978-1118821893
}}
</ref>

===Heat of reaction===
{{Main|Standard enthalpy of reaction}}
The total enthalpy of a system cannot be measured directly; the ''enthalpy change'' of a [[system (thermodynamics)|system]] is measured instead. Enthalpy change is defined by the following equation:
<math display="block">
 \Delta H = H_\text{f} - H_\text{i},
</math>
where
: {{math|Δ''H'' }} is the "enthalpy change",
: {{mvar|H}}{{sub|f}} is the final enthalpy of the system (in a chemical reaction, the enthalpy of the products or the system at equilibrium),
: {{mvar|H}}{{sub|i}} is the initial enthalpy of the system (in a chemical reaction, the enthalpy of the reactants).

For an [[exothermic reaction]] at constant [[pressure]], the system's change in enthalpy, {{math|Δ''H''}}, is negative due to the products of the reaction having a smaller enthalpy than the reactants, and equals the heat released in the reaction if no electrical or mechanical work is done. In other words, the overall decrease in enthalpy is achieved by the generation of heat.<ref name=Laidler-Meiser-1982>
{{cite book
 |last1=Laidler |first1=K. J. |author-link = Keith J. Laidler
 |last2=Meiser  |first2=John H. 
 |year=1982
 |title=Physical Chemistry
 |publisher=Benjamin / Cummings
 |isbn=978-0-8053-5682-3
 |page=53
}}
</ref>
Conversely, for a constant-pressure [[endothermic]] reaction, {{math|Δ''H''}} is positive and equal to the heat ''absorbed'' in the reaction.

From the definition of enthalpy as {{nobr|{{mvar|H {{=}} U + pV}},}} the enthalpy change at constant pressure is {{nobr|{{math|Δ''H'' {{=}} Δ''U'' + ''p''{{tsp}}Δ''V''}}.}} However, for most chemical reactions, the work term {{math|''p''{{tsp}}Δ''V''}} is much smaller than the internal energy change {{math|Δ''U''}}, which is approximately equal to {{math|Δ''H''}}. As an example, for the combustion of carbon monoxide {{nobr|2 CO(g) + O{{sub|2}}(g) → 2 CO{{sub|2}}(g),}} {{nobr|{{math|Δ''H'' {{=}} −566.0}} kJ}} and {{nobr|{{math|Δ''U'' {{=}} −563.5}} kJ.}}<ref>
{{cite book
 |first1=Ralph H.    |last1=Petrucci
 |first2=William S.  |last2=Harwood
 |first3=F. Geoffrey |last3=Herring
 |year=2002
 |title=General Chemistry  |edition=8th
 |publisher=Prentice Hall
 |isbn=978-0-13-014329-7
 |pages=[https://archive.org/details/generalchemistry00hill/page/237 237–238]
 |url=https://archive.org/details/generalchemistry00hill |url-access=registration
}}
</ref>
Since the differences are so small, reaction enthalpies are often described as reaction energies and analyzed in terms of [[bond energy|bond energies]].

===Specific enthalpy===
The ''specific enthalpy'' of a uniform system is defined as {{nobr|{{math|''h'' {{=}} ''H''/''m''}}}}, where {{mvar|m}} is the mass of the system. Its [[SI unit]] is joule per kilogram. It can be expressed in other specific quantities by {{nobr|{{math|''h'' {{=}} ''u'' + ''pv''}},}} where {{mvar|u}} is the specific [[internal energy]], {{mvar|p}} is the pressure, and {{mvar|v}} is [[specific volume]], which is equal to {{math|1/''ρ''}}, where {{mvar|ρ}} is the [[density]].

===Enthalpy changes===
An enthalpy change describes the change in enthalpy observed in the constituents of a thermodynamic system when undergoing a transformation or chemical reaction. It is the difference between the enthalpy after the process has completed, i.e. the enthalpy of the [[Product (chemistry)|products]] assuming that the reaction goes to completion, and the initial enthalpy of the system, namely the reactants. These processes are specified solely by their initial and final states, so that the enthalpy change for the reverse is the negative of that for the forward process.

