Hess’s Law: Definition, Formula, Calculator, Examples

Hess’s Law

Edited By Shivani Poonia | Updated on Jul 02, 2025 06:30 PM IST

Hess's Law is a basic rule in thermodynamics and chemistry, named for Germain Hess. It simply states that the net enthalpy change for a chemical reaction is independent of the pathway taken. It is developed directly from the first law of thermodynamics, a conservation of energy law. In this respect, Hess's Law becomes very useful, since it allows one to calculate enthalpy changes for reactions where direct measurement is difficult. That is, if the enthalpy changes of individual steps or simpler reactions involved in a complex reaction are known, then its overall enthalpy change will be easily determined.

This Story also Contains

Hess's Law
Applications of Hess Law:-
Some Solved Examples
Summary

Hess’s Law

Hess's Law

This rule is a consequence of the Enthalpy or Internal energy being a state function.

According to Hess's Law, "The enthalpy change for a process is independent of path or way of a process. The enthalpy change ($\Delta$H or $\Delta$E for any physical or chemical process remains the same whether the process is carried out in one step or in many steps. "

Let us consider the following example

$\begin{aligned} & \mathrm{C}+\mathrm{O}_2 \rightarrow \mathrm{CO}_2 ; \Delta \mathrm{H}_1=-94.3 \mathrm{kcal} \\ & \mathrm{C}+\frac{1}{2} \mathrm{O}_2 \rightarrow \mathrm{CO} ; \Delta \mathrm{H}_2=-68.3 \mathrm{kcal} \\ & \mathrm{CO}+\frac{1}{2} \mathrm{O}_2 \rightarrow \mathrm{CO}_2 ; \Delta \mathrm{H}_3=-26 \mathrm{kcal}\end{aligned}$

It can be seen that $\Delta \mathrm{H}_1=\Delta \mathrm{H}_2+\Delta \mathrm{H}_3$

Hence it proves that

$\Delta$H or $\Delta$E is not proportional to the path or way of reaction
$\Delta$H or $\Delta$E is a state function that depends only on the initial and final state (state function).

Applications of Hess Law:-

It has the following applications:

1. It helps in finding enthalpy changes for those reactions also which are experimentally not possible.

2. It also helps in finding $\Delta \mathrm{H}_{\text {formation }}, \Delta \mathrm{H}_{\text {combustion }}$ etc.

3. For the determination of resonance energy and lattice energy.

4. For the determination of enthalpies of reactions occurring very slowly.

Some Solved Examples

Example 1: The enthalpy change for a reaction does not depend upon the

1)physical states of reactants and products

2)use of different reactants for the same product

3) nature of intermediate reaction steps

4)difference in initial or final temperatures of involved substances.

Solution

As we learned from the concept:

Hess's law of constant heat summation states that regardless of the multiple stages or intermediate steps of the reaction the total enthalpy change for the reaction is the sum of all changes.

The enthalpy of a chemical process is independent of the path taken from the initial and the final state.

Example 2: The enthalpy of combustion of propane, graphite and dihydrogen at 298 K are $-2220.0 \mathrm{~kJ} \mathrm{~mol}^{-1},-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $-285.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. The magnitude of enthalpy of formation of propane $\left(\mathrm{C}_3 \mathrm{H}_8\right)$ is ___________$\mathrm{kJ} \mathrm{mol}^{-1}$ (Nearest integer)

1) 103.7

2)120.25

3)456.22

4)653

Solution

Given the combustion enthalpy -

(1) $\mathrm{C}_3 \mathrm{H}_8(\mathrm{~g})+5 \mathrm{O}_2 \longrightarrow 3 \mathrm{CO}_2+4 \mathrm{H}_2 \mathrm{O}, \Delta \mathrm{H}_1=-2220.0 \mathrm{~kJ} / \mathrm{mol}$

