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Enthalpy is the amount of heat content used or released in a system at constant pressure. Enthalpy is usually expressed as the change in enthalpy. The change in enthalpy is related to a change in internal energy (U) and a change in the volume (V), which is multiplied by the constant pressure of the system.


Enthalpy (H) is the sum of the internal energy (U) and the product of pressure and volume (PV) given by the equation:

When a process occurs at constant pressure, the heat evolved (either released or absorbed) is equal to the change in enthalpy. Enthalpy is a state function which depends entirely on the state functions TP and U. Enthalpy is usually expressed as the change in enthalpy (ΔH) for a process between initial and final states:

If temperature and pressure remain constant through the process and the work is limited to pressure-volume work, then the enthalpy change is given by the equation:

Also at constant pressure the heat flow (q) for the process is equal to the change in enthalpy defined by the equation:

By looking at whether q is exothermic or endothermic we can determine a relationship between ΔH and q. If the reaction absorbs heat it is endothermic meaning the reaction consumes heat from the surroundings so q>0 (positive). Therefore, at constant temperature and pressure, by the equation above, if q is positive then ΔH is also positive. And the same goes for if the reaction releases heat, then it is exothermic, meaning the system gives off heat to its surroundings, so q<0 (negative). If q is negative, then ΔH will also be negative.

Enthalpy Change Accompanying a Change in State of Matter

When a liquid vaporizes the liquid must absorb heat from its surroundings to replace the energy taken by the vaporizing molecules in order for the temperature to remain constant. This heat required to vaporize the liquid is called enthalpy of vaporization (or heat of vaporization). For example, the vaporization of one mole of water the enthalpy is given as:
ΔH = 44.0 kJ at 298 K
When a solid melts, the required energy is similarly called enthalpy of fusion (or heat of fusion). For example, one mole of ice the enthalpy is given as:
ΔH = 6.01 kJ at 273.15 K
Enthalpy can also be expressed as a molar enthalpy, ΔHm, by dividing the enthalpy or change in enthalpy by the number of moles. Enthalpy is a state function. This implies that when a system changes from one state to another, the change in enthalpy is independent of the path between two states of a system.
If there is no non-expansion work on the system and the pressure is still constant, then the change in enthalpy will equal the heat consumed or released by the system (q).
This relationship can help to determine whether a reaction is endothermic or exothermic. At constant pressure, an endothermic reaction is when heat is absorbed. This means that the system consumes heat from the surroundings, so q is greater than zero. Therefore according to the second equation, the ΔH will also be greater than zero. On the other hand, an exothermic reaction at constant pressure is when heat is released. This implies that the system gives off heat to the surroundings, so q is less than zero. Furthermore, ΔH will be less than zero.

Effect of Temperature on Enthalpy

When the temperature increases, the amount of molecular interactions also increases. When the number of interactions increase, then the internal energy of the system rises. According to the first equation given, if the internal energy (U) increases then the ΔH increases as temperature rises. We can use the equation for heat capacity and Equation 2 to derive this relationship.

Under constant pressure, substitute Equation 2 into equation 3: 

where the subscript P indicates the derivative is done under constant pressure.

The Enthalpy of Phase Transition

Enthalpy can be represented as the standard enthalpy, ΔHo. This is the enthalpy of a substance at standard state. The standard state is defined as the pure substance held constant at 1 bar of pressure. Phase transitions, such as ice to liquid water, require or absorb a particular amount of standard enthalpy:
  • Standard Enthalpy of Fusion  (ΔHofusis the energy that must be supplied as heat at constant pressure per mole of molecules melted (solid to liquid).
  • Standard Enthalpy of Sublimation (ΔHosubis the energy that must be supplied as heat at constant pressure per mole of molecules converted to vapor from a solid.

The enthalpy of condensation is the reverse of the enthalpy of vaporization and the enthalpy of freezing is the reverse of the enthalpy of fusion. The enthalpy change of a reverse phase transition is the negative of the enthalpy change of the forward phase transition. Also the enthalpy change of a complete process is the sum of the enthalpy changes for each of the phase transitions incorporated in the process.


  1. Atkins, Peter and de Paula, Julio; Physical Chemistry for the Life Sciences, United States, 2006.Katherine Hurley
  2. Petrucci, et al. General Chemistry Principles & Modern Applications. 9th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2007


  1. Calculate the enthalpy (ΔH) for the process in which 45.0 grams of water is converted from liquid at 10° C to vapor at 25° C.


Part 1: Heating water from 10.0 to 25.0 °C
ΔkJ = 45.0g H20 x (4.184J/gH2O °C) x (25.0 - 10.0) °C x 1kJ/1000J = 2.82 kJ
Part 2: Vaporizing water at 25.0 °C
ΔkJ = 45.0 g H2O x 1 mol H2O/18.02 g H2O x 44.0 kJ/1 mol H2O = 110 kJ
Part 3: Total Enthalpy Change
ΔH = 2.82 kJ + 110kJ

Assorted Definitions

This page explains what an enthalpy change is, and then gives a definition and brief comment for three of the various kinds of enthalpy change that you will come across.

Enthalpy changes

Enthalpy change is the name given to the amount of heat evolved or absorbed in a reaction carried out at constant pressure. It is given the symbol ΔH, read as "delta H".