A common standard enthalpy change is the [[enthalpy of formation]], which has been determined for a large number of substances. Enthalpy changes are routinely measured and compiled in chemical and physical reference works, such as the [[CRC Handbook of Chemistry and Physics]]. The following is a selection of enthalpy changes commonly recognized in thermodynamics.

When used in these recognized terms the qualifier ''change'' is usually dropped and the property is simply termed ''enthalpy of "process"''. Since these properties are often used as reference values, it is very common to quote them for a standardized set of environmental parameters, or [[standard conditions]], including:
* A [[pressure]] of one atmosphere (1&nbsp;atm = 1013.25&nbsp;hPa) or 1&nbsp;bar
* A [[temperature]] of 25&nbsp;°C = 298.15&nbsp;K
* A [[concentration]] of 1.0&nbsp;[[Molar concentration|M]] when the element or compound is present in solution
* Elements or compounds in their normal physical states, i.e. [[standard state]]
For such standardized values the name of the enthalpy is commonly prefixed with the term ''standard'', e.g. ''standard enthalpy of formation''.

====Chemical properties====
[[Enthalpy of reaction]] is defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of substance reacts completely.

[[Enthalpy of formation]] is defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a compound is formed from its elementary antecedents.

[[Enthalpy of combustion]] is defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a substance burns completely with oxygen.

[[Enthalpy of hydrogenation]] is defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of an unsaturated compound reacts completely with an excess of hydrogen to form a [[Saturated and unsaturated compounds|saturated compound]].

[[Enthalpy of atomization]] is defined as the enthalpy change required to separate one mole of a substance into its constituent [[atom]]s completely.

[[Enthalpy of neutralization]] is defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of water is formed when an acid and a base react.

Standard [[enthalpy of solution]] is defined as the enthalpy change observed in a constituent of a thermodynamic system when one mole of a solute is dissolved completely in an excess of solvent, so that the solution is at infinite dilution.

Standard enthalpy of [[Denaturation (biochemistry)|denaturation]] is defined as the enthalpy change required to denature one mole of compound.

[[Hydration energy|Enthalpy of hydration]] is defined as the enthalpy change observed when one mole of gaseous ions is completely dissolved in water forming one mole of aqueous ions.

====Physical properties====
[[Enthalpy of fusion]] is defined as the enthalpy change required to completely change the state of one mole of substance from solid to liquid.

[[Enthalpy of vaporization]] is defined as the enthalpy change required to completely change the state of one mole of substance from liquid to gas.

[[Enthalpy of sublimation]] is defined as the enthalpy change required to completely change the state of one mole of substance from solid to gas.

[[Lattice enthalpy]] is defined as the energy required to separate one mole of an ionic compound into separated gaseous ions to an infinite distance apart (meaning no force of attraction).

[[Enthalpy of mixing]] is defined as the enthalpy change upon mixing of two (non-reacting) chemical substances.

===Open systems===
In [[thermodynamic]] [[Open system (systems theory)|open systems]], mass (of substances) may flow in and out of the system boundaries. The first law of thermodynamics for open systems states: The increase in the internal energy of a system is equal to the amount of energy added to the system by mass flowing in and by heating, minus the amount lost by mass flowing out and in the form of work done by the system:
<math display="block">
 \mathrm{d}U = \delta Q + \mathrm{d}U_\text{in} - \mathrm{d}U_\text{out} - \delta W,
</math>
where {{mvar|U}}{{sub|in}} is the average internal energy entering the system, and {{mvar|U}}{{sub|out}} is the average internal energy leaving the system.

[[Image:First law open system.svg|250px|thumb|right|During [[Steady-state (chemical engineering)|steady, continuous]] operation, an energy balance applied to an open system equates shaft work performed by the system to heat added plus net enthalpy added]]

The region of space enclosed by the boundaries of the open system is usually called a [[control volume]], and it may or may not correspond to physical walls. If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of mass into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of mass out as if it were driving a piston of fluid. There are then two types of work performed: ''flow work'' described above, which is performed on the fluid (this is also often called ''{{mvar|pV}} work''), and ''mechanical work'' (''shaft work''), which may be performed on some mechanical device such as a turbine or pump.

