The reaction enthalpy, \(\Delta H_{\mathrm{rxn}}\), is the heat released or absorbed by a chemical reaction carried out at constant pressure. Since most laboratory reactions occur at approximately constant pressure, reaction enthalpies are among the most commonly measured thermodynamic quantities in chemistry.
Consider the combustion of methane:
\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \]
This reaction releases heat to the surroundings and is therefore exothermic:
\[ \Delta H_{\mathrm{rxn}} < 0 \]
The magnitude of \(\Delta H_{\mathrm{rxn}}\) tells us how much heat is released when the reaction occurs according to the stoichiometry shown in the balanced equation.
Because enthalpy is a state function, the reaction enthalpy depends only on the initial and final states of the reactants and products and not on the pathway by which the reaction occurs.
Thermodynamic quantities depend on temperature, pressure, and phase. In order to tabulate thermodynamic data, a reference condition called the standard state is defined.
Definition: The standard state of a substance is its most stable form at \(1\ \mathrm{atm}\) pressure (or unit concentration for solutes) and the specified temperature.
| Substance | Standard State at 25°C |
|---|---|
| \(O_2\) | \(O_2(g)\) |
| \(H_2O\) | \(H_2O(l)\) |
| Cu | Cu(s) |
| \(Na^+(aq)\) | \(1.0\ \mathrm{M}\) aqueous solution |
The standard reaction enthalpy, \(\Delta H^\circ_{\mathrm{rxn}}\), is the reaction enthalpy measured when all reactants and products are in their standard states at the specified temperature.
Most tabulated thermodynamic data are standard-state quantities measured at \(25^\circ\mathrm{C}\) and \(1\ \mathrm{atm}\).
Since enthalpy is a state function, the enthalpy change for a reaction is independent of the pathway followed between the reactants and products. This observation is known as Hess' Law.
Hess' Law allows reaction enthalpies to be determined indirectly by combining other reactions whose enthalpies are known.
As an example, consider the reaction
\[ Mg(s) + H_2O(l) \rightarrow MgO(s) + H_2(g) \]
This reaction is difficult to study directly because magnesium rapidly develops an oxide coating and reacts only slowly with liquid water.
Instead, consider the following two experimentally accessible reactions:
\[ Mg(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + H_2(g) \qquad \Delta H_1 \]
\[ MgO(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + H_2O(l) \qquad \Delta H_2 \]
Reversing the second reaction gives
\[ MgCl_2(aq) + H_2O(l) \rightarrow MgO(s) + 2HCl(aq) \qquad -\Delta H_2 \]
Adding the two equations together cancels \(MgCl_2(aq)\) and \(2HCl(aq)\), yielding
\[ Mg(s) + H_2O(l) \rightarrow MgO(s) + H_2(g) \]
Therefore,
\[ \Delta H_{\mathrm{target}} = \Delta H_1 - \Delta H_2 \]
Hess' Law allows the enthalpy of a difficult-to-measure reaction to be obtained from the enthalpies of reactions that are easy to perform experimentally.
Big picture: Because enthalpy is a state function, reaction enthalpies can be added, subtracted, and manipulated in the same way as the corresponding chemical equations. This makes Hess' Law one of the most powerful tools in thermochemistry.
Use the following standard enthalpies of formation to calculate the standard reaction enthalpy for the combustion of methane:
\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \]
| Formation reaction | \(\Delta H_f^\circ\) |
|---|---|
| \(C(gr)+2H_2(g)\rightarrow CH_4(g)\) | \(-74.6\ \mathrm{kJ\,mol^{-1}}\) |
| \(C(gr)+O_2(g)\rightarrow CO_2(g)\) | \(-393.5\ \mathrm{kJ\,mol^{-1}}\) |
| \(H_2(g)+\frac{1}{2}O_2(g)\rightarrow H_2O(l)\) | \(-285.8\ \mathrm{kJ\,mol^{-1}}\) |
To construct the target reaction, reverse the methane formation reaction:
\[ CH_4(g)\rightarrow C(gr)+2H_2(g) \qquad \Delta H^\circ=+74.6\ \mathrm{kJ} \]
Keep the carbon dioxide formation reaction as written:
\[ C(gr)+O_2(g)\rightarrow CO_2(g) \qquad \Delta H^\circ=-393.5\ \mathrm{kJ} \]
Multiply the water formation reaction by 2:
\[ 2H_2(g)+O_2(g)\rightarrow 2H_2O(l) \qquad \Delta H^\circ=-571.6\ \mathrm{kJ} \]
Adding these equations cancels \(C(gr)\) and \(2H_2(g)\), giving:
\[ CH_4(g)+2O_2(g)\rightarrow CO_2(g)+2H_2O(l) \]
Therefore, the reaction enthalpy is
\[ \Delta H^\circ_{\mathrm{rxn}} = (+74.6) + (-393.5) + (-571.6) \]
\[ \Delta H^\circ_{\mathrm{rxn}} = -890.5\ \mathrm{kJ} \]
Therefore, the combustion of one mole of methane releases
\[ 890.5\ \mathrm{kJ} \]
Physical interpretation: The negative sign indicates that methane combustion is exothermic. The value \(-890.5\ \mathrm{kJ}\) applies to the balanced reaction as written: one mole of \(CH_4(g)\) reacts with two moles of \(O_2(g)\) to form one mole of \(CO_2(g)\) and two moles of \(H_2O(l)\).
Combine the data reactions to obtain the target reaction, then choose the correct reaction enthalpy.
Big picture: Hess' Law is a direct consequence of enthalpy being a state function. By combining known reactions and their enthalpies, the enthalpy change of a difficult or impossible-to-measure reaction can be determined from experimentally accessible data.