# 8.2: Enthalpy

Learning Objectives
• State the first law of thermodynamics
• Define enthalpy
• Identify endothermic and exothermic reactions from their enthalpy values

Thermochemistry is a branch of chemical thermodynamics, the science that deals with the relationships between heat, work, and other forms of energy in the context of chemical and physical processes. As we concentrate on thermochemistry in this chapter, we need to consider some widely used concepts of thermodynamics.

Substances act as reservoirs of energy, meaning that energy can be added to them or removed from them. Energy is stored in a substance when the kinetic energy of its atoms or molecules is raised. The greater kinetic energy may be in the form of increased motions, vibrations, or rotations of the atoms or molecules. When thermal energy is lost, the intensities of these motions decrease and the kinetic energy falls. The total of all possible kinds of energy present in a substance is called the internal energy.

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system. Energy is transferred into a system when it absorbs heat (q) from the surroundings or when the surroundings do work (w) on the system. For example, energy is transferred into room-temperature metal wire if it is immersed in hot water (the wire absorbs heat from the water), or if you rapidly bend the wire back and forth (the wire becomes warmer because of the work done on it). Both processes increase the internal energy of the wire, which is reflected in an increase in the wire’s temperature. Conversely, energy is transferred out of a system when heat is lost from the system, or when the system does work on the surroundings.

Chemists ordinarily use a property known as enthalpy ($$H$$) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum of a system’s internal energy ($$U$$) and the mathematical product of its pressure ($$P$$) and volume ($$V$$).

Since it is derived from three state functions ($$U$$, $$P$$, and $$V$$), enthalpy is also a state function. Enthalpy values for specific substances cannot be measured directly; only enthalpy changes for chemical or physical processes can be determined.

The heat given off when you operate a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place, since it occurs at the essentially constant pressure of the atmosphere. On the other hand, the heat produced by a reaction measured in a bomb calorimeter is not equal to $$ΔH$$ because the closed, constant-volume metal container prevents expansion work from occurring. Chemists usually perform experiments under normal atmospheric conditions, at constant external pressure with $$q = ΔH$$, which makes enthalpy the most convenient choice for determining heat.

The following conventions apply when we use $$ΔH$$:

1. Chemists use a thermochemical equation to represent the changes in both matter and energy. In a thermochemical equation, the enthalpy change of a reaction is shown as a ΔH value following the equation for the reaction. This $$ΔH$$ value indicates the amount of heat associated with the reaction involving the number of moles of reactants and products as shown in the chemical equation. For example, consider this equation: $\ce{H2(g) + 1/2 O2(g) ⟶ H2O (l)} \;\; ΔH=\mathrm{−286\:kJ} \label{5.4.6}$ This equation indicates that when 1 mole of hydrogen gas and 12 mole of oxygen gas at some temperature and pressure change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released to the surroundings. If the coefficients of the chemical equation are multiplied by some factor, the enthalpy change must be multiplied by that same factor (ΔH is an extensive property).

\begin {align*} &\textrm{(two-fold increase in amounts)}\label{5.4.7}\\ &\ce{2H2}(g)+\ce{O2}(g)⟶\ce{2H2O}(l)\hspace{20px}ΔH=\mathrm{2×(−286\:kJ)=−572\:kJ}\\ &\textrm{(two-fold decrease in amounts)}\\ &\frac{1}{2}\ce{H2}(g)+\dfrac{1}{4}\ce{O2}(g)⟶\frac{1}{2}\ce{H2O}(l)\hspace{20px}ΔH=\mathrm{\frac{1}{2}×(−286\:kJ)=−143\:kJ} \end {align*} \label{5.4.6B}

1. The enthalpy change of a reaction depends on the physical state of the reactants and products of the reaction (whether we have gases, liquids, solids, or aqueous solutions), so these must be shown. For example, when 1 mole of hydrogen gas and 12 mole of oxygen gas change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released. If gaseous water forms, only 242 kJ of heat are released.

$\ce{ H2(g) + 1/2 O2(g) ⟶ H2O(g)} \;\;\; ΔH=\ce{−242\:kJ} \label{5.4.7B}$

1. A negative value of an enthalpy change, ΔH, indicates an exothermic reaction; a positive value of ΔH indicates an endothermic reaction. If the direction of a chemical equation is reversed, the arithmetic sign of its ΔH is changed (a process that is endothermic in one direction is exothermic in the opposite direction).
Example $$\PageIndex{1}$$: Measurement of an Enthalpy Change

When 0.0500 mol of HCl(aq) reacts with 0.0500 mol of NaOH(aq) to form 0.0500 mol of NaCl(aq), 2.9 kJ of heat are produced. What is ΔH, the enthalpy change, per mole of acid reacting, for the acid-base reaction run under the conditions described ?

