Enthalpy change, ∆rH, of a reaction is defined as the difference between the sum of the enthalpies of the products and the sum of the enthalpies of the reactants, all measured at the same temperature and pressure. Mathematically, it is expressed as:
∆rH = ∑(enthalpy of products) - ∑(enthalpy of reactants)
Where the summations are taken over all the species involved in the reaction.
If the value of ∆rH is negative, it means that the reaction is exothermic, i.e., heat is released during
the reaction. On the other hand, if the value of ∆rH is positive, it means that the reaction is endothermic, i.e., heat is absorbed during the reaction.
Enthalpy change is an important concept in thermodynamics and is used to calculate the amount of heat absorbed or released in a reaction. It is often measured experimentally using calorimetry, which involves measuring the heat exchanged between the system and its surroundings.
Standard Enthalpy of Reactions
The standard enthalpy of a reaction, denoted as ΔrH°, is defined as the enthalpy change that occurs in a reaction when all reactants and products are in their standard states, at a constant pressure of 1 bar (or 1 atm) and a specified temperature, usually 25°C or 298 K.
The standard state of a substance is its most stable form at a pressure of 1 bar (or 1 atm) and a specified temperature, usually 25°C or 298 K. For example, the standard state of an element is usually its most stable form at room temperature and pressure.
Enthalpy Changes during Phase transformation
Enthalpy changes occur during phase transformations, such as melting or vaporization, because the intermolecular forces between the molecules change as they transition from one phase to another. When a substance changes phase, there is a change in the energy required to hold the molecules together. This change in energy is known as the enthalpy of fusion (ΔHfus) or enthalpy of vaporization (ΔHvap) for melting and vaporization, respectively.
During melting, a solid absorbs heat and its temperature rises until it reaches the melting point. At this point, the solid begins to transform into a liquid. During this transformation, the temperature remains constant, even though heat is still being added to the system. This heat is being used to overcome the intermolecular forces holding the solid together and to increase the potential energy of the molecules in the liquid state. The enthalpy of fusion is the amount of heat required to melt one mole of a solid at its melting point and is given by:
ΔH(fus) = q/m
where q is the heat absorbed by the substance during the melting process, m is the mass of the substance melted and ΔH(fus) is the enthalpy of fusion.
During vaporization, a liquid absorbs heat and its temperature rises until it reaches its boiling point. At this point, the liquid begins to transform into a gas. During this transformation, the temperature remains constant, even though heat is still being added to the system. This heat is being used to overcome the intermolecular forces holding the liquid together and to increase the potential energy of the molecules in the gas state. The enthalpy of vaporization is the amount of heat required to vaporize one mole of a liquid at its boiling point and is given by:
ΔHvap = q/m
where q is the heat absorbed by the substance during the vaporization process, m is the mass of the substance vaporized and ΔHvap is the enthalpy of vaporization.
The enthalpy change during a phase transformation can be calculated using the following equation:
ΔH = nΔHfus or ΔH = nΔHvap
where n is the number of moles of the substance undergoing the phase transformation. The enthalpy change is positive for endothermic processes (melting and vaporization) and negative for exothermic processes (freezing and condensation).
Standard Enthalpy of Formation
The standard enthalpy of formation (ΔH°f) is the change in enthalpy that occurs when one mole of a compound is formed from its constituent elements in their standard states under standard conditions (25°C and 1 atm pressure). The standard state of an element is the most stable form of the element at the given temperature and pressure.
For example, the standard enthalpy of formation of water (H2O) is the enthalpy change that occurs when one mole of water is formed from its constituent elements hydrogen and oxygen under standard conditions. The balanced chemical equation for the formation of water is:
2H2(g) + O2(g) → 2H2O(l)
The standard enthalpy of formation of water is -285.8 kJ/mol, which means that 285.8 kJ of heat is released when one mole of water is formed from its constituent elements under standard conditions.