(2) $\mathrm{C}_{(\mathrm{s})}+\mathrm{O}_2 \longrightarrow \mathrm{CO}_2 \quad \Delta_{\mathrm{c}} \mathrm{H}_2=-393.5 \mathrm{~kJ} / \mathrm{mol}$

(3) $\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2 \rightarrow \mathrm{H}_2 \mathrm{O} \quad \Delta_{\mathrm{c}} \mathrm{H}_3=-285.8 \mathrm{~kJ} / \mathrm{mol}$

After doing $3 \times(2)+4 \times(3)----(1)$

(4) $3 \mathrm{C}_{(\mathrm{s})}+4 \mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{C}_3 \mathrm{H}_{8(\mathrm{~g})} \quad \Delta \mathrm{H}=103.7 \mathrm{~kJ} / \mathrm{mol}$

(4) is the enthalpy of formation propane $\left(\mathrm{C}_3 \mathrm{H}_6\right)$

Answer = 103.7

Example 3: The enthalpy change for a reaction does not depend on the

1)Physical state of reactants and products.

2)Use of different reactants for the same products.

3) Nature of intermediate reaction steps.

4)Difference in initial or final temperature of involved substances.

Solution

Hess's Law -The total amount of heat change in a chemical reaction is the same whether the reaction is carried out in one or several steps by one or more methods.

$C_{(s)}+O_{2(g)} \rightarrow C O_{2(g)}$

$\Delta H_1=110.5 \mathrm{~kJ}$

$\mathrm{CO}_{(g)}+\frac{1}{2} \mathrm{O}_{2(g)} \rightarrow \mathrm{CO}_{2(g)}$

$\Delta H_2=283.0 \mathrm{~kJ}$

$\Delta H=\Delta H_1+\Delta H_2$

Hess's law of constant heat summation states that regardless of the multiple stages or intermediate steps of the reaction the total enthalpy change for the reaction is the sum of all changes. The enthalpy of a chemical process is independent of the path taken from the initial and the final state.

Hence, the answer is the option (3).

Example 4: The enthalpies of combustion of carbon and carbon monoxide are –393.5 and –283 kJ mol^-1respectively. The enthalpy of formation (in kJ) of carbon monoxide per mole is

1)110.5

2)676.5

3)-676.5

4) -110.5

Solution

From the concept:

(i) $\mathrm{C}+\mathrm{O}_2 \longrightarrow \mathrm{CO}_2, \Delta \mathrm{H}=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-}$

(ii) $\mathrm{CO}+\frac{1}{2} \mathrm{O}_2 \longrightarrow \mathrm{CO}_2, \Delta \mathrm{H}=-283 \mathrm{~kJ} \mathrm{~mol}^{-}$

Subtracting (ii) from (i)

(iii) $\mathrm{C}+\frac{1}{2} \mathrm{O}_2 \rightarrow \mathrm{CO}, \Delta \mathrm{H}=-110.5 \mathrm{~kJ} \mathrm{~mol}^{-}$

Reaction (iii) represents the formation enthalpy of carbon monoxide.

Example 5: At $25^{\circ} \mathrm{C}$ , the enthalpy of the following processes are given:

$\mathrm{H}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{OH}(\mathrm{g}) \quad \Delta \mathrm{H}^{\circ} \quad=78 \mathrm{~kJ} \mathrm{~mol}^{-1}$

$\mathrm{H}_2(\mathrm{~g})+1 / 2 \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \quad \Delta \mathrm{H}^{\circ}=-242 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $\begin{array}{rrr}\mathrm{H}_2(\mathrm{~g}) & \rightarrow 2 \mathrm{H}(\mathrm{g}) & \Delta \mathrm{H}^{\circ}=436 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ 1 / 2 \mathrm{O}_2(\mathrm{~g}) & \rightarrow \mathrm{O}(\mathrm{g}) & \Delta \mathrm{H}^{\circ}=249 \mathrm{~kJ} \mathrm{~mol}^{-1}\end{array}$

What would be the value of X for the following reaction?

