5.3 Enthalpy

The first law of thermodynamics governs energy changes in chemical reactions. It states that energy can't be created or destroyed, only converted between forms. This principle helps us understand how heat flows during reactions and introduces the concept of enthalpy.

Enthalpy measures a system's heat content and changes during reactions. As a state function, it depends only on the current state, not the path taken. Thermochemical equations and Hess's law allow us to calculate and predict enthalpy changes for various reactions.

First Law of Thermodynamics and Enthalpy

First law of thermodynamics in reactions

The first law of thermodynamics says energy cannot be created or destroyed, only converted from one form to another (thermal, chemical, mechanical, electrical). In a closed system, the change in internal energy ($\Delta U$) equals the heat ($q$) added to the system minus the work ($w$) done by the system:

$\Delta U = q - w$

At constant pressure (which is how most chemistry reactions happen, like in an open beaker on a lab bench), the heat exchanged equals the change in enthalpy ($\Delta H$). That's why enthalpy is so useful in chemistry: it directly tells you the heat absorbed or released during a reaction at constant pressure.

• Exothermic reactions release heat to the surroundings: $\Delta H < 0$
• Endothermic reactions absorb heat from the surroundings: $\Delta H > 0$

Enthalpy as a State Function

Enthalpy as state function

A state function is a property whose value depends only on the current state of the system, not on how the system got there. Enthalpy ($H$) is a state function, so the change in enthalpy ($\Delta H$) between two states is always the same regardless of the route taken. Think of it like elevation: whether you hike a mountain by the steep trail or the winding trail, the change in elevation from base to summit is identical.

This is a big deal because it means you can calculate $\Delta H$ for a reaction even if you can't measure it directly, as long as you can find an alternate path between the same starting and ending points (this is the basis of Hess's law, covered below).

Enthalpy is also an extensive property, meaning its value scales with the amount of substance. If you double the amount of reactants, the enthalpy change doubles too.

Thermochemical Equations and Enthalpy Changes

Notation for thermochemical equations

A thermochemical equation is a balanced chemical equation that includes the enthalpy change for the reaction. The $\Delta H$ value is written alongside the equation, typically on the right side.

The standard enthalpy of reaction ($\Delta H_{rxn}^{\circ}$) refers to the enthalpy change when all reactants and products are in their standard states: 1 atm pressure, 25°C (298 K), and 1 M concentration for solutions. The degree symbol (°) is what tells you "standard conditions."

Example (combustion of methane):

$CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \quad \Delta H_{rxn}^{\circ} = -890.4 \text{ kJ/mol}$

The negative sign tells you this reaction is exothermic. Notice that physical states (g, l, s, aq) are included because they affect the enthalpy value.

Calculation of enthalpy changes

The standard enthalpy of formation ($\Delta H_f^{\circ}$) is the enthalpy change when one mole of a compound forms from its elements, all in their standard states. By convention, $\Delta H_f^{\circ}$ for any element already in its standard state (like $O_2(g)$ or $C(graphite)$) is zero.

You can calculate the standard enthalpy of any reaction using this formula:

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

In words: add up the formation enthalpies of all products (each multiplied by its coefficient), then subtract the sum for all reactants. The "products minus reactants" pattern is one you'll see again in chemistry, so it's worth committing to memory.

Other ways to determine enthalpy changes:

• Calorimetry: Measure heat experimentally by tracking temperature changes in a known mass of water or solution.
• Bond enthalpies: Estimate $\Delta H$ for gas-phase reactions by comparing the energy needed to break bonds in reactants versus the energy released when forming bonds in products.

Application of Hess's law

Hess's law states that the overall enthalpy change for a reaction equals the sum of the enthalpy changes for any set of steps that add up to that overall reaction. This follows directly from enthalpy being a state function.

Why does this matter? Some reactions are too dangerous, too slow, or otherwise impractical to measure directly. Hess's law lets you piece together $\Delta H$ values from simpler, measurable reactions.

Here's how to apply it:

1. Write the target reaction you need $\Delta H$ for.
2. Find a set of reactions with known $\Delta H$ values whose reactants and products include all the species in your target reaction.
3. Manipulate the known reactions as needed: reverse a reaction (which flips the sign of $\Delta H$), or multiply through by a coefficient (which multiplies $\Delta H$ by the same factor).
4. Add the manipulated reactions together. Intermediate species should cancel, leaving only your target reaction.
5. Sum the adjusted $\Delta H$ values to get $\Delta H$ for the target reaction.

For example, if reaction A ($\Delta H_A$) and reaction B ($\Delta H_B$) add together to give reaction C, then $\Delta H_C = \Delta H_A + \Delta H_B$.

Thermodynamic Considerations

Spontaneity of reactions

Enthalpy alone doesn't determine whether a reaction happens spontaneously. Entropy ($S$), a measure of disorder in a system, also plays a role. A reaction can be endothermic and still spontaneous if the entropy increase is large enough.

Gibbs free energy ($\Delta G$) combines both factors to predict spontaneity. You'll explore this in more detail later, but the key takeaway for now is: a negative $\Delta H$ favors spontaneity, but it doesn't guarantee it.