Hess Law

Hess’s Law is a fundamental principle in thermodynamics that states that the total enthalpy change for a chemical reaction is independent of the pathway taken to reach the final state.

Hess’s Law is based on the first law of thermodynamics, which states that energy cannot be created or destroyed but can be converted from one form to another. Hess Law is also called Hess Law of Constant Heat. In this article, we will see Hess Law, its forms, applications, etc.

What is Hess Law?

Hess’s Law, named after Russian chemist Germain Hess, states that the total enthalpy change of a reaction is the sum of all the changes, regardless of the number of steps or stages in the reaction. It is based on the principle that enthalpy is a state function, allowing the calculation of the overall change in enthalpy by summing up the changes for each step until the product is formed.

Definition of Hess Law

“The total enthalpy change of a reaction is the same whether it occurs in one step or multiple steps.”

Hess Law can be used to calculate enthalpy changes that are difficult to measure directly. An example of using Hess’s Law is calculating the enthalpy change for methane formation from solid carbon and hydrogen gas. This reaction occurs too slowly to be measured in the laboratory.

Hess Law Formula

Formula to calculate the enthalpy change using Hess’s Law is expressed mathematically as the sum of the enthalpy changes for a series of reactions being equal to the enthalpy change for the overall reaction. The formula is:

ΔH°_reaction = ∑n × ΔH_f°_(products) − ∑n × ΔH_f°_(reactants)

Where,

• ΔH°_reaction is the enthalpy change for the reaction of interest,
• ΔH°_products is the standard enthalpy of formation of the products,
• ΔH°_reactants ​ is the standard enthalpy of formation of the reactants, and
• ∑n is the coefficient of each substance in the balanced chemical equation.

Enthalpy Change

Enthalpy change of a reaction is a measure of the heat evolved or absorbed during the reaction at constant pressure.

Enthalpy, denoted as H, is the heat content of a system at constant pressure. It is determined by the energies needed to break chemical bonds and the energies needed to form new bonds. The heat that is absorbed or released by a reaction at constant pressure is the same as the enthalpy change, given the symbol ΔH.

Example of Hess Law

For example, to find the enthalpy change for the reaction of carbon with hydrogen gas to form acetylene (C₂H₂), you could use the following equations:

C(s) + O₂(g) → CO₂(g) ΔH = -393.5 kJ/mol

2H₂(g) + O₂(g) → 2H₂O(l) ΔH = -572 kJ/mol

C₂H₂(g) + 2O₂(g) → 2CO(g) + H₂O(l) ΔH = +1299.6 kJ/mol

To find the enthalpy change for the formation of one mole of acetylene, you would add the enthalpy changes for the first two equations and then subtract the enthalpy change for the third equation, multiplied by a factor of 1/2 (since there is half a mole of CO₂ in the third equation):

ΔH(acetylene) = ΔH(CO₂) + ΔH(H₂O) – (1/2)ΔH(CO)

⇒ ΔH(acetylene) = (-393.5 kJ/mol) + (-572 kJ/mol) – (1/2)(1299.6 kJ/mol)

⇒ ΔH(acetylene) = -965.5 kJ/mol + 649.8 kJ/mol – 649.8 kJ/mol

⇒ ΔH(acetylene) = -315.7 kJ/mol

Forms of Hess Law

Hess law can take place in many forms i.e.,

• Multi-Step Reaction
• Multi-Different Reaction

These forms are discussed in detail as follows:

For Multi-Step Reaction

In chemistry, a multi-step chemical reaction occurs through a sequence of two or more elementary steps. An elementary step is a single, simple step involving one or two molecules. One or more intermediates are formed and subsequently consumed in a multi-step reaction.

These reactions are characterized by their specific elementary steps, each representing a single molecular event. In multi-step reactions, the enthalpy change of the overall reaction is a sum of the heat released and absorbed in all the individual steps.

Steps to Apply Hess Law for Multi-Step Reaction

To apply Hess’s Law to multi-step reactions, follow these steps:

• Write down the balanced chemical equations for each step of the reaction.
• Using known data or experimental measurements, calculate each step’s enthalpy change (ΔH).
• If necessary, reverse or multiply the equations by coefficients to obtain a set of equations that add up to the overall reaction.
• Sum the enthalpy changes (ΔH) for the set of equations that add up to the overall reaction.
• The reaction’s overall enthalpy change (ΔH) will equal the sum of the enthalpy changes for the individual steps.

