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Enthalpy (H) is a thermodynamic property defined as the sum of the internal energy of a thermodynamic system (U) and the product of its pressure and volume (PV). That is, the enthalpy is defined as:
This property is characterized by being a state function. This means that the value of the enthalpy of a system at a given moment depends only on the state it is in and not on the state immediately before or the one that will come after. That is, the enthalpy does not depend on the path that led the system to the state it is in, but only on what the current state is.
enthalpy change
The definition of enthalpy as a state function has several implications. One of them is that when a system undergoes a change of state, this change may in turn imply a change in the enthalpy of the system. In other words, each process to which a system is subjected has an associated change or variation in enthalpy; this variation is denoted as ΔH and can be positive, negative or even zero.
Due to the way enthalpy is defined, and as a consequence of the first law of thermodynamics, the enthalpy change of a process in which the system only carries out expansion work at constant pressure is equal to the heat that said system absorbs. . In other words, in the absence of other types of work,
where qP is the heat absorbed by the system during a process at constant pressure. This result is of great importance because a large number of chemical reactions occur at constant pressure; For this reason, the experimental measurement of the amount of heat released or absorbed during these processes makes it possible to indirectly measure the change in the enthalpy of the system.
This characteristic gives rise to what is known as thermochemistry, which is nothing more than the part of thermodynamics (or chemistry) that studies heat transfers caused by the occurrence of chemical reactions.
Hess’s law
The second implication that enthalpy is a state function is expressed in the form of Hess’s law. In relation to chemical reactions, this law says that “when reactants are converted into products, the enthalpy change is the same regardless of whether the reaction is carried out in a single step or in a series of steps.” This means that if we start with reactant A and end up with product B, the ΔH of said reaction is independent of the way in which the reaction occurred. This, in turn, implies that we can calculate the ΔH of a reaction simply by adding the ΔH values of a set of reactions that manage to transform the same reactants into the same products. The latter is one of the most common practices in thermochemistry and is precisely what the following sample problem is about.
Solved problem of calculating the enthalpy change of a reaction using Hess’s law
Statement:
Calculate the enthalpy change for the following reaction using Hess’s Law,
Given the enthalpies of the following reactions:
Solution
To calculate the enthalpy variation or change using Hess’s law, we must find a way to combine the chemical equations that we are given as data so that, when added, they result in the equation of the chemical reaction whose enthalpy change we want to calculate .
This involves manipulating chemical equations in a variety of ways, including inverting them, multiplying by constant values, or dividing by constant values. The most important thing to keep in mind is that everything that is done to the chemical equation must also be done to its value of ΔH. That is:
- When inverting or flipping a thermochemical equation, the sign of its enthalpy change must also be reversed.
- When multiplying an entire equation by a constant, then the enthalpy change must also be multiplied by the same constant.
- When dividing a chemical equation by a constant, then the enthalpy change must also be divided by the same constant.
Let’s look at the steps needed to apply these principles effectively:
Step 1: Locate the reactants and products that appear in the given reactions on the correct side of the equation
A general strategy that can be applied in most of these problems is to search one by one for the reactants and products of the unknown reaction, that is, the one whose enthalpy we want to calculate, in all the reactions that we are given as data. Next, you have to make sure that the compound you’re interested in is on the right side of the equation; otherwise, the equation is reversed.
For example, in the present problem, we are interested in elemental aluminum and iron oxide appearing among the reactants of reactions whose enthalpies are known. As can be seen, this implies inverting both equations, as well as inverting the sign of their enthalpy changes:
By inverting these equations we can place the reactants on the side where we need them, but at the same time we place the products on the correct side. However, the process is not yet ready since, as can be seen, the sum of these two reactions does not give the required reaction.
Step 2: Multiply or divide the stoichiometric coefficients when necessary
It should be understood that you want the sum of the given chemical equations to give the unknown equation. This implies that every species that does not appear in the last one must be canceled and all other species must have the appropriate stoichiometric coefficients.
In our problem it can be seen that the reactions given as data involve molecular oxygen, which is not present in the reaction we are looking for, so we must make sure that it cancels when adding the equations. For this to happen and, furthermore, for the coefficients of iron and ferric oxide to be correct, the second equation must be divided by 2, as well as its enthalpy. That is to say:
Which results in:
Step 3: Add the equations
By having all the reactants and products on the correct side and with the correct coefficients, the equations and their respective enthalpies can be added, in order to obtain the enthalpy we are looking for:
Finally, we have that the enthalpy change of the reaction is:
Answer:
The reaction between aluminum and ferric oxide to give iron and aluminum oxide has a standard enthalpy change of -845.6 kJ/mol.
References
- Atkins, P., & dePaula, J. (2008). Physical Chemistry (8th ed .). Panamerican Medical Editorial.
- Britannica, The Editors of Encyclopaedia. (2020, April 9). Enthalpy | Definition, Equation, & Units . Encyclopedia Britannica. https://www.britannica.com/science/enthalpy
- Chang, R., & Goldsby, K. (2013). Chemistry (11th ed .). McGraw-Hill Interamericana de España SL
- Drafting Concept definition. (2020, December 16). Hess’s Law . Concept of – Definition of. https://conceptodefinicion.de/ley-de-hess/
- Suárez, T., Fontal, B., Reyes, M., Bellandi, F., Contreras, R., & Romero, I. (2005). Principles of Thermochemistry . VII Venezuelan School for the Teaching of Chemistry. http://www.saber.ula.ve/bitstream/handle/123456789/16744/termoquimica.pdf?sequence=1&isAllowed=y
