Hess's law

Last updated November 19, 2024

Hess's law of constant heat summation, also known simply as Hess's law, is a relationship in physical chemistry and thermodynamics ^[1] named after Germain Hess, a Swiss-born Russian chemist and physician who published it in 1840. The law states that the total enthalpy change during the complete course of a chemical reaction is independent of the sequence of steps taken.^[2]^[3]

Hess's law is now understood as an expression of the fact that the enthalpy of a chemical process is independent of the path taken from the initial to the final state (i.e. enthalpy is a state function). According to the first law of thermodynamics, the enthalpy change in a system due to a reaction at constant pressure is equal to the heat absorbed (or the negative of the heat released), which can be determined by calorimetry for many reactions. The 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). Hess'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. This affords the compilation of standard enthalpies of formation, which may be used to predict the enthalpy change in complex synthesis.

Theory

Hess'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. Enthalpy is an extensive property, meaning that its value is proportional to the system size.^[4] Because of this, the enthalpy change is proportional to the number of moles participating in a given reaction.

In 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). If this were not true, then one could violate the first law of thermodynamics.

Hess's law allows the enthalpy change (ΔH) for a reaction to be calculated even when it cannot be measured directly. This is accomplished by performing basic algebraic operations based on the chemical equations of reactions using previously determined values for the enthalpies of formation.

Combination of chemical equations leads to a net or overall equation. If the enthalpy changes are known for all the equations in the sequence, their sum will be the enthalpy change for the net equation. If the net enthalpy change is negative ( $\Delta H_{\text{net}}<0$ ), the reaction is exothermic and is more likely to be spontaneous; positive ΔH values correspond to endothermic reactions. (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.)

Use of enthalpies of formation

Hess's law states that enthalpy changes are additive. Thus the value of the standard enthalpy of reaction can be calculated from standard enthalpies of formation of products and reactants as follows:

\Delta H_{\text{reaction}}^{\ominus }=\sum _{i}a_{i}\Delta _{\text{f}}H_{products}^{\ominus }-\sum _{i}b_{i}\Delta _{\text{f}}H_{reactants}^{\ominus }

Here, the first sum is over all products and the second over all reactants, $a_{i}$ and $b_{i}$ are the stoichiometric coefficients of products and reactants respectively, $\Delta _{\text{f}}H_{products}^{\ominus }$ and $\Delta _{\text{f}}H_{reactants}^{\ominus }$ are the standard enthalpies of formation of products and reactants respectively, and the ^o superscript indicates standard state values. This may be considered as the sum of two (real or fictitious) reactions:

Reactants → Elements (in their standard states)

\Delta H_{\text{RE}}^{\ominus }=-\sum _{i}b_{i}\Delta _{\text{f}}H_{reactants}^{\ominus }

and Elements → Products

\Delta H_{\text{EP}}^{\ominus }=\sum _{i}a_{i}\Delta _{\text{f}}H_{products}^{\ominus }

Examples

Given:
1. C_graphite + O₂ → CO₂(g) ( ΔH = −393.5 kJ/mol) (direct step)
2. C_graphite + 1/2 O₂ → CO(g) (ΔH = −110.5 kJ/mol)
3. CO(g) +1/2 O₂ → CO₂(g) (ΔH = −283.0 kJ/mol)
Reaction (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).
Given:
- B₂O₃(s) + 3H₂O(g) → 3O₂(g) + B₂H₆(g) (ΔH = 2035 kJ/mol)
- H₂O(l) → H₂O(g) (ΔH = 44 kJ/mol)
- H₂(g) + 1/2 O₂(g) → H₂O(l) (ΔH = −286 kJ/mol)
- 2B(s) + 3H₂(g) → B₂H₆(g) (ΔH = 36 kJ/mol)
Find the Δ_fH of:
- 2B(s) + 3/2 O₂(g) → B₂O₃(s)
After multiplying the equations (and their enthalpy changes) by appropriate factors and reversing the direction when necessary, the result is:
- B₂H₆(g) + 3O₂(g) → B₂O₃(s) + 3H₂O(g) (ΔH = 2035 × (−1) = −2035 kJ/mol)
- 3H₂O(g) → 3H₂O(l) (ΔH = 44 × (−3) = −132 kJ/mol)
- 3H₂O(l) → 3H₂(g) + (3/2) O₂(g) (ΔH = −286 × (−3) = 858 kJ/mol)
- 2B(s) + 3H₂(g) → B₂H₆(g) (ΔH = 36 kJ/mol)
Adding these equations and canceling out the common terms on both sides, we obtain
- 2B(s) + 3/2 O₂(g) → B₂O₃(s) (ΔH = −1273 kJ/mol)