(Nearest integer)

$\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{H}(\mathrm{g})+\mathrm{OH}(\mathrm{g}) \quad \Delta \mathrm{H}^{\circ}=\mathrm{X} \mathrm{kJmol}^{-1}$

1) 499

2)124

3)456

4)210

Solution

$2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{H}_2(\mathrm{~g})+2(\mathrm{~g})$ & $+(242 \times 2)$
$\mathrm{H}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{OH}$ & +78
$\mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2$ & +436
$2 \mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{H}+2 \mathrm{OH}$ & $+998 \mathrm{KJ} / \mathrm{mole}$
$\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{H}+\mathrm{OH}$ & $998 \times \frac{1}{2}=+499 \mathrm{KJ} / \mathrm{mole}$

Hence, the answer is (499).

Summary

Hess's Law states that the total enthalpy change of a chemical reaction is the same, regardless of the pathway taken, depending only on the initial and final states. This principle allows for the calculation of reaction enthalpies by summing the enthalpy changes of individual steps, making it especially useful for reactions where direct measurement is challenging. Hess's Law underscores the conservation of energy, as enthalpy is a state function. By using standard enthalpies of formation and combustion, chemists can determine the enthalpy changes of complex reactions. This law is a fundamental tool in thermochemistry, aiding in the understanding and design of chemical processes by providing insights into reaction energetics and enabling accurate energy balance calculations.

Frequently Asked Questions (FAQs)

1. Can Hess's Law be applied to both exothermic and endothermic reactions?

Yes, Hess's Law applies to both exothermic and endothermic reactions. It doesn't discriminate between heat released or absorbed; it simply deals with the overall enthalpy change, which can be positive (endothermic) or negative (exothermic).

2. Why do we use standard enthalpies of formation in Hess's Law calculations?

Standard enthalpies of formation provide a common reference point for all substances, making calculations more consistent and comparable. They represent the enthalpy change when one mole of a compound is formed from its elements in their standard states, which allows us to construct various reactions using these values.

3. How does Hess's Law help in determining bond energies?

Hess's Law allows us to calculate bond energies indirectly by comparing the enthalpies of formation of different molecules. By analyzing the energy changes in various reactions involving the bond of interest, we can deduce the energy required to break or form that specific bond.

4. What's the difference between state functions and path functions in the context of Hess's Law?

State functions, like enthalpy, depend only on the initial and final states of a system, not the path taken. Path functions, however, depend on the specific route taken. Hess's Law works because enthalpy is a state function, allowing us to manipulate reaction pathways without affecting the overall enthalpy change.

5. How can Hess's Law be used to determine the enthalpy of reaction for a combustion process?

To determine the enthalpy of a combustion reaction using Hess's Law, we can break down the process into steps with known enthalpies. Typically, this involves using the enthalpies of formation of reactants and products, and applying Hess's Law to calculate the overall enthalpy change for the combustion reaction.

6. What is Hess's Law and why is it important in thermochemistry?

Hess's Law states that the total enthalpy change for a reaction is independent of the pathway taken, and depends only on the initial and final states. It's important because it allows us to calculate enthalpy changes for reactions that are difficult or impossible to measure directly, by breaking them down into simpler steps with known enthalpy values.

7. How does Hess's Law relate to the conservation of energy?

Hess's Law is a direct application of the law of conservation of energy. It shows that energy is neither created nor destroyed in chemical reactions, but merely transformed. The total energy change remains constant regardless of the reaction pathway, reflecting the conservation principle.

8. Why might the experimental value of a reaction's enthalpy differ from the value calculated using Hess's Law?

Discrepancies between experimental and calculated values can arise due to experimental errors, impurities in reactants, incomplete reactions, or heat loss to the surroundings. Additionally, the tabulated values used in calculations may have their own uncertainties. Hess's Law calculations assume ideal conditions, which may not always be met in real experiments.

