{"history":[],"article":{"id":"06a81510-1e39-4f1b-91af-77ea59455a8f","title":"Hess's law","slug":"hess-s-law","content":":::summary\n:::\n\n# \n****Hess's law** of constant heat summation**, also known simply as **Hess's law**, is a relationship in [physical chemistry](https://bliptext.com/articles/physical-[chemist](https://bliptext.com/articles/chemist)ry) and [thermodynamics](https://bliptext.com/articles/thermodynamics) named after [Germain Hess](https://bliptext.com/articles/germain-henri-hess), a [Swiss](https://bliptext.com/articles/switzerland)-born [Russian](https://bliptext.com/articles/russia) [chemist](https://bliptext.com/articles/chemist) and [physician](https://bliptext.com/articles/physician) who published it in 1840.\nThe law states that the total [enthalpy](https://bliptext.com/articles/enthalpy) change during the complete course of a [chemical reaction](https://bliptext.com/articles/chemical-reaction) is independent of the sequence of steps taken.\nHess's law is now understood as an expression of the fact that the [enthalpy of a chemical process](https://bliptext.com/articles/standard-enthalpy-of-reaction) is independent of the path taken from the initial to the final state (i.e. enthalpy is a [state function](https://bliptext.com/articles/state-function)).\nAccording to the [first law of thermodynamics](https://bliptext.com/articles/first-law-of-thermodynamics), the enthalpy change in a system due to a reaction at [constant pressure](https://bliptext.com/articles/isobaric-process) is equal to the heat absorbed (or the negative of the heat released), which can be determined by [calorimetry](https://bliptext.com/articles/calorimetry) for many reactions.\nThe values are usually stated for reactions with the same initial and final temperatures and pressures (while conditions are allowed to vary during the course of the reactions).\nHess's law can be used to determine the overall energy required for a chemical reaction that can be divided into synthetic steps that are individually easier to characterize.\nThis affords the compilation of [standard enthalpies of formation](https://bliptext.com/articles/standard-enthalpy-of-formation), which may be used to predict the enthalpy change in complex synthesis.\n# [A representation of Hess's law (where H represents enthalpy) | upload.wikimedia.org/wikipedia/commons/b/b8/Hess///cycle.svg]\n\n# Theory\nHess's law states that the change of enthalpy in a chemical reaction is the same regardless of whether the reaction takes place in one step or several steps, provided the initial and final states of the reactants and products are the same.\nEnthalpy is an [extensive property](https://bliptext.com/articles/intensive-and-extensive-properties), meaning that its value is proportional to the system size.\nBecause of this, the enthalpy change is proportional to the number of moles participating in a given reaction.\nIn other words, if a chemical change takes place by several different routes, the overall enthalpy change is the same, regardless of the route by which the chemical change occurs (provided the initial and final condition are the same).\nIf this were not true, then one could violate the [first law of thermodynamics](https://bliptext.com/articles/first-law-of-thermodynamics).\nHess's law allows the [enthalpy](https://bliptext.com/articles/enthalpy) change (ΔH) for a reaction to be calculated even when it cannot be measured directly.\nThis is accomplished by performing basic algebraic operations based on the [chemical equations](https://bliptext.com/articles/chemical-equation) of reactions using previously determined values for the enthalpies of formation.\nCombination of chemical equations leads to a net or overall equation.\nIf the enthalpy changes are known for all the equations in the sequence, their sum will be the enthalpy change for the net equation.\nIf the net enthalpy change is negative, the reaction is [exothermic](https://bliptext.com/articles/exothermic-reaction) and is more likely to be [spontaneous](https://bliptext.com/articles/gibbs-free-energy); positive ΔH values correspond to [endothermic](https://bliptext.com/articles/endothermic) reactions.\n([Entropy](https://bliptext.com/articles/entropy) also plays an important role in determining spontaneity, as some reactions with a positive enthalpy change are nevertheless spontaneous due to an entropy increase in the reaction system.)\n\n# Use of enthalpies of formation\nHess's law states that enthalpy changes are additive.\nThus the value of the [standard enthalpy of reaction](https://bliptext.com/articles/standard-enthalpy-of-reaction) can be calculated from [standard enthalpies of formation](https://bliptext.com/articles/standard-enthalpy-of-formation) of products and reactants as follows:\nHere, the first sum is over all products and the second over all reactants, a_i and b_i are the [stoichiometric coefficients](https://bliptext.com/articles/stoichiometric-coefficients) of products and reactants respectively, and are the standard enthalpies of formation of products and reactants respectively, and the o superscript indicates [standard state](https://bliptext.com/articles/standard-state) values.\nThis may be considered as the sum of two (real or fictitious) reactions:\nand Elements → Products\n\n# Examples\n

