Chapter 9: Internal Energy, Heat, and Work – Study Notes

Internal Energy, Heat, and Work

Internal Energy vs. Heat

Internal energy is the total energy contained within a system, arising from the motion and interactions of its molecules. Heat refers to the energy that is transferred from one body or location to another due to a difference in temperature. This is distinct from work, which is energy transferred due to a force acting over a distance. Heat is only considered energy when it is transferred between bodies.

• Example: A hot potato possesses internal energy due to molecular motion. When placed in cold water, heat flows from the potato to the water, decreasing the potato's internal energy and increasing the water's by the same amount.

Heat, Work, and Internal Energy

Heat and work are two primary ways energy can be transferred between a system and its surroundings. The internal energy of a system can change when heat is added or removed, or when work is done by or on the system.

• The temperature of a gas is proportional to its average kinetic energy.

• Adding heat increases internal energy; expansion (work done by the system) decreases it.

• The first law of thermodynamics keeps track of the balance between heat, work, and internal energy.

Energy, Work, and Heat: Equations

• The change in internal energy ($\Delta E$) is given by:

$\Delta E = w + q$

• $w$ = work done on/by the system

• $q$ = heat absorbed (+) or released (–)

• Work done by a gas at constant pressure (PV work):

$w = -P_{\text{ext}} \Delta V$

• $\Delta V = V_f - V_i$ (change in volume)

• $P_{\text{ext}}$ is the external pressure the system expands against.

Exothermic and Endothermic Processes

• Exothermic reactions release heat ($q$ is negative for the system).

• Endothermic reactions absorb heat ($q$ is positive for the system).

Energy flow:

• If $\Delta E_{\text{sys}} < 0$, energy leaves the system (exothermic).

• If $\Delta E_{\text{sys}} > 0$, energy enters the system (endothermic).

Sign Conventions for $q$, $w$, and $\Delta E$

Process	Sign of $q$	Sign of $w$	Sign of $\Delta E$
System gains heat	+		+
System loses heat	–		–
Work done on system		+	+
Work done by system		–	–

Heat Capacity and Calorimetry

Heat Capacity and Specific Heat

The heat capacity ($C$) of a substance is the amount of heat required to raise its temperature by 1°C. The specific heat capacity ($c$) is the amount of heat required to raise 1 gram of a substance by 1°C.

• Equation: $q = m c \Delta T$

• $q$ = heat (J), $m$ = mass (g), $c$ = specific heat (J/g·°C), $\Delta T$ = temperature change (°C)

Example: Calculating the final temperature when a hot metal is placed in water, using the equation $q_{\text{metal}} = -q_{\text{water}}$.

Thermal Energy Transfer

When two substances at different temperatures are mixed, heat flows from the hotter to the cooler substance until thermal equilibrium is reached.

• Equation: $m_1 c_1 \Delta T_1 = -m_2 c_2 \Delta T_2$

Calorimetry

Calorimetry is the measurement of heat flow in a chemical or physical process. Two common types are:

• Coffee-cup calorimeter: Measures heat at constant pressure (used for reactions in solution).

• Bomb calorimeter: Measures heat at constant volume (used for combustion reactions).

Constant-pressure calorimetry: $\Delta H = q_p$

Bomb calorimetry: $q_{\text{cal}} = C_{\text{cal}} \Delta T$

Enthalpy and Thermochemical Equations

Enthalpy ($\Delta H$)

Enthalpy is the heat content of a system at constant pressure. The change in enthalpy ($\Delta H$) is the heat absorbed or released during a chemical reaction at constant pressure.

• Exothermic: $\Delta H < 0$ (heat released)

• Endothermic: $\Delta H > 0$ (heat absorbed)

Stoichiometry Involving $\Delta H$

Thermochemical equations relate the amount of heat released or absorbed to the amount of reactants or products.

• Example: For the combustion of propane, $C_3H_8(g) + 5 O_2(g) \rightarrow 3 CO_2(g) + 4 H_2O(g)$, $\Delta H_{\text{rxn}} = -2044$ kJ.

• To find the heat produced by a given mass, use stoichiometry to convert mass to moles, then multiply by $\Delta H_{\text{rxn}}$ per mole.

Hess's Law and Bond Energies

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. Enthalpy is a state function.

• To find $\Delta H$ for a reaction, add or subtract the $\Delta H$ values for known reactions to match the target reaction.

Bond Energies

The enthalpy change for a reaction can be estimated using average bond energies:

$\Delta H_{\text{rxn}} = \sum (\text{Bond energies of bonds broken}) - \sum (\text{Bond energies of bonds formed})$

• Bonds broken: energy absorbed (positive)

• Bonds formed: energy released (negative)

Standard Enthalpies of Formation

Definition and Calculation

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when 1 mole of a compound is formed from its elements in their standard states.

• Equation for a reaction:

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

• Where $n_p$ and $n_r$ are the stoichiometric coefficients of products and reactants, respectively.

Lattice Energy

Definition and Trends

Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. It is a measure of the strength of the forces holding the ions together in the solid.

• Lattice energy increases with higher ionic charge and smaller ionic radius.

• Example trend (in kJ/mol): KBr < KCl < SrO < CaO

Compound	Lattice Energy (kJ/mol)
KBr	671
KCl	701
SrO	3217
CaO	3414

Born-Haber Cycle

The Born-Haber cycle is a thermochemical cycle used to calculate lattice energies by relating them to other measurable quantities such as ionization energy, electron affinity, and enthalpy of formation.

Summary Table: Key Equations

Concept	Equation
First Law of Thermodynamics	$\Delta E = q + w$
Work (PV work)	$w = -P_{\text{ext}} \Delta V$
Heat (specific heat)	$q = m c \Delta T$
Enthalpy change (reaction)	$\Delta H_{\text{rxn}} = \sum n_p \Delta H_f^\circ (\text{products}) - \sum n_r \Delta H_f^\circ (\text{reactants})$
Bond energies	$\Delta H_{\text{rxn}} = \sum (\text{Bonds broken}) - \sum (\text{Bonds formed})$
Bomb calorimeter	$q_{\text{cal}} = C_{\text{cal}} \Delta T$

Additional info: These notes include both conceptual explanations and worked examples, as well as tables of specific heat capacities and lattice energies, to support problem-solving and exam preparation in thermochemistry.