9. Can Hess's Law be used to predict the spontaneity of a reaction?

While Hess's Law is useful for calculating enthalpy changes, it alone cannot predict the spontaneity of a reaction. Spontaneity depends on both enthalpy and entropy changes, as described by the Gibbs free energy equation. However, the enthalpy change calculated using Hess's Law is a crucial component in determining spontaneity.

10. What is the relationship between Hess's Law and calorimetry experiments?

Calorimetry experiments measure heat changes in reactions directly, while Hess's Law allows us to calculate heat changes indirectly. The results from calorimetry can be used as input data for Hess's Law calculations, and conversely, Hess's Law can be used to predict results that can be verified through calorimetry.

11. How does Hess's Law relate to the First Law of Thermodynamics?

Hess's Law is a specific application of the First Law of Thermodynamics, which states that energy is conserved. Hess's Law demonstrates this conservation principle in chemical reactions by showing that the total enthalpy change is independent of the pathway and depends only on the initial and final states.

12. What is the significance of the "state" in standard state enthalpies when using Hess's Law?

The standard state (typically 1 atm pressure, 25°C, 1 M concentration for solutions) provides a consistent reference point for enthalpy values. This consistency is crucial when applying Hess's Law, as it ensures that all values used in calculations are comparable and combinable, regardless of their source or the conditions under which they were measured.

13. What is the significance of the sign (positive or negative) in enthalpy changes calculated using Hess's Law?

The sign of the enthalpy change indicates whether the reaction is endothermic (positive ΔH, heat absorbed) or exothermic (negative ΔH, heat released). When using Hess's Law, it's crucial to pay attention to these signs as they determine whether equations should be added or subtracted when combining reactions.

14. What is the relationship between Hess's Law and the concept of bond energy?

Hess's Law and bond energies are closely related. Bond energies are often calculated using Hess's Law by comparing the enthalpies of formation of molecules with and without the bond in question. Conversely, known bond energies can be used in Hess's Law calculations to determine enthalpies of reactions where bonds are broken and formed.

15. How does Hess's Law relate to the concept of activation energy?

While Hess's Law deals with the overall enthalpy change of a reaction, it doesn't directly address activation energy. However, by using Hess's Law to calculate enthalpy changes for different possible reaction pathways, we can gain insights into the most energetically favorable route, which often correlates with the pathway of lowest activation energy.

16. What is the relationship between Hess's Law and the concept of entropy in thermodynamics?

While Hess's Law primarily deals with enthalpy, it indirectly relates to entropy through the Gibbs free energy equation. The enthalpy changes calculated using Hess's Law are crucial in determining the Gibbs free energy change of a reaction, which, combined with entropy changes, determines the spontaneity and equilibrium of reactions.

17. What is the significance of Hess's Law in understanding the energetics of allotropes?

Hess's Law helps in understanding the energy relationships between different allotropes of an element. By calculating the enthalpy changes involved in the conversion between allotropes using known thermochemical data, we can determine which form is more stable under given conditions and predict the energy required for allotropic transformations.

18. How does Hess's Law relate to the concept of enthalpy of solution?

Hess's Law can be applied to understand and calculate enthalpies of solution. The process of dissolving a substance can be broken down into steps: breaking bonds in the solute, breaking bonds in the solvent, and forming new bonds between solute and solvent. By applying Hess's Law to these steps, we can determine the overall enthalpy change of the dissolution process.

19. How does Hess's Law help in understanding the concept of lattice energy?

Hess's Law is instrumental in determining lattice energies, which are difficult to measure directly. By using a thermochemical cycle (Born-Haber cycle) and applying Hess's Law, we can calculate the lattice energy of ionic compounds using more easily measurable quantities like enthalpies of formation, ionization energies, and electron affinities.

20. Can Hess's Law be applied to non-chemical processes?

Yes, Hess's Law can be applied to any process where energy changes can be measured or calculated, including physical processes. For example, it can be used to calculate energy changes in phase transitions, mixing processes, or even in some mechanical systems where energy conservation applies.

