Hess Law

In 1840, Chemist G.H. Hess put forward an important law governing the enthalpies of reaction. According to Hess' law:

The enthalpy of a reaction depends upon nature and state reactants and products. It is independent of the path followed by the chemical reaction. The law is, in fact, merely a special case of the first law of thermodynamics (law of conservation of energy).

Proof: A theoretical proof of Hess law can be obtained from the following considerations. 

Let a substance A be converted into B by a process involving a single step reaction which is accompanied by the evolution of Q kJ of heat. In the second process, let A be converted into B in two steps, i.e., A to C and then C to B. Let Q₁and Q₂ be the heat involved in the two-step respectively, so that Q₁+Q₂=Q Where Q' is the total heat produced in going from A to B. Suppose Q is greater than Q'. 

Now if we go from A to B, in a single step, Q kJ of heat will be evolved while returning from B to A through C, Q'kJ of heat will be absorbed. In this way, Q-Q'kJ heat will be produced by transforming A to B in a single step and then B to A via C. 

In other words, a large amount of heat can be produced without doing any external work by merely repeating the above cycle several times. However, this is against the law of conservation of energy. Hence, Q' must be equal to Q as required by Hess’ law.   

Illustration of Hess law

Illustration 1) As a further illustration of the law, consider the formation of carbon dioxide. There are two ways in which CO₂ can be formed. 

(i) In the first step, by burning carbon in excess of oxygen. 

C(s)+O₂CO₂(g); ΔrH= -393.5 k J

(ii) In the second step, by burning carbon in a limited supply of oxygen to form CO and then CO is converted to CO₂.

C(s)+12O₂(g)CO(g);  ΔrH  = -110.54 kJ

CO(g)+12O₂(g)CO₂(g);  ΔrH  = -393.5 kJ

On adding, we get

C(s)+O₂(g)CO₂(g);  ΔrH  = -393.5 kJ

Thus, in both cases,  ΔrH   is the same. This proves the law. 

Illustration 2) Now consider the formation of an aqueous solution of ammonium chloride from NH₃HCL and water. There are two ways in which the reaction can be brought about. 

(i) NH₃(g) + HCL(g) → NH₄CL(s); ΔrH  =175.73 kJ

NH₄CL(s)+aq → NH₄CL(aq); ΔrH  = +16.32 kJ

On adding, 

NH₃(g)+HCL(g)+aq → NH₄CL(aq); ΔrH  = -159.41kJ

(ii) NH₃(g) +aq → NH₃(aq);  ΔrH  = -35.15 kJ

HCL (g)+aq →HCL(aq); ΔrH  = -72.38 kJ

NH₃(aq)+HCL(aq)  → NH₄CL(aq); ΔrH  = -51.36 kJ

On adding NH₃(g) + HCL(g)+aq → NH₄CL(aq)  ΔrH  = -158.99 kJ

Thus, in both cases, the net enthalpy change is nearly the same. The difference in 0.42kJ may be due to experimental error. 

Hess Law Examples

Example 1) Calculate the enthalpy of formation of methane from the following data:

i) C(s)+O₂(g)CO₂(g);   ΔrH^Ⓗ   = -394 kJ

ii) H₂(g)+12O₂(g)H₂O(l);  ΔrH^Ⓗ    = -286 kJ

iii) CH4(g) +2O2(g)CO2(g) +2H2O(l);   ΔrH^Ⓗ    = -890.0 kJ

Solution 1) The required Hess law equation is:

C(s)+2H₂(g)CH₄(g);  ΔrH^Ⓗ    =?

In order to get the required Hess law equation from equation (i), (ii), and (iii), multiply equation (ii) by two and add to equation (i), i.e., 2 x equation (ii) + equation (i)

2H₂(g)+O₂(g)2H₂O(l);   ΔrH^Ⓗ    = -572 kJ

C(s)+O₂(g)CO₂(g);  ΔrH^Ⓗ  = -394

(iv) C(s) + 2H₂(g)+2O₂(g)CO₂(g) +2H₂O(l)   ΔrH^Ⓗ    = -966 kJ

Subtracting equation (iii) from (iv) we get,

C(s)+2H₂(g)CH₄(g)  ΔrHⒽ  = -76.0 kJ

Thus, enthalpy of formation of methane is -76.0 kJ

Practice more Hess law examples to have a clear underlying of the concept. 

Hess Law

Hess's Law asserts that the total enthalpy change for a reaction is the sum of all changes, regardless of how many stages or steps there are. The fact that enthalpy is a state function is demonstrated by this law.

Hess's Law is named after Germain Hess, a Russian chemist and doctor. Hess was a key figure in the development of thermochemistry's early ideas. Hess's Law, his most well-known publication, is named after Russian chemist and doctor Germain Hess. Hess was a key figure in the development of thermochemistry's early ideas. His law on thermochemistry was included in his most renowned article, which was published in 1840. Hess's law is based on the fact that enthalpy is a state function, allowing us to determine the overall change in enthalpy by simply adding the changes for each step until the product is formed. All steps must be completed at the same temperature, and the equations for each step must be balanced.

Application of Hess Law

Hess' law can be used to calculate the enthalpies of the following substances.

• Heats associated with the creation of unstable intermediates such as CO(g) and NO (g).

• In phase transitions and allotropic transitions, heat changes.

• If the electron affinity to create the anion is known, lattice energies of ionic compounds can be calculated by constructing Born–Haber cycles, or

• A Born–Haber cycle with a theoretical lattice energy is used to calculate electron affinities.

According to Hess's Law, if you convert reactants A to products B in one step, two steps, or however many steps, the overall enthalpy change will be the same.

I'll give you an easy example. You're on the ground floor of a five-star hotel, and you'd want to go to the third storey. You can do it in one of three ways: (a) take the elevator straight to the third floor from the ground floor. (b) You can take the elevator from the ground floor to the second floor, then take the elevator from the second floor to the third floor after stopping for a bit on the second floor. (c) You can take the elevator from the ground floor to the first floor, then take the elevator from the first floor to the third floor after stopping for a bit on the first floor.No matter which route you choose, the elevator will consume the same amount of energy.