The standard enthalpy of formation is a useful tool for calculating the enthalpy change of a reaction. If the enthalpies of formation of the reactants and products are known, the enthalpy change of the reaction can be calculated using the equation:
ΔH°rxn = ΣnΔH°f(products) - ΣnΔH°f(reactants)
where ΔH°rxn is the standard enthalpy change of the reaction, ΣnΔH°f (products) is the sum of the standard enthalpies of formation of the products, and ΣnΔH°f (reactants) is the sum of the standard enthalpies of formation of the reactants.
A balanced chemical equation together with the value of its ∆rH is called a thermochemical equation. We specify the physical state (alongwith allotropic state) of the substance in an equation. For example:
C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l);
∆rH⊖= – 1367 kJ mol–1
The above equation describes the combustion of liquid ethanol at constant temperature and pressure. The negative sign of enthalpy change indicates that this is an exothermic reaction.
It would be necessary to remember the following conventions regarding thermo-chemical equations.
1. The coefficients in a balanced thermo-chemical equation refer to the number of moles (never molecules) of reactants and products involved in the reaction.
2. The numerical value of ∆rH⊖ refers to the number of moles of substances specified by an equation. Standard enthalpy change ∆rH⊖ will have units as kJ mol–1.
To illustrate the concept, let us consider the calculation of heat of reaction for the following reaction
From the Table (6.2) of standard enthalpy of formation (∆f H⊖), we find :
∆f H⊖ (H2O,l) = –285.83 kJ mol–1;
∆f H⊖ (Fe2O3,s) = – 824.2 kJ mol–1;
Also ∆f H⊖ (Fe, s) = 0 and
∆f H⊖ (H2, g) = 0 as per convention
∆f H1⊖ = 3(–285.83 kJ mol–1)
– 1(– 824.2 kJ mol–1)
= (–857.5 + 824.2) kJ mol–1
= –33.3 kJ mol–1
Note that the coefficients used in these calculations are pure numbers, which are equal to the respective stoichiometric coefficients. The unit for ∆rH⊖ is kJ mol–1, which means per mole of reaction. Once we balance the chemical equation in a particular way, as above, this defines the mole of reaction. If we had balanced the equation differently, for example,
then this amount of reaction would be one mole of reaction and ∆rH⊖ would be
∆f H2⊖ = (–285.83 kJ mol–1)
– (–824.2 kJ mol–1)
= (– 428.7 + 412.1) kJ mol–1
= –16.6 kJ mol–1 = ½ ∆r H1⊖
It shows that enthalpy is an extensive quantity.
3. When a chemical equation is reversed, the value of ∆rH⊖is reversed in sign. For example
N2(g) + 3H2 (g) → 2NH3 (g);
∆r H⊖= – 91.8 kJ. mol–1
2NH3(g) → N2(g) + 3H2 (g);
∆r H⊖= + 91.8 kJ mol–1
Hess's Law, also known as Hess's Law of Constant Heat Summation, states that the enthalpy change of a reaction is independent of the pathway between the initial and final states, as long as the initial and final states are the same. In other words, if a chemical reaction can take place through different routes, the total enthalpy change for the reaction will be the same regardless of which pathway is taken.
This principle can be applied to determine the enthalpy change of a reaction that cannot be directly measured by experiment. It involves breaking down the reaction into a series of simpler reactions for which the enthalpy changes are known, and then using Hess's Law to calculate the overall enthalpy change.
Mathematically, Hess's Law can be expressed as:
∆H = ∑n∆Hf(products) - ∑m∆Hf(reactants)
- ∆H is the enthalpy change of the reaction
- ∆Hf is the standard enthalpy of formation of a species
- n and m are the stoichiometric coefficients of the products and reactants, respectively.
This equation shows that the enthalpy change of a reaction is equal to the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants. The standard enthalpies of formation can be obtained from reference tables, and are defined as the enthalpy change for the formation of one mole of a compound from its constituent elements in their standard states at a specified temperature and pressure.