21. How does Hess's Law help in understanding reaction mechanisms?

While Hess's Law doesn't directly reveal reaction mechanisms, it can provide insights. By breaking down a complex reaction into simpler steps and analyzing the energy changes at each step, we can gain understanding about potential intermediate stages and energy barriers in the reaction pathway.

22. How can Hess's Law be used to determine the energy content of foods?

Hess's Law can be applied to calculate the energy content of foods by considering the enthalpy changes of the combustion reactions of the food's components (carbohydrates, fats, proteins). By breaking down the overall process into these known reactions and applying Hess's Law, we can estimate the total energy released when the food is metabolized.

23. What role does Hess's Law play in understanding and calculating electron affinities?

Electron affinities, like many other atomic and molecular properties, can be difficult to measure directly. Hess's Law allows us to calculate electron affinities indirectly by constructing thermochemical cycles that involve known enthalpy changes, such as ionization energies and bond dissociation energies.

24. How does Hess's Law help in understanding the energy changes in photosynthesis and cellular respiration?

Hess's Law allows us to break down complex biological processes like photosynthesis and cellular respiration into simpler chemical reactions. By applying Hess's Law to these component reactions, we can calculate the overall energy change of these processes, helping us understand how energy is captured, stored, and utilized in living systems.

25. Can Hess's Law be applied to electrochemical reactions?

Yes, Hess's Law can be applied to electrochemical reactions. It's particularly useful in calculating the standard cell potential of a galvanic cell by combining the standard reduction potentials of the half-reactions. This application of Hess's Law demonstrates the connection between electrochemistry and thermodynamics.

26. How does Hess's Law relate to bond dissociation energies?

Hess's Law can be used to calculate bond dissociation energies by constructing a series of reactions involving the formation and breaking of specific bonds. By applying Hess's Law to these reactions and their known enthalpy changes, we can deduce the energy required to break a particular bond.

27. How can Hess's Law be used to understand the concept of resonance energy?

Resonance energy can be calculated using Hess's Law by comparing the actual enthalpy of formation of a molecule with resonance structures to the theoretical enthalpy if it existed in only one of its resonance forms. The difference between these values, determined through Hess's Law calculations, represents the stabilization due to resonance.

28. What is the relationship between Hess's Law and the heat of neutralization?

Hess's Law can be applied to understand and calculate heats of neutralization. By breaking down the neutralization reaction into component steps (like the dissociation of the acid and base, and the formation of water), we can use Hess's Law to calculate the overall enthalpy change of the neutralization process.

29. How does Hess's Law help in understanding the energy changes in phase transitions?

Hess's Law allows us to calculate the enthalpy changes associated with phase transitions by breaking the process into steps. For example, the enthalpy of vaporization can be calculated by considering the enthalpy of fusion and the enthalpy of sublimation. This approach helps in understanding the energy requirements for various phase changes.

30. Can Hess's Law be applied to reactions occurring at different temperatures?

While Hess's Law is typically applied to reactions at constant temperature, it can be extended to reactions at different temperatures by incorporating heat capacity data. This involves calculating the enthalpy change for heating or cooling the reactants and products, in addition to the reaction enthalpy at a standard temperature.

31. How does Hess's Law relate to the concept of enthalpy of dilution?

Hess's Law can be used to calculate the enthalpy of dilution by considering the process as a series of steps. By breaking down the dilution process into the separation of solvent molecules and the dispersion of solute particles, and applying Hess's Law to these steps, we can determine the overall enthalpy change of dilution.

32. What is the significance of Hess's Law in fuel cell technology?

In fuel cell technology, Hess's Law is crucial for understanding and predicting the energy output of different fuel-oxidizer combinations. It allows engineers to calculate the theoretical maximum energy output of a fuel cell by considering the enthalpies of formation of reactants and products, helping in the design and optimization of fuel cell systems.