Given:\n
Cgraphite + O2 → CO2 ( ΔH = −393.5 kJ/mol) (direct step)
Cgraphite + 1/2 O2 → CO (ΔH = −110.5 kJ/mol)
CO +1/2 O2 → CO2 (ΔH = −283.0 kJ/mol)

\nReaction (a) is the sum of reactions (b) and (c), for which the total ΔH = −393.5 kJ/mol, which is equal to ΔH in (a).\n\n

Given:\nFind the ΔfH of:\nAfter multiplying the equations (and their enthalpy changes) by appropriate factors and reversing the direction when necessary, the result is:\nAdding these equations and canceling out the common terms on both sides, we obtain\n

\n\n\n# Extension to free energy and entropy\nThe concepts of Hess's law can be expanded to include changes in [entropy](https://bliptext.com/articles/entropy) and in [Gibbs free energy](https://bliptext.com/articles/gibbs-free-energy), since these are also [state functions](https://bliptext.com/articles/state-function).\nThe [Bordwell thermodynamic cycle](https://bliptext.com/articles/bordwell-thermodynamic-cycle) is an example of such an extension that takes advantage of easily measured [equilibria](https://bliptext.com/articles/chemical-equilibrium) and [redox potentials](https://bliptext.com/articles/redox-potential) to determine experimentally inaccessible [Gibbs free energy](https://bliptext.com/articles/gibbs-free-energy) values.\nCombining ΔGo values from Bordwell thermodynamic cycles and ΔHo values found with Hess's law can be helpful in determining entropy values that have not been measured directly and therefore need to be calculated through alternative paths.\nFor the free energy:\nFor [entropy](https://bliptext.com/articles/entropy), the situation is a little different.\nBecause entropy can be measured as an absolute value, not relative to those of the elements in their reference states (as with ΔHo and ΔGo), there is no need to use the entropy of formation; one simply uses the absolute entropies for products and reactants:\n\n# Applications\nHess's law is useful in the determination of enthalpies of the following:","current_revision":null,"created_by":"kACnuQmH5k9Nr5VNVEpVeg7XpvUmMctD","created_at":"2025-01-25T18:51:13.469Z","updated_at":"2025-01-25T18:51:13.469Z","search_vector":"'hess':1 'law':3","search_content":" \n \n\n# \n****Hess's law** of constant heat summation**, also known simply as **Hess's law**, is a relationship in [physical [chemist](https://bliptext.com/articles/chemist)ry](https://bliptext.com/articles/physical-[chemist](https://bliptext.com/articles/chemist)ry) and [thermodynamics](https://bliptext.com/articles/thermodynamics) named after [Germain Hess](https://bliptext.com/articles/germain-henri-hess), a [Swiss](https://bliptext.com/articles/switzerland)-born [Russian](https://bliptext.com/articles/russia) [chemist](https://bliptext.com/articles/chemist) and [physician](https://bliptext.com/articles/physician) who published it in 1840.\nThe law states that the total [enthalpy](https://bliptext.com/articles/enthalpy) change during the complete course of a [chemical reaction](https://bliptext.com/articles/chemical-reaction) is independent of the sequence of steps taken.\nHess's law is now understood as an expression of the fact that the [enthalpy of a chemical process](https://bliptext.com/articles/standard-enthalpy-of-reaction) is independent of the path taken from the initial to the final state (i.e. enthalpy is a [state function](https://bliptext.com/articles/state-function)).\nAccording to the [first law of thermodynamics](https://bliptext.com/articles/first-law-of-thermodynamics), the enthalpy change in a system due to a reaction at [constant pressure](https://bliptext.com/articles/isobaric-process) is equal to the heat absorbed (or the negative of the heat released), which can be determined by [calorimetry](https://bliptext.com/articles/calorimetry) for many reactions.\nThe values are usually stated for reactions with the same initial and final temperatures and pressures (while conditions are allowed to vary during the course of the reactions).\nHess's law can be used to determine the overall energy required for a chemical reaction that can be divided into synthetic steps that are individually easier to characterize.\nThis affords the compilation of [standard enthalpies of formation](https://bliptext.com/articles/standard-enthalpy-of-formation), which may be used to predict the enthalpy change in complex synthesis.\n# [A representation of Hess's law (where H represents enthalpy) | upload.wikimedia.org/wikipedia/commons/b/b8/Hess///cycle.svg]\n\n# Theory\nHess's law states that the change of enthalpy in a chemical reaction is the same regardless of whether the reaction takes place in one step or several steps, provided the initial and final states of the reactants and products are the same.