REACTION ENTHALPY: DEFINITION, THERMOCHEMISTRY, EXERCISES - PHYSICAL - 2025

The enthalpy of reaction is a thermodynamic function that allows calculating the heat gained or delivered in a chemical reaction, provided that this reaction has occurred at constant pressure. It is defined as the internal energy U plus the product of the pressure P by the volume V of the substances that take part in a chemical reaction, as follows: H = U + P ∙ V

Therefore enthalpy has dimensions of energy, and in the International System of measurements it is measured in Joules. To understand the relationship of enthalpy with the heat exchanged in a chemical reaction, it is necessary to remember the first law of thermodynamics, which states the following: Q = ΔU + W

Figure 1. In the combustion of a gas the enthalpy decreases. Source: pixabay

The first law establishes that the heat exchanged in a thermodynamic process is equal to the variation of the internal energy of the substances involved in the process plus the work done by these substances in the process.

In any process, the work W is calculated by the following relationship:

In the above expression Vi is the initial volume, Vf the final volume and P the pressure. If the process is carried out at constant pressure P, then the resulting work will be:

Where ΔV is the change in volume.

Definition

Chemical reactions are thermodynamic processes that generally occur at constant pressure and very frequently at atmospheric pressure. This type of thermodynamic process is called "isobaric", since it occurs at constant pressure.

In this case the first law of thermodynamics can be written like this:

Qp = ΔU + P ∙ ΔV

Where Qp indicates that the heat has been exchanged at constant pressure. If the definition of enthalpy H = U + P ∙ V is introduced in the previous expression, then we obtain:

Qp = ΔH

Hence, a positive enthalpy change indicates a reaction that has taken heat from the environment. This is an endothermic reaction.

On the contrary, if the enthalpy change is negative then it is an exothermic reaction.

In fact, the word enthalpy comes from the Greek word enthalpien, which means "to heat."

Enthalpy is also often called heat. But it should be clear that it is not the same as heat, but it is the heat exchange during the thermodynamic process that changes the enthalpy.

Relationship with heat

Unlike heat, enthalpy is a function of state. When you calculate the enthalpy change, you are calculating the difference of two functions that depend exclusively on the state of the system, such as internal energy and volume.

ΔH = ΔU + P ∙ ΔV

Since the pressure remains constant in the reaction, then the enthalpy of reaction is a function of state that only depends on the internal energy and the volume.

In a chemical reaction, the enthalpy of the reactants can be defined as the sum of that of each of them; and that of the products as the sum of the enthalpy of all the products.

The enthalpy change in a reaction is the difference of the products minus that of the reactants:

Figure 2. Enthalpy diagram. Source: self made.

In an endothermic reaction the enthalpy of the products is greater than that of the reactants; that is, the reaction takes heat from the environment. On the contrary, in an exothermic reaction the enthalpy of the reactants is greater than that of the products, since the reaction gives up heat to the environment.

Standard enthalpy

Since the enthalpy change in a chemical reaction can depend on pressure and temperature, it is customary to define standard reaction conditions:

Standard reaction temperature: 25 ° C.

Standard reaction pressure: 1 atm = 1 bar.

The standard enthalpy is denoted like this: H °

Thermochemistry

In a thermochemical equation, not only the reactants and products matter, the enthalpy change also matters. Enthalpy is understood as the reaction to the change that took place during it.

As an example, let's look at the following reactions:

2 H2 (gas) + O2 (gas) → 2 H2O (liquid); ΔH ° = -571.6 kJ (exothermic).

H2 (gas) + (½) O2 (gas) → H2O (liquid); ΔH ° = -285.8 kJ (exothermic).

2 H2O (liquid) → 2 H2 (gas) + O2 (gas); ΔH ° = +571.6 kJ (endothermic).

Enthalpy is an extensive thermodynamic quantity

If the terms of a chemical equation are multiplied or divided by a certain factor, then the enthalpy is multiplied or divided by the same.

If the reaction is reversed, then the sign of the reaction enthalpy is also reversed.

Solved exercises

-Exercise 1

Acetylene gas C2H2 is obtained from the reaction of calcium carbide CaC2 that comes in granulated form with water at ambient temperature and pressure.

As data we have the enthalpies of formation of the reactants:

ΔH ° (CaC2) = -59.0 kJ / mol

ΔH ° (H20) = -285.8 kJ / mol

And the enthalpy of formation of the products:

ΔH ° (C2H2) = +227.0 kJ / mol

ΔH ° (Ca (OH) 2) = -986.0 kJ / mol

Find the standard entropy of the reaction.

Solution

The first thing is to raise the balanced chemical equation:

CaC2 (s) + 2H20 (l) → Ca (OH) 2 (s) + C2H2 (g)

And now the enthalpies of the reactants, products and of the reaction:

- Reagents: -59.0 kJ / mol -2 ∙ 285.8 kJ / mol = -630.6 kJ / mol

- Products: -986.0 kJ / mol + 227.0 kJ / mol = -759 kJ / mol

- Reaction: ΔH ° = -759 kJ / mol - (-630 kJ / mol) = -129 kJ / mol

It is an exothermic reaction.

-Exercise 2

When 1 liter of acetylene is burned under standard conditions, how much heat is released?

Solution

Once balanced, the combustion reaction of acetylene looks like this:

C2H2 (g) + (5/2) O2 (g) → 2 CO2 (g) + H20 (l)

We need the enthalpies of formation of the products:

ΔH ° (CO2) = -393.5 kJ / mol

ΔH ° (H2O (l)) = -285.8 kJ / mol

Calculation of enthalpies

With these data we can calculate the enthalpy of the products:

ΔH ° (products) = 2 * (- 393.5 kJ / mol) + (-285.8 kJ / mol) = -1072.8 kJ / mol

And the enthalpy of formation of the reactants:

ΔH ° (C2H2) = 227.0 kJ / mol

ΔH ° (O2) = 0.0 kJ / mol

The enthalpy of the reactants will be:

227.0 kJ / mol + (5/2) * 0.0 = 227.0 kJ / mol

The molar reaction enthalpy will then be: ΔH ° (products) - ΔH ° (reactants) = -1072.8kJ / mol - 227.0 kJ / mol = -1299.8 kJ / mol

Enthalpy of combustion

Now we need to know how many moles of acetylene are a liter of acetylene under standard conditions. For this we will use the equation of state of an ideal gas, from which we will solve for the number of moles.

Number of moles n = P * V / (R * T)

P = 1 atm = 1.013 x 10⁵ Pa

V = 1 l = 1.0 x 10 ^ -3 m³

R = 8.31 J / (mol * K)

T = 25 ° C = 298.15 K

n = 0.041 mol

The enthalpy of combustion of 1 liter of acetylene is 0.041 mol * (-1299.8 kJ / mol) = -53.13 kJ

The negative sign indicates that it is an exothermic reaction that releases 53.13 kJ = 12.69 kcal.

References

1. Chestnuts E. Enthalpy in chemical reactions. Recovered from: lidiaconlaquimica.wordpress.com
2. Thermochemistry. Enthalpy of reaction. Recovered from: recursostic.educacion.es
3. Thermochemistry. Definition of standard reaction enthalpy. Recovered from: quimitube.com
4. Wikipedia. Standard enthalpy of reaction. Recovered from: wikipedia.com
5. Wikipedia. Formation enthalpy. Recovered from: wikipedia.com