For example, consider the following multi-step reaction:

A + B → C (ΔH₁ = -10 kJ)

C + D → E (ΔH₂ = -20 kJ)

E + F → G (ΔH₃ = -30 kJ)

To find the enthalpy change for the overall reaction (A + B + D → G), we must manipulate the given reactions to obtain the desired reaction. In this case, we can reverse reaction 1 and add it to reactions 2 and 3:

C → A + B (ΔH_1′ = +10 kJ)

C + D → E (ΔH₂ = -20 kJ)

E + F → G (ΔH₃ = -30 kJ)

Now, we can sum the enthalpy changes for the set of equations that add up to the overall reaction:

ΔH_total = ΔH₁‘ + ΔH₂ + ΔH₃ = (+10 kJ) + (-20 kJ) + (-30 kJ) = -40 kJ

The overall enthalpy change for the reaction (A + B + D → G) is -40 kJ. This method is particularly useful when the enthalpy change for the overall reaction cannot be measured directly, as it allows us to calculate the enthalpy change using known enthalpy changes for individual steps.

For Multi-Different Reaction

Multi-different or multi-component reactions (MCRs) are chemical reactions where three or more compounds react in a single reaction vessel to form a single product. These reactions are characterized by combining more than two reactants, which can lead to highly selective products.

Example of Hess Law for Multi-Step Reaction

To illustrate this with an example, let’s consider a multi-step reaction:

A + B → C

C + D → E

E → F

The overall reaction is: A + B + D → F

To find the enthalpy change for the overall reaction, you can use Hess’s Law by summing the enthalpy changes of each step:

ΔH_total = ΔH₁ + ΔH₂ + ΔH₃

If you have the enthalpy changes for each step, you can calculate the overall enthalpy change for the reaction. This principle helps us understand the thermodynamics of complex reactions and the design of synthetic routes.

It is essential to note that Hess’s Law is applicable to enthalpy changes, not to the reaction rates or the order of the reactions. The order of the reactions and the rate constants are not affected by Hess’s Law.

Hess Law of Heat Summation

Hess’s Law of Constant Heat Summation, also known as Hess’s Law, is a fundamental principle in chemistry that allows calculating the overall enthalpy change of a reaction by summing up the enthalpy changes of individual steps. The formula to calculate the enthalpy change using Hess’s Law is expressed mathematically as the sum of the enthalpy changes for a series of reactions equal to the enthalpy change for the overall reaction.

Application of Hess Law

Hess’s Law of Constant Heat Summation, also known as Hess’s Law, has several applications in chemistry. Some specific applications and uses of Hess’s Law include:

Determination of Enthalpy of Formation

Hess Law can be used to determination of enthalpy of formation of any reaction. For example, lets calculate the enthalpy of formation of methane.

The enthalpy change for the reaction of carbon with hydrogen to form methane is -74.8 kJ/mol, and the enthalpy change for the combustion of methane to form carbon dioxide and water is -890.3 kJ/mol.

Therefore, the enthalpy of formation of methane is -74.8 kJ/mol + (-890.3 kJ/mol) = -965.1 kJ/mol.

Calculation of Standard Enthalpies of Reaction

Hess’s Law can be applied to calculate the standard enthalpies of reaction. For example, consider the reaction:

2H2(g) + O2(g) → 2H2O(l)

The standard enthalpies of formation for hydrogen gas and water are 0 kJ/mol and -285.8 kJ/mol, respectively. Using Hess’s Law, we can calculate the standard enthalpy change for the reaction as:

ΔH° = 2ΔH°_f(H₂O_(l)) – 2ΔH°_f(H_2(g)) – ΔH°_f(O_2(g))

ΔH° = 2(-285.8 kJ/mol) – 0 – 0 = -571.6 kJ/mol

Therefore, the standard enthalpy change for the reaction is -571.6 kJ/mol. This example illustrates how Hess’s Law can be used to calculate the standard enthalpy change for a reaction of interest by summing up the enthalpy changes of a series of reactions that lead to the formation of the products and reactants of the reaction of interest

Example Problems on Hess Law

Problem 1: Calculate the reaction’s standard enthalpy change using the following reaction.

CO_2(g) + H_2(g) → CO_(g) + H₂O_(g)

Given that, Δ_rH^o for CO_(g), CO_2(g), and H₂O_(g) as -110.5 kJ/mol, -393.5 kJ/mol, and 241.8kJ/mol respectively.

