6.2 Enthalpy changes in chemical reactions

Enthalpy and Chemical Reactions

Enthalpy tracks the heat absorbed or released during a chemical reaction at constant pressure. Since most reactions in the lab (and in life) happen at constant atmospheric pressure, enthalpy is the go-to quantity for understanding energy flow. It connects directly to whether a reaction gives off heat or requires it, and it plays a central role in predicting thermodynamic favorability alongside entropy and Gibbs free energy.

Enthalpy in Chemical Reactions

Enthalpy ($H$) is defined as the total heat content of a system at constant pressure. Formally:

$H = U + PV$

where $U$ is internal energy, $P$ is pressure, and $V$ is volume. In practice, you almost never calculate $H$ directly. What matters is the enthalpy change ($\Delta H$), which represents the heat exchanged during a reaction at constant pressure.

• A negative $\Delta H$ means the reaction is exothermic: it releases heat to the surroundings. Combustion of methane ($\Delta H = -890 \text{ kJ/mol}$) is a classic example.
• A positive $\Delta H$ means the reaction is endothermic: it absorbs heat from the surroundings. Photosynthesis is endothermic because plants must absorb light energy to drive the reaction.

One common misconception: a large negative $\Delta H$ does not automatically mean a reaction is spontaneous. Spontaneity depends on Gibbs free energy ($\Delta G$), which also accounts for entropy. A highly exothermic reaction is thermodynamically favorable in terms of enthalpy, but you need the full picture from Unit 6.3 to determine spontaneity.

Calculation Methods for Enthalpy Changes

There are three main ways to determine $\Delta H$ for a reaction.

1. Hess's Law

Hess's law states that the total enthalpy change for a reaction depends only on the initial and final states, not on the pathway taken. Because enthalpy is a state function, you can break a complex reaction into simpler steps, look up their $\Delta H$ values, and add them together.

To apply Hess's law:

1. Write the target reaction you need $\Delta H$ for.
2. Identify known reactions whose equations can be combined to give the target reaction.
3. If you need to reverse a reaction, flip the sign of its $\Delta H$.
4. If you need to multiply a reaction by a coefficient, multiply its $\Delta H$ by the same factor.
5. Sum all the adjusted $\Delta H$ values to get $\Delta H$ for the target reaction.

2. Standard Enthalpies of Formation

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound forms from its elements in their standard states (1 atm, 25°C). By definition, $\Delta H_f^\circ$ for any element in its standard state is zero.

You can calculate the standard enthalpy of any reaction using:

$\Delta H_r^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})$

Remember to multiply each $\Delta H_f^\circ$ by the stoichiometric coefficient from the balanced equation. This is probably the most common enthalpy calculation you'll see on exams.

3. Calorimetry

Calorimetry measures heat experimentally. A reaction runs inside a calorimeter, and the temperature change of the surrounding solution (or the calorimeter itself) tells you how much heat was transferred.

$q = mc\Delta T$

where $m$ is the mass of the solution (in grams), $c$ is the specific heat capacity (for dilute aqueous solutions, use $4.184 \text{ J/g·°C}$), and $\Delta T$ is the temperature change. For example, dissolving NaOH in water raises the solution temperature, so $q$ for the surroundings is positive, meaning the dissolution process is exothermic ($q_{rxn}$ is negative).

Keep the sign convention straight: $q_{rxn} = -q_{solution}$. If the solution heats up, the reaction released that heat.

Predicting Enthalpy Changes

Different reaction types follow predictable enthalpy patterns:

• Combustion reactions are almost always highly exothermic. Burning natural gas (methane) releases about $-890 \text{ kJ/mol}$. The strong bonds formed in $CO_2$ and $H_2O$ products account for the large energy release.
• Formation reactions can go either way. Compounds with strong bonds (like $H_2O$, with $\Delta H_f^\circ = -286 \text{ kJ/mol}$) have negative formation enthalpies, meaning their formation is exothermic. Less stable compounds may have positive $\Delta H_f^\circ$ values.
• Phase transitions involve enthalpy changes without any change in chemical identity:
  • Melting and vaporization are endothermic (positive $\Delta H$) because energy is needed to overcome intermolecular forces. The enthalpy of vaporization of water is $+40.7 \text{ kJ/mol}$.
  • Freezing and condensation are exothermic (negative $\Delta H$) because intermolecular forces form and release energy.

Interpretation of Enthalpy Diagrams

Enthalpy diagrams plot enthalpy (y-axis) against reaction progress (x-axis). They give you a visual snapshot of the energy story of a reaction.

• If the products sit lower on the diagram than the reactants, the reaction is exothermic ($\Delta H < 0$). The vertical drop represents the heat released. Combustion of propane is a good example.
• If the products sit higher than the reactants, the reaction is endothermic ($\Delta H > 0$). The vertical rise represents the heat absorbed. Thermal decomposition of calcium carbonate ($CaCO_3 \rightarrow CaO + CO_2$) looks like this.

Most enthalpy diagrams also show a hump between reactants and products. The peak of that hump represents the transition state, and the energy difference between the reactants and the peak is the activation energy ($E_a$). A higher $E_a$ means the reaction is kinetically slower, since fewer molecules have enough energy to get over the barrier at a given temperature. Note that $E_a$ tells you about reaction rate, not about $\Delta H$. A reaction can be very exothermic but still have a high activation energy (like the combustion of gasoline, which needs a spark to get started).