AP Chemistry 6.6-6.7: Enthalpy of Reaction and Bond Enthalpies

First law of thermodynamics

Energy is conserved: the change in a system’s internal energy equals heat transferred to the system plus work done on the system, $\Delta U=q+w$.

How do the signs of $q$ and $w$ indicate energy transfer for a chemical system?

For the system, $q>0$ means heat is absorbed and $q<0$ means heat is released. Also, $w>0$ means work is done on the system, while $w<0$ means the system does work on its surroundings.

Internal energy ($U$)

Internal energy is the total energy contained within a substance, including microscopic translational, vibrational, rotational, and other forms of energy.

Expansion work (pressure-volume work)

Expansion work occurs when a system expands against an external pressure or when the surroundings compress the system. For pressure-volume work, $P\Delta V=-w$.

State function

A state function is a property whose change depends only on the initial and final states, not on the pathway between them. Internal energy and enthalpy are state functions; heat and work are not.

Enthalpy ($H$)

Enthalpy is defined as $H=U+PV$, where $U$ is internal energy, $P$ is pressure, and $V$ is volume. Absolute enthalpy cannot generally be measured directly, but enthalpy changes can be determined.

What is the relationship between enthalpy change and internal energy change at constant pressure?

For constant pressure, $\Delta H=\Delta U+P\Delta V$. When only pressure-volume work occurs, this becomes $\Delta H=q_p$, so the heat transferred at constant pressure equals the enthalpy change.

How do exothermic and endothermic processes relate to the sign of $\Delta H$?

An exothermic process releases heat and has $\Delta H<0$. An endothermic process absorbs heat and has $\Delta H>0$.

Why is a reaction’s heat measured in a bomb calorimeter generally not equal to $\Delta H$?

A bomb calorimeter operates at constant volume, so it measures heat at constant volume rather than constant pressure. The measured heat is related to $\Delta U$, whereas $\Delta H=q_p$ applies under constant pressure with only pressure-volume work.

Thermochemical equation

A thermochemical equation is a balanced chemical equation that includes the enthalpy change for the reaction as written. The physical states of all reactants and products must be specified because they affect $\Delta H$.

What does $\mathrm{H_2(g)+\frac{1}{2}O_2(g)\rightarrow H_2O(l)}\quad \Delta H=-286\ \mathrm{kJ}$ communicate?

The reaction of the stated amounts—1 mol $\mathrm{H_2(g)}$ and $\frac{1}{2}$ mol $\mathrm{O_2(g)}$ forming 1 mol $\mathrm{H_2O(l)}$—releases 286 kJ of heat under the stated conditions.

How does multiplying a thermochemical equation affect its enthalpy change?

The enthalpy change is multiplied by the same factor as every stoichiometric coefficient. Enthalpy is extensive, so doubling the reacting amounts doubles $\Delta H$.

What happens to $\Delta H$ when a thermochemical equation is reversed?

Reversing the reaction reverses the direction of heat flow, so the sign of $\Delta H$ changes while its magnitude remains the same.

How can experimental heat data be converted into an enthalpy change per mole of reaction?

Convert the measured reactant or product amount to moles, account for the balanced-equation stoichiometry, and scale the measured heat to the amount represented by the equation. The sign is negative for released heat and positive for absorbed heat.

How should limiting reactants be handled when determining a reaction enthalpy from measured heat?

Determine the limiting reactant before scaling the heat. Use the moles of the limiting reactant that actually react, then convert to the amount of reaction represented by the balanced equation.

What is a bond enthalpy?

A bond enthalpy is the average energy required to break 1 mol of a particular type of bond in gaseous molecules. Bond enthalpies are reported as positive values because bond breaking requires energy.

What are the energy changes associated with breaking and forming chemical bonds?

Breaking bonds is endothermic and requires energy. Forming bonds is exothermic and releases energy.

How is reaction enthalpy estimated using bond enthalpies?

Estimate it with $\Delta H_{\mathrm{rxn}}\approx\sum D(\text{bonds broken})-\sum D(\text{bonds formed})$. Count each bond broken in the reactants and each bond formed in the products.

Why is the bond-enthalpy method based on the difference between bonds broken and bonds formed?

Energy must be absorbed to break the reactant bonds, while energy is released when product bonds form. The net enthalpy change is therefore the energy required for breaking minus the energy released by forming bonds.

What sign is expected from a bond-enthalpy calculation for an exothermic reaction?

If forming the product bonds releases more energy than is required to break the reactant bonds, the calculated value is negative, indicating an exothermic reaction.

Why does the bond-enthalpy method give an estimate rather than an exact reaction enthalpy?

Tabulated bond enthalpies are averages from many different molecules. A particular bond’s energy depends on its molecular environment, so the calculated value may differ from the actual enthalpy change.

What limitation of molecular phase is associated with bond-enthalpy calculations?

Bond enthalpies apply to bonds in gaseous species. If reactants or products are liquids or solids, additional phase-change or intermolecular-energy effects may make the bond-enthalpy estimate less accurate.

How should bonds be counted when using the bond-enthalpy method?

Use the balanced reaction and molecular structures to count every bond broken in the reactants and every bond formed in the products. A double or triple bond is counted as one double or triple bond with its corresponding bond enthalpy, not as multiple single bonds.

What is a major advantage of the bond-enthalpy method?

It allows a reaction enthalpy to be estimated from bond energies without requiring a direct calorimetry measurement or a complete table of standard enthalpies of formation.