# Heat of reaction

The heat of reaction is the heat released or absorbed by a chemical reaction .

In the course of a chemical reaction, part of the energy difference between starting materials and reaction products is usually released or absorbed in the form of heat. The investigation of the heat of reaction allows conclusions to be drawn about the thermodynamic properties of the substances involved. When designing the reaction vessels, it is also very useful to be able to determine the expected heat release in advance.

However, the heat of reaction is not a state variable , but a process variable . Even if the starting and product materials and their thermodynamic states are precisely defined, the expected heat of reaction is therefore still not defined, since it also depends on how the reaction process is carried out. Tables for the expected heat of reaction would therefore not only have to list all possible combinations of substances, but also all possible process controls, which would not be practicable.

However, under certain conditions - namely for reactions that take place at constant volume or at constant pressure - the heat of reaction can be expressed as the difference between state variables:

• For reactions at constant volume, the heat of reaction converted is the difference between the internal energies of the product and starting materials.
• For reactions at constant pressure, the heat of reaction converted is the difference between the enthalpies of the product and the starting materials.

This considerably simplifies the tabulation. It is not even necessary to tabulate all possible combinations of substances. It is sufficient to tabulate the internal energy or the enthalpy of the individual substances in suitable reference states (such as the standard state ).

• In the case of a reaction at constant volume, the expected heat of reaction can be determined as the sum of the internal energies of the product substances minus the sum of the internal energies of the starting substances.
• In the case of a reaction at constant pressure, which occurs particularly frequently, the expected heat of reaction can be determined as the sum of the enthalpies of the product substances minus the sum of the enthalpies of the starting substances.

## Explanation

The first law of thermodynamics states that a change in the internal energy of a system is equal to the sum of the heat and work exchanged with the system : ${\ displaystyle \ mathrm {d} U}$ ${\ displaystyle \ mathrm {d} Q}$ ${\ displaystyle \ mathrm {d} W}$ ${\ displaystyle \ mathrm {d} U = \ mathrm {d} Q + \ mathrm {d} W}$ .

In addition to the statement that an increase in the energy content requires energy supply ( energy conservation ), it is also established that there are two different mechanisms for the exchange of energy between the system and its environment: heat and work . The difference between the two is that entropy is transported with heat, but not with work ( Second Law of Thermodynamics ). If the energy exchange occurs due to a chemical reaction in the system, the two transfer mechanisms are also referred to as reaction heat and reaction work.

Heat of reaction and work of reaction are important and informative parameters in the thermodynamic investigation of the system and its processes, but they also play an essential role in the design of the equipment in practical work.

The conventionally used sign convention for the heat of reaction considers the heat exchange from the point of view of the system, i.e. sets the heat input as positive (gain) and heat dissipated as negative (loss).

The term heat tint , which is rarely used today, describes the heat released during the reaction , i.e. it uses the opposite convention of signs: released heat corresponds to a positive heat tone, the heat that is expended corresponds to a negative heat tone.

Depending on the type of reaction, the heat of reaction can also be referred to as heat of combustion, heat of solution, heat of decomposition, heat of polymerization and so on.

## Relationship with enthalpy of reaction and energy of reaction

### State and process variables

A state variable is clearly defined by the current state of the system. In particular, it is independent of the previous history of the system, i.e. of the process through which it came to the present state. Examples are the internal energy of the system and the enthalpy of the system.

A process variable describes the process that transfers the system from one state to another. If there are different process controls that lead from a given initial state to a given final state, the respective process variables can be different despite fixed initial and final states.

The heat of reaction and the work of the reaction are process variables. If a system is converted from an initial to a final state by a process, the total energy converted and thus the sum of heat of reaction and reaction work is clearly defined by the initial and final state (namely as the difference between the state variables, final and initial energy). How this total energy consumption is broken down into heat and work generally depends on the respective process management. It follows from this that, in particular, the heat of reaction cannot generally be calculated without detailed knowledge of the process management used.

Under certain circumstances, however, the heat of reaction can be attributed to state variables. In these cases, knowledge of the initial and final state is sufficient to be able to calculate the heat of reaction. Details of the process used are not required, which greatly simplifies the arithmetic handling of the heat of reaction. In the following only systems are considered that can not do any other type of work (e.g. electrical work) apart from volume change work.

### Response at constant volume

If the reaction is carried out at a constant volume ( i.e. isochoric ), no volume change work is performed and the heat supplied or removed leads to an equally large change in the internal energy: ${\ displaystyle \ mathrm {d} Q}$ ${\ displaystyle \ mathrm {d} U}$ ${\ displaystyle \ mathrm {d} Q = \ mathrm {d} U}$ .

The difference between the internal energies of the final and initial state is called reaction energy. It only depends on the initial and final state. ${\ displaystyle \ Delta U}$ As explained above, the heat of reaction at constant volume is identical to the reaction energy and is therefore determined solely by the initial and final state: ${\ displaystyle \ Delta Q _ {\ mathrm {V}}}$ ${\ displaystyle \ Delta U}$ ${\ displaystyle \ Delta Q _ {\ mathrm {V}} = \ Delta U}$ .

