Understanding Hess Law: Definition, Importance, Forms, and Applications - Testbook

Understanding Hess Law

Hess's Law, otherwise known as the law of constant heat summation, is a fundamental principle in the field of chemistry. This law asserts that the total enthalpy change (ΔHrec) in a chemical reaction remains constant, regardless of the reaction pathway taken, provided the temperature remains constant.

This law is grounded in the state function characteristic of enthalpy and the first law of thermodynamics. The energy (or enthalpy) of a system (molecule) is a state function, meaning its value is determined by the current state of the system and not the path taken to reach that state. Therefore, the enthalpy of reactant and product molecules remains constant and is independent of the path of formation.

The first law of thermodynamics states that the total energy of the substances before and after any physical or chemical change should remain equal. According to this law, the total energy of the reactant should be equal to the total energy of the product. Any difference in the energy between the reactants and products is also fixed at a particular temperature and will not change with the path followed by the reactants to form products. Therefore, heat energy can also be considered as a reactant or product of the reaction and can be included in the reaction.

This principle allows us to express exothermic reactions as: A + B → C + D + ΔH

Similarly, endothermic reactions can be expressed as: A + B + ΔH → C + D

This understanding allows us to treat reactions containing reactants and products as algebraic equations, enabling mathematical operations to be performed on them. It is important to remember that an exothermic reaction in one direction will be endothermic in the reverse direction, and vice-versa.

The Significance of Hess Law

All substances, whether they are atoms or molecules, possess inherent energy. The internal energy of a substance is dependent on the nature of the forces within the substance and the temperature. When a substance undergoes a chemical reaction, some bonds connecting atoms are broken and new bonds are formed. This process of breaking and forming bonds involves energy.

Therefore, in chemical reactions, the products may have less, the same, or more energy than the reacting substances. Depending on this, reactions may either release heat (exothermic) or absorb heat (endothermic). Reactants may react to produce the product in a single step, multiple steps, or alongside other products.

1. In a single step
2. In multiple steps
3. Alongside other products

Understanding the energy changes in any reaction is crucial for manipulating the reactants and products in a chemical process to meet our requirements.

Heat energy changes of reactions measured at constant volume are known as the internal energy change (ΔE), and energy measured at constant pressure is known as the enthalpy change (ΔH).

Experimental measurements can only provide the net value of all reactions or products formed. It is not possible to experimentally measure the enthalpy change of an intermediary reaction step or any intermediary product.

For instance, carbon reacts with oxygen to form carbon dioxide in excess oxygen. The reaction can either occur directly or in two steps - initially forming carbon monoxide and then carbon dioxide. However, measurements will only provide the energy changes for the formation of carbon dioxide, not for carbon monoxide.

Similarly, measuring the enthalpy of formation of benzene from carbon and hydrogen is not feasible because carbon and hydrogen can combine to form not only benzene but also other types of hydrocarbons under given conditions.

Hess’s law proves to be useful and is the only way of calculating such non-measurable enthalpy changes in physical and chemical changes.

Variations of Hess Law

Hess’ law can be stated in several ways.

For multi-step reactions:

If reactants react to form products not in a single step but in a number of consecutive steps involving many intermediary products, the sum of all the reactants, products, and the corresponding energy changes will give the reactant, products, and heat energy changes of the overall reaction. Therefore, like molecules, heat energy changes also can be subjected to mathematical operations.

For multi-different reactions:

If the reactants and products of a required chemical reaction can be obtained by the summation of many other chemical reactions, the enthalpy of the required reaction of reactants to the products also can be obtained by the sum of the enthalpy changes of all those chemical reactions.

a) Hess law and multi-step reaction:

A reactant can form a product by following three different steps. C, D, and E are intermediates in the other stepwise reactions. Hess’ law states that the enthalpy of the reaction (ΔH1) is the same irrespective of the path.

Therefore, the enthalpy of a direct single-step reaction and other paths giving intermediates C, D, and E should be the same. ΔH1 = ΔH2+ ΔH3 = ΔH4 + ΔH5 + ΔH6.