33. How can Hess's Law be used to understand the energy changes in complex organic reactions?

For complex organic reactions, Hess's Law allows us to break down the process into simpler steps with known enthalpy changes. This is particularly useful when direct measurement is challenging. By applying Hess's Law to these component reactions, we can calculate the overall enthalpy change of complex transformations, aiding in the understanding of organic reaction energetics.

34. How does Hess's Law help in understanding the concept of electron affinity?

Electron affinity, the energy change when an atom in the gas phase accepts an electron, can be difficult to measure directly. Hess's Law allows us to calculate electron affinities indirectly by constructing a thermochemical cycle involving known enthalpy changes, such as ionization energies and bond dissociation energies.

35. Can Hess's Law be applied to biochemical reactions in living systems?

Yes, Hess's Law is applicable to biochemical reactions. It's particularly useful in understanding the energetics of metabolic pathways. By breaking down complex biochemical processes into simpler reactions with known enthalpy changes, we can use Hess's Law to calculate the overall energy change of biological processes, helping to explain how energy is utilized in living systems.

36. What is the significance of Hess's Law in understanding the greenhouse effect?

Hess's Law is crucial in understanding the energetics of greenhouse gases. It allows us to calculate the enthalpy changes associated with the absorption and emission of infrared radiation by greenhouse gas molecules. This helps in quantifying the energy trapping capacity of different gases and their impact on global warming.

37. How can Hess's Law be used to predict the stability of chemical compounds?

Hess's Law can be used to calculate the enthalpy of formation of compounds, which is a measure of their stability. By comparing the enthalpies of formation of different compounds or different arrangements of the same atoms, we can predict which structures are more stable and likely to form under given conditions.

38. How does Hess's Law help in understanding the energy changes in nuclear reactions?

Although typically associated with chemical reactions, Hess's Law can be extended to nuclear reactions. It allows us to calculate the energy released or absorbed in nuclear processes by considering the mass-energy equivalence and applying the law to the changes in nuclear binding energies.

39. Can Hess's Law be applied to calculate the energy required for chemical bonding?

Yes, Hess's Law can be used to calculate bonding energies. By constructing a series of reactions involving the formation and breaking of specific bonds and applying Hess's Law to their known enthalpy changes, we can deduce the energy required to form or break particular chemical bonds.

40. How does Hess's Law relate to the concept of lattice energy in ionic compounds?

Hess's Law is crucial in calculating lattice energies, which are difficult to measure directly. By using a Born-Haber cycle and applying Hess's Law, we can determine the lattice energy of ionic compounds using more easily measurable quantities like enthalpies of formation, ionization energies, and electron affinities.

41. How can Hess's Law be applied to understand the energy changes in redox reactions?

Hess's Law is valuable in analyzing redox reactions by breaking them down into half-reactions. By applying Hess's Law to the enthalpy changes of the oxidation and reduction half-reactions, we can calculate the overall enthalpy change of the redox process, providing insights into the energetics of electron transfer reactions.

42. What role does Hess's Law play in understanding the concept of bond dissociation energy?

Hess's Law is instrumental in determining bond dissociation energies. By constructing a series of reactions involving the breaking of specific bonds and applying Hess's Law to their known enthalpy changes, we can calculate the energy required to break a particular bond, which is its dissociation energy.

43. How does Hess's Law help in understanding the concept of heat capacity?

While Hess's Law primarily deals with enthalpy changes, it can be used in conjunction with heat capacity data to understand temperature-dependent enthalpy changes. By incorporating heat capacity into Hess's Law calculations, we can determine how the enthalpy of a reaction varies with temperature.

44. Can Hess's Law be applied to calculate the energy changes in photochemical reactions?

Yes, Hess's Law can be applied to photochemical reactions. By considering the energy input from light absorption and the subsequent chemical changes, we can use Hess's Law to calculate the overall