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Hess’s Law

hess's law definition

Core Concepts

So what is Hess’s Law? In this tutorial, you will be introduced to Hess’s Law, as well as the equation that goes along with this concept. In addition, you will further master this concept by going through some example problems.

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What is Hess’s Law?

Russian Chemist and Physicist Germain Hess developed the concepts of thermochemistry and physical chemistry. He introduced the concept known as Hess’s Law of Constant Heat of Summation or Hess’s Law for short.

Hess’s law has to do with net enthalpy in a reaction or set of thermodynamic processes. Overall, it states that the total enthalpy change of a reaction is the sum of all the changes, no matter the number of steps or stages in the reaction (i.e. net enthalpy and the number of steps in a reaction are independent of each other).

There are some requirements that the reaction has to follow in order to use Hess’s Law. For example, if there are multiple steps to the reactions, each equation must be correctly balanced. Also, all the steps of the reaction must start and end at constant temperatures and pressures in order to keep reaction conditions constant.

Hess’s Law Equation

To put this definition into mathematical terms, here is the Hess’s Law equation:

∆Hnet=∑∆Hr


net enthalpy change = ∆Hnet
the sum of all enthalpy change steps = ∆Hr

Enthalpy Change

Enthalpy change, ∆H, can be defined as the amount of heat absorbed or released during a reaction. Remember that enthalpy is only equal to the heat of reaction when the pressure and volume of the system are constant. In each individual step of a multistep reaction, there is a beginning and end enthalpy value with the difference between them being the enthalpy change. This value can either be negative if heat was absorbed, or positive if heat was released. If you add up all the enthalpy changes of each reaction step (∆Hr), you have net enthalpy change, which is found by finding the difference between the final product enthalpy and the beginning reactant enthalpy (∆Hnet). That is Hess’s Law!

what is hess's law

Hess’s Law Example Problems

Now that we understand the concept and equation of Hess’s Law, let’s expand on our knowledge with practice problems. These word problems may ask for some manipulation of reactions (i.e. changing the direction of equation, multiplication, division), but the general idea is the same for all Hess’s Law problems. Let’s go through some examples below!

Example Problem 1

Find the net enthalpy change (∆Hnet) of the reaction below, given the reaction steps and their ∆H values.

Overall reaction: N2H4(l) +H2(g) → 2NH3 (g)

(i) N2H4(l) + CH4O(l) → CH2O(g) + N2(g) + 3H2(g) ∆H= – 37kJ/mol
(ii) N2(g) + 3H2(g) → 2NH3(g) ∆H= -46kJ/mol
(iii) CH4O(l) → CH2O(g) + H2(g) ∆H= -65kJ/mol

1. Make sure the steps are (a) balanced (b) in the right direction and (c) result in the overall reaction.

To make sure all the steps given are necessary for the overall reaction, add the equations and cross off repeated compounds to make a overall equation.

However, if we do this step with the reactions as they are, we do not end up with the correct reaction because we have compounds on the wrong side as well as extra compounds. Because of this, we can analyze if one, or more than one, of the steps, go in the opposite direction.

Since reaction (i) is the only one with N2H4(l), which is a reactant in the overall equation, it is assumed that it is going in the correct direction. Next, reaction (ii) has the product 2NH3(g) on the right side, so that equation remains the same as well. In the above attempt to find the overall equation, the hydrogen gas from equations (i) and (ii) cancel each other out, meaning the hydrogen gas from reaction (iii) is the only one left to make it to the overall equation, which belongs on the left. Because of this, we can flip the equation reactants and products to go the backward direction; however, because the reaction is going in the opposite way, the enthalpy also becomes the “opposite”. If you change the direction of a reaction, the reciprocal of the enthalpy becomes the new enthalpy.

The “new” equation steps look like this:

(i) N2H4(l) + CH4O(l) → CH2O(g) + N2(g) + 3H2(g) ∆H= – 37kJ/mol
(ii) N2(g) + 3H2(g) → 2NH3(g) ∆H= -46kJ/mol
(iii) CH2O(g) + H2(g) → CH4O(l) ∆H= +65kJ/mol

With reaction (iii) switched the method of adding all the equations results in the correct overall reaction:

hess's law practice problem

N2H4(l) +H2(g) → 2NH3 (g)

2. Find Net Enthalpy Change

Now that we have the official enthalpy values, we can use Hess’s Law equation to solve.

∆Hnet=∑∆Hr = (-37 kJ/mol) + (-46 kJ/mol) + 65 kJ/mol = -18kJ/mol

Example Problem 2

Find the net enthalpy change (∆Hnet) of the reaction below, given the reaction steps and their ∆H values.

Overall Reaction: CS2(l) + 3O2(g) → CO2(g) + 2SO2(g)

(i) C(s) + O2(g) → CO2(g) ∆H= -395 kJ/mol
(ii) S(s) + O2(g) → SO2(g) ∆H= -295 kJ/mol
(iii) C(s) + 2S(s) → CS2(l) ∆H= +90 kJ/mol

1. Make sure the steps are (a) balanced (b) in the right direction and (c) result in the overall reaction.

First, using the same methods as above, we check if all the step reactions are going in the correct direction to make the correct reaction. Reaction (i) has the desired CO2(g) product, which means it can remain unchanged. Reaction (iii) has CS2(l) as a product, but is a desired reactant in the overall reaction; therefore, we flip this reaction and use the reciprocal ∆H value.

As for reaction (ii), the direction is correct because O2(g) as a reactant and SO2(g) as a product are both seen in the desired reaction; however, when adding the equations together, one O2(g) and one SO2(g) are missing (there is also an extra S(s) that needs to be canceled out). This can be fixed by multiplying reaction (ii) by a factor of 2. If you multiply(or divide) this, you also have to multiply (or divide) the ∆H value by the same coefficient.

(i) C(s) + O2(g) → CO2(g) ∆H= -395 kJ/mol
(ii) 2S(s) + 2O2(g) → 2SO2(g) ∆H= -590 kJ/mol
(iii) CS2(l)→ C(s) + 2S(s) ∆H= -90 kJ/mol

With reactions (ii) and (iii) manipulated, the method of adding all the equations results in the correct overall reaction:

hess's law examples

CS2(l) + 3O2(g) → CO2(g) + 2SO2(g)

2. Find Net Enthalpy Change

Now that we have the official enthalpy values, we can use Hess’s Law equation to solve.

∆Hnet=∑∆Hr = (-395 kJ/mol) + (-590 kJ/mol) + (-90 kJ/mol) = -1075 kJ/mol

For More Help, Watch Our Interactive Video Explaining Hess’s Law!

Further Reading