Extension to free energy and entropy

The concepts of Hess's law can be expanded to include changes in entropy and in Gibbs free energy, since these are also state functions. The Bordwell thermodynamic cycle is an example of such an extension that takes advantage of easily measured equilibria and redox potentials to determine experimentally inaccessible Gibbs free energy values. Combining ΔG^o values from Bordwell thermodynamic cycles and ΔH^o 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.

For the free energy:

\Delta G_{\text{reaction}}^{\ominus }=\sum \nu _{\text{p}}\Delta G_{\mathrm {f} \,({\text{p}})}^{\ominus }-\sum \nu _{\text{r}}\Delta G_{\mathrm {f} \,({\text{r}})}^{\ominus }.

For entropy, the situation is a little different. Because entropy can be measured as an absolute value, not relative to those of the elements in their reference states (as with ΔH^o and ΔG^o), there is no need to use the entropy of formation; one simply uses the absolute entropies for products and reactants:

\Delta S_{\text{reaction}}^{\ominus }=\sum \nu _{\text{p}}S_{({\text{p}})}^{\ominus }-\sum \nu _{\text{r}}S_{({\text{r}})}^{\ominus }.

Applications

Hess's law is useful in the determination of enthalpies of the following:^[2]

Heats of formation of unstable intermediates like CO_(g) and NO_(g).
Heat changes in phase transitions and allotropic transitions.
Lattice energies of ionic substances by constructing Born–Haber cycles if the electron affinity to form the anion is known, or
Electron affinities using a Born–Haber cycle with a theoretical lattice energy.

Related Research Articles

In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.

Enthalpy is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function in thermodynamics used in many measurements in chemical, biological, and physical systems at a constant external pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work $that was done against constant external pressure to establish the system's physical dimensions from to some final volume, i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation, and other chemical "energies" are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.$

In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Currently, it is best seen as an empirical relationship. It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally induced processes and reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.

In chemistry and thermodynamics, the standard enthalpy of formation or standard heat of formation of a compound is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements in their reference state, with all substances in their standard states. The standard pressure value $p ⦵$ = 10⁵ Pa(= 100 kPa = 1 bar) is recommended by IUPAC, although prior to 1982 the value 1.00 atm (101.325 kPa) was used. There is no standard temperature. Its symbol is Δ_fH^⦵. The superscript Plimsoll on this symbol indicates that the process has occurred under standard conditions at the specified temperature (usually 25 °C or 298.15 K).

In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction from the standard electrode potential, absolute temperature, the number of electrons involved in the redox reaction, and activities of the chemical species undergoing reduction and oxidation respectively. It was named after Walther Nernst, a German physical chemist who formulated the equation.

In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. These are often chosen to be the standard temperature and pressure.

In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as $Where:$

The standard enthalpy of reaction for a chemical reaction is the difference between total product and total reactant molar enthalpies, calculated for substances in their standard states. The value can be approximately interpreted in terms of the total of the chemical bond energies for bonds broken and bonds formed.

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In chemical kinetics, a reaction rate constant or reaction rate coefficient is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants.

In thermodynamics, the entropy of vaporization is the increase in entropy upon vaporization of a liquid. This is always positive, since the degree of disorder increases in the transition from a liquid in a relatively small volume to a vapor or gas occupying a much larger space. At standard pressure ⁠ $⁠$ = 1 bar, the value is denoted as ⁠ $⁠$ and normally expressed in joules per mole-kelvin, J/(mol·K).