Solution:

Δ_rH^o for the reaction can be given as:

△_rH^o = Σ△_fH^o_(Products) – Σ△_fH^o_(Reactants)

Given:

• Δ_f​H^∘(CO(g)) = −110.5kJ/mol
• Δ_f​H^∘(CO₂​(g)) = −393.5kJ/mol
• Δ_f​H^∘(H₂​O(g)) = 241.8kJ/mol
• We know, △_fH^o (H₂) = 0

Thus, △_rH^o= [△_fH^o (H₂O) + △_fHo(CO)] – [△_fH^o (CO₂) + △_fH^o (H₂)]

⇒ △_rH^o=[−110.5+241.8]−[−393.5+0]

⇒ △_rH^o= (131.3) − (−393.5)

⇒ △_rH^o= 131.3 + 393.5

⇒ △_rH^o= 524.8kJ/mol

Problem 2: Hess’s law states that a chemical reaction is independent of the route of chemical reactions while keeping the same

(a) Initial and Final Conditions

(b) Initial conditions only

(c ) Final conditions only

(d) None of the above

Solution:

Hess’s law states that a chemical reaction is independent of the route of chemical reactions while keeping the same initial and final conditions.

Problem 3: Calculate the enthalpy change for the following reaction:

CH₄ ​_(g) + 2 O_{2 ​(g)} ⟶ CO_{2 ​(g)} + 2 H₂​O _(l).

Given that enthalpies of formation of CH₄, CO₂ and H₂​O are 74.8 kJmol⁻¹,− 393.5 kJ mol⁻¹, and − 286 kJmol⁻¹, respectively.

Solution:

We know, ΔH^o = ΔH^o_(products) ​− ΔH^o_(reactants)​

⇒ ΔH^o = [ΔH^o(CO₂) ​+ 2 x ΔH^o(H₂O)] − [ΔH^o(CH₄) + 2 x ΔH^o(O₂)​]

⇒ ΔH^o = [− 393.5 + 2 X (−286.2)] − [74.8 + 2 X 0]

⇒ ΔH^o = − 393.5 – 572.4 – 74.8

⇒ ΔH^o = − 1040.7 kJ

Practice Problems Hess Law

Problem 1: Use Hess’s Law to calculate the enthalpy change for the reaction:

2SO₂(g)+O₂(g) → 2SO₃(g)

Given that the standard enthalpies of formation for sulfur dioxide and sulfur trioxide are -296.8 kJ/mol and -395.7 kJ/mol, respectively.

Problem 2: Calculate the enthalpy change for the reaction:

2C₂H₆(g) + 7O₂(g) → 4CO₂(g) + 6H₂O(l)

Given that the standard enthalpies of formation for ethane, carbon dioxide, and water are -84.7 kJ/mol, -393.5 kJ/mol, and -285.8 kJ/mol, respectively.

Problem 3: Calculate the enthalpy change for the reaction:

2C₂H₂(g) + 5O₂(g) →4CO₂(g) + 2H₂O(g)

Given that the standard enthalpies of formation for acetylene, carbon dioxide, and water are 226.7 kJ/mol, -393.5 kJ/mol, and -285.8 kJ/mol, respectively.

Hess Law Frequently Asked Questions

State Hess Law.

Hess’s Law states that the total enthalpy change for a reaction is the same, regardless of the route taken. It’s about the total energy change during a reaction, which remains constant.

On which Law of Thermodynamics is Hess Law based?

Hess’s Law is based on the first law of thermodynamics, which states that energy cannot be created or destroyed; it can only be transferred or converted.

What is Meant by ΔH?

ΔH represents the change in enthalpy, which is the heat absorbed or released during a reaction at constant pressure.

What does Hess’s Law State?

“The total enthalpy change of a reaction is the same whether it occurs in one step or multiple steps.”

What is the Basis of Hess’s Law?

It’s based on the principle of energy conservation, meaning the total energy change in a reaction is independent of the pathway taken.

What is the Meanig of Entropy?

Entropy refers to the measure of disorder or randomness in a system. It tends to increase in natural processes.

Why is Hess Law Important?

Hess’s Law is essential because it allows us to indirectly calculate the enthalpy change of a reaction, using known enthalpy changes of other reactions.

What is Hess Law Equation?

Equation of Hess Law is given as:

△H_net = Σ△H_r