Enthalpy, Calorimetry, and Bond Enthalpies: Study Notes for General Chemistry

Thermodynamics in Chemistry

Internal Energy, Heat, and Work

Thermodynamics is the study of energy changes in chemical processes. Internal energy, heat, and work are fundamental concepts for understanding how energy is transferred in chemical reactions.

• Internal Energy (U): The total energy contained within a system, including kinetic and potential energy at the molecular level.

• Heat (q): Energy transferred between a system and its surroundings due to a temperature difference.

• Work (w): Energy transferred when an object is moved by a force.

• Sign Conventions:

  • q > 0: Heat absorbed by the system (endothermic)

  • q < 0: Heat released by the system (exothermic)

  • w > 0: Work done on the system

  • w < 0: Work done by the system

• First Law of Thermodynamics: The change in internal energy ($\Delta U$) of a system is equal to the heat added to the system plus the work done on the system: $\Delta U = q + w$

Enthalpy, Calorimetry, and Hess's Law

Enthalpy (H)

Enthalpy is a thermodynamic quantity that represents the heat content of a system at constant pressure. It is especially useful for describing energy changes in chemical reactions.

• Definition: $H = U + PV$ (where U is internal energy, P is pressure, V is volume)

• Enthalpy Change ($\Delta H$): The heat absorbed or released at constant pressure: $\Delta H = H_{products} - H_{reactants}$

• Extensive Property: Enthalpy depends on the amount of substance (stoichiometric coefficients matter).

• Exothermic vs. Endothermic:

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

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

Calorimetry

Calorimetry is the measurement of heat flow in a chemical reaction or physical process.

• Constant Pressure Calorimetry: Used to measure $q_p$ (heat at constant pressure), which equals $\Delta H$ for the process.

• Equation: $q = m c \Delta T$

  • m = mass of substance (g)

  • c = specific heat capacity (J/g·K)

  • $\Delta T$ = change in temperature (K or °C)

• Heat Capacity (C): The amount of heat required to raise the temperature of an object by 1 K (or 1 °C).

• Specific Heat Capacity (c): The amount of heat required to raise the temperature of 1 gram of a substance by 1 K.

• Extensive vs. Intensive Properties:

  • Extensive: Depends on the amount of substance (e.g., heat capacity).

  • Intensive: Independent of amount (e.g., specific heat capacity).

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. This allows calculation of $\Delta H$ for reactions by combining known enthalpy changes of other reactions.

• Equation: $\Delta H_{rxn} = \sum \Delta H_{steps}$

• Application: Add or subtract equations and their enthalpy changes to find the overall $\Delta H$.

Standard Enthalpy of Formation

Definition and Calculation

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound is formed from its elements in their standard states at 1 bar (or 1 atm) and 25°C.

• Standard State: The most stable physical form of an element or compound at 1 bar and 25°C.

• For Elements: $\Delta H_f^\circ = 0$ (e.g., $\ce{O2(g)}$, $\ce{Na(s)}$)

• Writing Formation Reactions: Use fractional coefficients if necessary to ensure exactly 1 mole of product is formed.

• Example: Formation of $\ce{Na2CO3(s)}$:

  • Reaction: $2\ce{Na(s)} + \ce{C(graphite)} + 1.5\ce{O2(g)} \rightarrow \ce{Na2CO3(s)}$

Bond Enthalpy and Bond Energy

Bond Enthalpy (Bond Dissociation Energy)

Bond enthalpy is the energy required to break one mole of a specific type of bond in a gaseous molecule. It is always a positive value because energy must be supplied to break bonds.

• Average Bond Enthalpy: The average energy needed to break a particular type of bond in a range of molecules.

• Calculating $\Delta H$ Using Bond Energies:

  • Sum the energies of bonds broken (reactants) and subtract the sum of energies of bonds formed (products):

  $\Delta H_{rxn} = \sum \text{Bond Energies}_{\text{broken}} - \sum \text{Bond Energies}_{\text{formed}}$

• Example: For the reaction $2\ce{H2} + \ce{O2} \rightarrow 2\ce{H2O}$:

  • Bonds broken: 2 H–H, 1 O=O

  • Bonds formed: 4 O–H

  • Use bond enthalpy values from a table to calculate $\Delta H$.

Sample Bond Enthalpy Table (Selected Values)

Bond	Bond Enthalpy (kJ/mol)
H–H	436
O=O	498
O–H	463
C–H	413
C=O	799
Cl–Cl	243
H–Cl	431
F–F	155
H–F	567
Cl–F	253
Additional info:	Values are averages and may vary slightly between sources.

Worked Examples and Applications

Example 1: Calculating Heat Released in Combustion

• Given: 4.50 g methane ($\ce{CH4}$), $\Delta H_{comb}$ for 1 mol = –890 kJ

• Moles of methane: $4.50\,\text{g} / 16.04\,\text{g/mol} = 0.281\,\text{mol}$

• Heat released: $0.281\,\text{mol} \times (–890\,\text{kJ/mol}) = –250\,\text{kJ}$

Example 2: Calculating $\Delta H$ from Calorimetry Data

• Given: 50 g solution, $\Delta T = 5.2\,\text{K}$, $c = 4.18\,\text{J/g·K}$

• Heat absorbed: $q = m c \Delta T = 50 \times 4.18 \times 5.2 = 1085\,\text{J}$

• Convert to kJ: $1085\,\text{J} = 1.09\,\text{kJ}$

Example 3: Calculating $\Delta H$ Using Bond Energies

• Reaction: $2\ce{H2} + \ce{O2} \rightarrow 2\ce{H2O}$

• Bonds broken: 2 H–H (2 × 436), 1 O=O (1 × 498)

• Bonds formed: 4 O–H (4 × 463)

• $\Delta H = [2 \times 436 + 498] - [4 \times 463] = [872 + 498] - 1852 = 1370 - 1852 = -482\,\text{kJ}$

Summary Table: Key Thermodynamic Quantities

Quantity	Symbol	Definition	Units
Internal Energy	U	Total energy of a system	J (joules)
Enthalpy	H	Heat content at constant pressure	J (joules)
Heat	q	Energy transfer due to temperature difference	J (joules)
Work	w	Energy transfer due to force	J (joules)
Specific Heat Capacity	c	Heat required to raise 1 g by 1 K	J/g·K
Standard Enthalpy of Formation	$\Delta H_f^\circ$	Enthalpy change to form 1 mol from elements in standard state	kJ/mol

Additional info:

• Electrostatic potential energy between two charges: $E_{el} = \dfrac{kQ_1Q_2}{d}$, where k is Coulomb's constant.

• Standard enthalpy of formation for any element in its standard state is zero.

• Bomb calorimeter measures internal energy change ($\Delta U$), not enthalpy ($\Delta H$), because volume is constant.