\nEnthalpy is an [extensive property](https://bliptext.com/articles/intensive-and-extensive-properties), meaning that its value is proportional to the system size.\nBecause of this, the enthalpy change is proportional to the number of moles participating in a given reaction.\nIn other words, if a chemical change takes place by several different routes, the overall enthalpy change is the same, regardless of the route by which the chemical change occurs (provided the initial and final condition are the same).\nIf this were not true, then one could violate the [first law of thermodynamics](https://bliptext.com/articles/first-law-of-thermodynamics).\nHess's law allows the [enthalpy](https://bliptext.com/articles/enthalpy) change (ΔH) for a reaction to be calculated even when it cannot be measured directly.\nThis is accomplished by performing basic algebraic operations based on the [chemical equations](https://bliptext.com/articles/chemical-equation) of reactions using previously determined values for the enthalpies of formation.\nCombination of chemical equations leads to a net or overall equation.\nIf the enthalpy changes are known for all the equations in the sequence, their sum will be the enthalpy change for the net equation.\nIf the net enthalpy change is negative, the reaction is [exothermic](https://bliptext.com/articles/exothermic-reaction) and is more likely to be [spontaneous](https://bliptext.com/articles/gibbs-free-energy); positive ΔH values correspond to [endothermic](https://bliptext.com/articles/endothermic) reactions.\n([Entropy](https://bliptext.com/articles/entropy) also plays an important role in determining spontaneity, as some reactions with a positive enthalpy change are nevertheless spontaneous due to an entropy increase in the reaction system.)\n\n# Use of enthalpies of formation\nHess's law states that enthalpy changes are additive.\nThus the value of the [standard enthalpy of reaction](https://bliptext.com/articles/standard-enthalpy-of-reaction) can be calculated from [standard enthalpies of formation](https://bliptext.com/articles/standard-enthalpy-of-formation) of products and reactants as follows:\nHere, the first sum is over all products and the second over all reactants, a_i and b_i are the [stoichiometric coefficients](https://bliptext.com/articles/stoichiometric-coefficients) of products and reactants respectively, and are the standard enthalpies of formation of products and reactants respectively, and the o superscript indicates [standard state](https://bliptext.com/articles/standard-state) values.\nThis may be considered as the sum of two (real or fictitious) reactions:\nand Elements → Products\n\n# Examples\n \n Given:\n Cgraphite + O2 → CO2 ( ΔH = −393.5 kJ/mol) (direct step) \n Cgraphite + 1/2 O2 → CO (ΔH = −110.5 kJ/mol) \n CO +1/2 O2 → CO2 (ΔH = −283.0 kJ/mol) \n \nReaction (a) is the sum of reactions (b) and (c), for which the total ΔH = −393.5 kJ/mol, which is equal to ΔH in (a).\n \n Given:\nFind the ΔfH of:\nAfter multiplying the equations (and their enthalpy changes) by appropriate factors and reversing the direction when necessary, the result is:\nAdding these equations and canceling out the common terms on both sides, we obtain\n \n \n\n# Extension to free energy and entropy\nThe concepts of Hess's law can be expanded to include changes in [entropy](https://bliptext.com/articles/entropy) and in [Gibbs free energy](https://bliptext.com/articles/gibbs-free-energy), since these are also [state functions](https://bliptext.com/articles/state-function).\nThe [Bordwell thermodynamic cycle](https://bliptext.com/articles/bordwell-thermodynamic-cycle) is an example of such an extension that takes advantage of easily measured [equilibria](https://bliptext.com/articles/chemical-equilibrium) and [redox potentials](https://bliptext.com/articles/redox-potential) to determine experimentally inaccessible [Gibbs free energy](https://bliptext.com/articles/gibbs-free-energy) values.\nCombining ΔGo values from Bordwell thermodynamic cycles and ΔHo values found with Hess's law can be helpful in determining entropy values that have not been measured directly and therefore need to be calculated through alternative paths.\nFor the free energy:\nFor [entropy](https://bliptext.com/articles/entropy), the situation is a little different.\nBecause entropy can be measured as an absolute value, not relative to those of the elements in their reference states (as with ΔHo and ΔGo), there is no need to use the entropy of formation; one simply uses the absolute entropies for products and reactants:\n\n# Applications\nHess's law is useful in the determination of enthalpies of the following:","revisionCount":0},"hasMore":false,"nextCursor":null}

History