For example, carbon reacts with oxygen to form carbon dioxide, releasing 94.3 kcals of heat in a single step. Carbon can also react in a two-step process, forming an intermediate carbon mono-oxide, which is then converted to carbon dioxide. (ΔH = – Heat released)

C + O₂ → CO + 26.0 kcals

CO + O₂ → CO₂ + 68.3kcals

On adding the two reactions, C + O₂ → CO₂ + 94.3 kcals

As per Hess law, ΔH = ΔH1 + ΔH2 = -26.0 + 68.3 = 94.3 kcals

The net reaction enthalpy of both reactions is the same as that of single-step formation. Therefore, the enthalpy of the reaction does not change on the path followed by the reactants.

b) Hess law and multi-different reactions:

The combustion of carbon, sulphur, and carbon disulphide are exothermic with enthalpy values of -393.5kJ, -296.8kJ, and -1075kJ, respectively.

The reactions are as follows-

C(s) + O₂(g) → CO₂(g) + 393.5 kJ ……..(1)

S(s) + O₂(g) → SO₂(g) + 296.8 kJ .…….(2)

CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g) + 1075.0 kJ ..…….(3)

These reactions and enthalpy changes can be treated as algebraic equations to calculate the heat of formation of carbon disulphide, even without conducting experiments.

Equation 1: C(s) + O₂(g) → CO₂(g) + 393.5 kJ

2x equation 2:2S(s) + 2O₂(g) → 2SO₂(g) + 593.6 kJ

Reverse of equation3: CO₂(g) + 2SO₂(g) → CS₂(l) + 3O₂(g) -1075.0 kJ

Adding the three reactions: C (s) + 2S (s) → CS₂(l) -87.9 kJ

The formation of carbon disulphide is an endothermic reaction.

Applications of Hess Law of Heat Summation

The Hess’ law of heat summation serves as an efficient method to estimate heat changes that cannot be measured experimentally.

1. Enthalpy change in a physical change

Carbon and diamond are allotropes of carbon. However, measuring the energy change in the conversion of graphite to diamond is impossible, as the process cannot be carried out. Yet, the heat changes for this hypothetical physical change can be calculated using Hess law.

Graphite and diamond combine with oxygen, with the heat of reaction as -393.4kJ and – 395.4kJ, respectively.

C (graphite) + O₂ → CO₂ ΔHgr = -393.4kJ

C (diamond) + O₂ → CO₂ ΔHdi = -395.4kJ

Reversing the combustion reaction of diamond as-

CO₂ → C (diamond) + O₂ ΔHdi = + 395.4kJ

Adding,

C (graphite) + O₂ → CO₂ ΔHgr = – 393.4kJ

C (graphite) → C (diamond) ΔHtr = +2.kJ

The enthalpy change in the allotrope transition of graphite to diamond is endothermic of 2KJ.

2. Enthalpy change of a chemical reaction

The bond energy of hydrogen, iodine, and hydrogen iodide are 218, 107kJ, and 299kJ, respectively.

To estimate the enthalpy of hydrogen iodide formation and determine whether the reaction is endothermic or exothermic, consider the formation of hydrogen iodide from hydrogen and iodine.

The enthalpy of formation of hydrogen iodide is the heat changes occurring when one atom of hydrogen and one atom of iodine react to form one mole of hydrogen iodide under standard conditions (as a gas). To get one atom of hydrogen or iodine, the molecular bond has to be broken.

Heat of formation = Bond energy of HI – Bond dissociation of H₂ – Bond dissociation energy of I₂.

= 299 – (218 + 107) = 299-325 =-26kJ

As the heat of formation is negative, the reaction is exothermic.

3. Enthalpy of formation

When carbon combines with hydrogen, it can form many hydrocarbons. Therefore, the heat of formation of benzene cannot be determined experimentally. However, the heat change can be calculated using Hess law.

6C + 3H₂ → C₆H₆ ΔH C₆H₆ = ?

The heat of formation of carbon dioxide and water are -393.5kJ and -285.8KJ, respectively, while the heat of combustion of benzene is -3301kJ.

C + O₂ → CO₂ ΔH1 = -393.5kJ…..1

H₂ + O₂ → H₂O ΔH2 = -285.8kJ……2

C₆H₆ + 9O₂ → 6CO₂ + 3H₂O ΔH3 = -3301kJ …….3

6 x Reaction 1: 6C + 6O₂ → 6CO₂ 6ΔH1 = -2361kJ…..1

3 x Reaction2: 3H₂ + 3O₂ → 3H₂O 3ΔH2 = -857.4kJ……2

Reverse of reaction 3: 6CO₂ + 3H₂O → C₆H₆ + 9O₂ -ΔH3 = +3301kJ …….3

Adding the three reactions- 6C + 3H₂ → C₆H₆ ΔH= +82.6kJ

The heat of formation of benzene is 82.6kJ.

4. Bond energy

5. Lattice energy