These two types of work are expressed in the equation
<math display="block">
 \delta W = \mathrm{d}(p_\text{out} V_\text{out}) - \mathrm{d}(p_\text{in} V_\text{in}) + \delta W_\text{shaft}.
</math>
Substitution into the equation above for the control volume (cv) yields
<math display="block">
 \mathrm{d}U_\text{cv} = \delta Q + \mathrm{d}U_\text{in} + \mathrm{d}(p_\text{in} V_\text{in}) - \mathrm{d}U_\text{out} - \mathrm{d}(p_\text{out} V_\text{out}) - \delta W_\text{shaft}.</math>

The definition of enthalpy {{mvar|H}} permits us to use this [[thermodynamic potential]] to account for both internal energy and {{mvar|pV}} work in fluids for open systems:
<math display="block">
 \mathrm{d}U_\text{cv} = \delta Q + \mathrm{d}H_\text{in} - \mathrm{d}H_\text{out} - \delta W_\text{shaft}.
</math>

If we allow also the system boundary to move (e.g. due to moving pistons), we get a rather general form of the first law for open systems.<ref>
{{cite book
 |first1=M. J. |last1=Moran
 |first2=H. N. |last2=Shapiro
 |year=2006
 |title=Fundamentals of Engineering Thermodynamics |edition=5th
 |url=https://archive.org/details/fundamentalsengi00mora_077
 |url-access=limited
 |publisher=John Wiley & Sons
 |isbn=9780470030370
 |page=[https://archive.org/details/fundamentalsengi00mora_077/page/n141 129]
}}
</ref>
In terms of time derivatives, using [[Notation for differentiation#Newton's notation|Newton's dot notation]] for time derivatives, it reads:
<math display="block">
 \frac{\mathrm{d}U}{\mathrm{d}t} = \sum_k \dot Q_k + \sum_k \dot H_k - \sum_k p_k\frac{\mathrm{d}V_k}{\mathrm{d}t} - P,
</math>
with sums over the various places {{mvar|k}} where heat is supplied, mass flows into the system, and boundaries are moving. The {{mvar| {{overset|'''.'''|H}}{{sub|k}}}} terms represent enthalpy flows, which can be written as
<math display="block">
 \dot H_k = h_k \dot m_k = H_\text{m} \dot n_k,
</math>
with <math>\dot m_k</math> the mass flow and <math>\dot n_k</math> the molar flow at position {{mvar|k}} respectively. The term {{math|d''V''{{sub|''k''}}/d''t''}} represents the rate of change of the system volume at position {{mvar|k}} that results in {{mvar|pV}} power done by the system. The parameter {{mvar|P}} represents all other forms of power done by the system such as shaft power, but it can also be, say, electric power produced by an electrical power plant.

Note that the previous expression holds true only if the kinetic energy flow rate is conserved between system inlet and outlet.{{clarify|reason=This new type of energy, kinetic energy, was not mentioned before. Is it part of {{mvar|U}}? Does it need to be conserved, or just the net flow across boundary be zero?|date=March 2015}} Otherwise, it has to be included in the enthalpy balance. During [[Steady-state (chemical engineering)|steady-state]] operation of a device (see [[Turbine]], [[Pump]], and [[Engine]]), the average {{math|d''U''/d''t''}} may be set equal to zero. This yields a useful expression for the average [[Power (physics)|power]] generation for these devices in the absence of chemical reactions:
<math display="block">
 P = \sum_k \big\langle \dot Q_k \big\rangle
  + \sum_k \big\langle \dot H_k \big\rangle
  - \sum_k \left\langle p_k \frac{\mathrm{d}V_k}{\mathrm{d}t} \right\rangle,
</math>
where the [[angle bracket]]s denote time averages. The technical importance of the enthalpy is directly related to its presence in the first law for open systems, as formulated above.