Standard enthalpy changes

Standard enthalpy changes refer to reactions done under standard conditions, and with everything present in their standard states. Standard states are sometimes referred to as "reference states".

Standard conditions

Standard conditions are:
  • 298 K (25°C)
  • a pressure of 1 bar (100 kPa).
  • where solutions are involved, a concentration of 1 mol dm-3

Standard states

For a standard enthalpy change everything has to be present in its standard state. That is the physical and chemical state that you would expect to find it in under standard conditions.
That means that the standard state for water, for example, is liquid water, H2O(l) - not steam or water vapour or ice.
Oxygen's standard state is the gas, O2(g) - not liquid oxygen or oxygen atoms.
For elements which have allotropes (two different forms of the element in the same physical state), the standard state is the most energetically stable of the allotropes.
For example, carbon exists in the solid state as both diamond and graphite. Graphite is energetically slightly more stable than diamond, and so graphite is taken as the standard state of carbon.
Similarly, under standard conditions, oxygen can exist as O2 (simply called oxygen) or as O3 (called ozone - but it is just an allotrope of oxygen). The O2 form is far more energetically stable than O3, so the standard state for oxygen is the common O2(g).

The symbol for standard enthalpy changes

The symbol for a standard enthalpy change is ΔH°, read as "delta H standard" or, perhaps more commonly, as "delta H nought".

Standard enthalpy change of reaction, ΔH°r

Remember that an enthalpy change is the heat evolved or absorbed when a reaction takes place at constant pressure. The standard enthalpy change of a reaction is the enthalpy change which occurs when equation quantities of materials react under standard conditions, and with everything in its standard state.
That needs exploring a bit. Here is a simple reaction between hydrogen and oxygen to make water:
  • First, notice that the symbol for a standard enthalpy change of reaction is ΔH°r. For enthalpy changes of reaction, the "r" (for reaction) is often missed off - it is just assumed.
  • The "kJ mol-1" (kilojoules per mole) doesn't refer to any particular substance in the equation. Instead it refers to the quantities of all the substances given in the equation. In this case, 572 kJ of heat is evolved when 2 moles of hydrogen gas react with 1 mole of oxygen gas to form 2 moles of liquid water.
  • Notice that everything is in its standard state. In particular, the water has to be formed as a liquid.
  • And there is a hidden problem! The figure quoted is for the reaction under standard conditions, but hydrogen and oxygen don't react under standard conditions.
    Whenever a standard enthalpy change is quoted, standard conditions are assumed. If the reaction has to be done under different conditions, a different enthalpy change would be recorded. That has to be calculated back to what it would be under standard conditions. Fortunately, you don't have to know how to do that at this level.

Standard enthalpy change of formation, ΔH°f

The standard enthalpy change of formation of a compound is the enthalpy change which occurs when one mole of the compound is formed from its elements under standard conditions, and with everything in its standard state.

The equation showing the standard enthalpy change of formation for water is:

When you are writing one of these equations for enthalpy change of formation, you must end up with 1 mole of the compound. If that needs you to write fractions on the left-hand side of the equation, that is OK. (In fact, it is not just OK, it is essential, because otherwise you will end up with more than 1 mole of compound, or else the equation won't balance!)
The equation shows that 286 kJ of heat energy is given out when 1 mole of liquid water is formed from its elements under standard conditions.
Standard enthalpy changes of formation can be written for any compound, even if you can't make it directly from the elements. For example, the standard enthalpy change of formation for liquid benzene is +49 kJ mol-1. The equation is:
If carbon won't react with hydrogen to make benzene, what is the point of this, and how does anybody know what the enthalpy change is?
How do we know this if the reaction doesn't happen? It is actually very simple to calculate it from other values which we can measure - for example, from enthalpy changes of combustion (coming up next). We will come back to this again when we look at calculations on another page.
Knowing the enthalpy changes of formation of compounds enables you to calculate the enthalpy changes in a whole host of reactions and, again, we will explore that in a bit more detail on another page.
And one final comment about enthalpy changes of formation:
The standard enthalpy change of formation of an element in its standard state is zero. That's an important fact. The reason is obvious . . .
For example, if you "make" one mole of hydrogen gas starting from one mole of hydrogen gas you aren't changing it in any way, so you wouldn't expect any enthalpy change. That is equally true of any other element. The enthalpy change of formation of any element has to be zero because of the way enthalpy change of formation is defined.

Standard enthalpy change of combustion, ΔH°c

The standard enthalpy change of combustion of a compound is the enthalpy change which occurs when one mole of the compound is burned completely in oxygen under standard conditions, and with everything in its standard state.
The enthalpy change of combustion will always have a negative value, of course, because burning always releases heat. Two examples:

  • Enthalpy of combustion equations will often contain fractions, because you must start with only 1 mole of whatever you are burning.
  • If you are talking about standard enthalpy changes of combustion, everything must be in its standard state. One important result of this is that any water you write amongst the products must be there as liquid water.
    Similarly, if you are burning something like ethanol, which is a liquid under standard conditions, you must show it as a liquid in any equation you use.
  • Notice also that the equation and amount of heat evolved in the hydrogen case is exactly the same as you have already come across further up the page. At that time, it was illustrating the enthalpy of formation of water. That can happen in some simple cases. Talking about the enthalpy change of formation of water is exactly the same as talking about the enthalpy change of combustion of hydrogen.

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