$\ce{HCl (aq) + NaOH(aq) \rightarrow NaCl (aq) + H2O(l)}$

Solution

For the reaction of 0.0500 mol acid (HCl), q = −2.9 kJ. This ratio

$\mathrm{\dfrac{−2.9 \; kJ}{0.0500\; mol\; HCl}}$

can be used as a conversion factor to find the heat produced when 1 mole of HCl reacts:

$ΔH =\mathrm{1\; \cancel{mol\; HCl} \times \dfrac{ −2.9\; kJ}{0.0500 \;\cancel{ mol\; HCl}} =−58\; kJ}$

The enthalpy change when 1 mole of HCl reacts is −58 kJ. Since that is the number of moles in the chemical equation, we write the thermochemical equation as:

$\ce{HCl}_{(aq)}+\ce{NaOH}_{(aq)}⟶\ce{NaCl}_{(aq)}+\ce{H_2O}_{(l)} \;\;\; ΔH=\mathrm{−58\;kJ}$

Exercise $$\PageIndex{1}$$

When 1.34 g Zn(s) reacts with 60.0 mL of 0.750 M HCl(aq), 3.14 kJ of heat are produced. Determine the enthalpy change per mole of zinc reacting for the reaction:

$\ce{Zn}_{(s)}+\ce{2HCl}_{(aq)}⟶\ce{ZnCl}_{(aq)}+\ce{H}_{2(g)}$

ΔH = −153 kJ

Be sure to take both stoichiometry and limiting reactants into account when determining the ΔH for a chemical reaction.

Example $$\PageIndex{2}$$: Another Example of the Measurement of an Enthalpy Change

A gummy bear contains 2.67 g sucrose, C12H22O11. When it reacts with 7.19 g potassium chlorate, KClO3, 43.7 kJ of heat are produced. Determine the enthalpy change for the reaction

$\ce{C12H22O11}(aq)+\ce{8KClO3}(aq)⟶\ce{12CO2}(g)+\ce{11H2O}(l)+\ce{8KCl}(aq)$

Solution

We have $$\mathrm{2.67\:\cancel{g}×\dfrac{1\:mol}{342.3\:\cancel{g}}=0.00780\:mol\:C_{12}H_{22}O_{11}}$$ available, and

$$\mathrm{7.19\:\cancel{g}×\dfrac{1\:mol}{122.5\:\cancel{g}}=0.0587\:mol\:KClO_3}$$ available.

Since

$$\mathrm{0.0587\:mol\:KClO_3×\dfrac{1\:mol\:\ce{C12H22O11}}{8\:mol\:KClO_3}=0.00734\:mol\:\ce{C12H22O11}}$$

is needed, C12H22O11 is the excess reactant and KClO3 is the limiting reactant.

The reaction uses 8 mol KClO3, and the conversion factor is $$\mathrm{\dfrac{−43.7\:kJ}{0.0587\:mol\:KClO_3}}$$, so we have $$ΔH=\mathrm{8\:mol×\dfrac{−43.7\:kJ}{0.0587\:mol\:KClO_3}=−5960\:kJ}$$. The enthalpy change for this reaction is −5960 kJ, and the thermochemical equation is:

$\ce{C12H22O11 + 8KClO3⟶12CO2 + 11H2O + 8KCl}\hspace{20px}ΔH=\ce{−5960\:kJ}$

Exercise $$\PageIndex{2}$$

When 1.42 g of iron reacts with 1.80 g of chlorine, 3.22 g of $$\ce{FeCl}_{2(s)}$$ and 8.60 kJ of heat is produced. What is the enthalpy change for the reaction when 1 mole of $$\ce{FeCl2(s)}$$ is produced?

ΔH = −338 kJ

Enthalpy changes are typically tabulated for reactions in which both the reactants and products are at the same conditions.

## Summary

If a chemical change is carried out at constant pressure and the only work done is caused by expansion or contraction, q for the change is called the enthalpy change with the symbol ΔH, or $$ΔH^\circ_{298}$$ for reactions occurring under standard state conditions. The value of ΔH for a reaction in one direction is equal in magnitude, but opposite in sign, to ΔH for the reaction in the opposite direction, and ΔH is directly proportional to the quantity of reactants and products. A negative value of an enthalpy change, ΔH, indicates an exothermic reaction; a positive value of ΔH indicates an endothermic reaction.

## Glossary

chemical thermodynamics
area of science that deals with the relationships between heat, work, and all forms of energy associated with chemical and physical processes
enthalpy (H)
sum of a system’s internal energy and the mathematical product of its pressure and volume
enthalpy change (ΔH)
heat released or absorbed by a system under constant pressure during a chemical or physical process
expansion work (pressure-volume work)
work done as a system expands or contracts against external pressure
first law of thermodynamics
internal energy of a system changes due to heat flow in or out of the system or work done on or by the system