### Reaction at constant pressure

If the reaction is carried out at constant pressure ( i.e. isobaric ), then the system usually changes its volume and thereby does the volume change work on the environment . Of the heat supplied , only the portion for increasing the internal energy is available: ${\ displaystyle p}$ ${\ displaystyle p \ \ mathrm {d} V}$ ${\ displaystyle \ mathrm {d} Q}$ ${\ displaystyle \ mathrm {d} Qp \ \ mathrm {d} V}$ ${\ displaystyle \ mathrm {d} U = \ mathrm {d} Qp \ \ mathrm {d} V}$ or moved

${\ displaystyle \ mathrm {d} Q = \ mathrm {d} U + p \ \ mathrm {d} V \ quad (*)}$ The change in the enthalpy of the system is on the other hand, according to its definition and using the product rule

${\ displaystyle \ mathrm {d} H = \ mathrm {d} (U + p \ V) = \ mathrm {d} U + p \ \ mathrm {d} V + V \ \ mathrm {d} p}$ ,

which in the present case is constant pressure ( ) reduced to ${\ displaystyle \ mathrm {d} p = 0}$ ${\ displaystyle \ mathrm {d} H = \ mathrm {d} U + p \ \ mathrm {d} V \ quad (*)}$ .

Comparison of the marked expressions provides

${\ displaystyle \ mathrm {d} Q = \ mathrm {d} H}$ .

In the isobaric case, added heat leads to an equally large change in the enthalpy of the system. ${\ displaystyle \ mathrm {d} Q}$ ${\ displaystyle \ mathrm {d} H}$ The difference between the enthalpies of the final and initial state is called the enthalpy of reaction . It only depends on the initial and final state. ${\ displaystyle \ Delta H}$ According to the above derivation, the heat of reaction at constant pressure is identical to the enthalpy of reaction and is therefore determined solely by the initial and final state: ${\ displaystyle \ Delta Q _ {\ mathrm {p}}}$ ${\ displaystyle \ Delta H}$ ${\ displaystyle \ Delta Q _ {\ mathrm {p}} = \ Delta H}$ .

The enthalpies in certain states are tabulated for numerous chemical systems, and the heat of reaction is then determined simply by forming the enthalpy difference. (If the reaction under consideration is isobaric - otherwise the enthalpy difference is obtained correctly, but this is then not identical to the heat of reaction. For more details see the article → Enthalpy .)

## Notation

The converted heat of reaction can be included in the reaction equation together with the converted substances . The sign convention for heats of reaction is maintained if the heat of reaction is written on the left side of the equation, i.e. how the starting materials are treated:

${\ displaystyle \ mathrm {N_ {2} + O_ {2} +180 {,} 5 \ kJ \ longrightarrow 2 \ NO}}$ The formation of two moles of nitrogen monoxide from the elements consumes 180.5 kJ of heat of reaction. The system absorbs this heat of reaction, so it is to be counted as positive.

${\ displaystyle \ mathrm {3H_ {2} + N_ {2} -92 {,} 2 \ kJ \ longrightarrow 2 \ NH_ {3}}}$ When two moles of ammonia are formed from the elements, 92.2 kJ of heat of reaction are released. The system gives off this heat of reaction, so count it as negative.

If you prefer to write the converted heat on the right-hand side of the equation, its sign must be reversed (according to the rules for equation transformations ). In this case, the respective heat tint should be applied:

${\ displaystyle \ mathrm {N_ {2} + O_ {2} \ longrightarrow 2 \ NO-180 {,} 5 \ kJ}}$ ${\ displaystyle \ mathrm {3H_ {2} + N_ {2} \ longrightarrow 2 \ NH_ {3} +92 {,} 2 \ kJ}}$ Another possibility is to list the converted energy separately. The formula symbol used can also explicitly indicate whether it is the heat of reaction, reaction energy or reaction enthalpy:

${\ displaystyle \ mathrm {H_ {2} + {\ tfrac {1} {2}} O_ {2} \ longrightarrow H_ {2} O}, \ quad \ Delta H = -286 {,} 02 \ mathrm {\ tfrac {kJ} {mol}}}$ When (liquid) water is formed from the elements, a reaction enthalpy of 286.02 kJ / mol is released. Since the table from which this numerical value was taken assumes an isobaric course of the reaction, it is also the numerical value for the heat of reaction released.

Since the energy unit (mostly kJ / mol) is explicitly stated, you may have the freedom to specify the energy conversion per mole instead of per formula conversion as in the above examples , which facilitates comparison with tabular values.

The sign results from the rule that the difference “energy of the right side minus energy of the left side” is to be formed. An energy gain of the system is expressed by a positive sign, an energy loss by a negative sign. This rule also corresponds to the sign convention for the heat of reaction described above.