The Van 't Hoff equation relates the change in the equilibrium constant, $K eq$ , of a chemical reaction to the change in temperature, T, given the standard enthalpy change, $Δ r H ⊖$ , for the process. The subscript $means "reaction" and the superscript means "standard". It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book Études de Dynamique chimique .$

Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa, or 100 kPa. Both of these definitions for the standard condition for pressure are in use.

In chemistry, transition state theory (TST) explains the reaction rates of elementary chemical reactions. The theory assumes a special type of chemical equilibrium (quasi-equilibrium) between reactants and activated transition state complexes.

Equilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant $K$ is expressed as a concentration quotient,

In thermodynamics, enthalpy–entropy compensation is a specific example of the compensation effect. The compensation effect refers to the behavior of a series of closely related chemical reactions, which exhibit a linear relationship between one of the following kinetic or thermodynamic parameters for describing the reactions:

Between the logarithm of the pre-exponential factors and the activation energies $where the series of closely related reactions are indicated by the index i, A i are the preexponential factors, E a, i are the activation energies, R is the gas constant, and α, β are constants.$
Between enthalpies and entropies of activation $where H ‡ i are the enthalpies of activation and S ‡ i are the entropies of activation.$
Between the enthalpy and entropy changes of a series of similar reactions $where H i are the enthalpy changes and S i are the entropy changes.$

Equilibrium chemistry is concerned with systems in chemical equilibrium. The unifying principle is that the free energy of a system at equilibrium is the minimum possible, so that the slope of the free energy with respect to the reaction coordinate is zero. This principle, applied to mixtures at equilibrium provides a definition of an equilibrium constant. Applications include acid–base, host–guest, metal–complex, solubility, partition, chromatography and redox equilibria.

In chemistry, thermochemical cycles combine solely heat sources (thermo) with chemical reactions to split water into its hydrogen and oxygen components. The term cycle is used because aside of water, hydrogen and oxygen, the chemical compounds used in these processes are continuously recycled.

References

↑ "5.6: Hess's Law". Chemistry LibreTexts. 2014-11-18. Retrieved 2024-11-09.
1 2 Mannam Krishnamurthy; Subba Rao Naidu (2012). "7". In Lokeswara Gupta (ed.). Chemistry for ISEET - Volume 1, Part A (2012 ed.). Hyderabad, India: Varsity Education Management Limited. p. 244.
↑ "Hess's Law - Conservation of Energy". University of Waterloo. Archived from the original on 9 January 2015. Retrieved 12 January 2014.
↑ Engel, Thomas; Reid, Philip (2006). Physical Chemistry. Pearson / Benjamin Cummings. p. 6. ISBN 0-8053-3842-X. A variable ... proportional to the size of the system is referred to as an extensive variable.

Chakrabarty, D.K. (2001). An Introduction to Physical Chemistry. Mumbai: Alpha Science. pp. 34–37. ISBN 1-84265-059-9.

External links

Hess's paper (1840) on which his law is based (at ChemTeam site)
a Hess's Law experiment Archived 2016-03-03 at the Wayback Machine

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[1] "5.6: Hess's Law". Chemistry LibreTexts. 2014-11-18. Retrieved 2024-11-09.

[Aakash1-2] 1 2 Mannam Krishnamurthy; Subba Rao Naidu (2012). "7". In Lokeswara Gupta (ed.). Chemistry for ISEET - Volume 1, Part A (2012 ed.). Hyderabad, India: Varsity Education Management Limited. p. 244.

[3] "Hess's Law - Conservation of Energy". University of Waterloo. Archived from the original on 9 January 2015. Retrieved 12 January 2014.

[4] Engel, Thomas; Reid, Philip (2006). Physical Chemistry. Pearson / Benjamin Cummings. p. 6. ISBN 0-8053-3842-X. A variable ... proportional to the size of the system is referred to as an extensive variable.

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