Enthalpy

Overview

Enthalpy (H) is a thermodynamic quantity that represents the total heat content of a system. Changes in enthalpy (ΔH) measure the heat absorbed or released during chemical reactions and physical changes at constant pressure.

Key Concepts

Enthalpy Change (ΔH)

$$\Delta H = H_{\text{products}} - H_{\text{reactants}}$$

Sign	Meaning	Heat Flow
$\Delta H < 0$	Exothermic	Heat released to surroundings
$\Delta H > 0$	Endothermic	Heat absorbed from surroundings

At Constant Pressure

$$\Delta H = q_p \quad \text{(heat at constant pressure)}$$

Types of Enthalpy Changes

Standard Enthalpy of Formation ($\Delta H_f°$)

Heat change when 1 mole of compound forms from elements in their standard states.

$$\text{Elements (standard states)} \rightarrow \text{Compound} \quad \Delta H_f°$$

Standard state: Most stable form at 25°C and 1 atm

Substance	$\Delta H_f°$ (kJ/mol)
H₂O(l)	-285.8
CO₂(g)	-393.5
NH₃(g)	-46.1
CH₄(g)	-74.8
C₂H₅OH(l)	-277.7
Elements	0 (by definition)

Standard Enthalpy of Combustion ($\Delta H_c°$)

Heat released when 1 mole of substance burns completely in O₂.

$$\text{Fuel} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \quad \Delta H_c°$$

Always exothermic ($\Delta H_c° < 0$).

Standard Enthalpy of Reaction ($\Delta H_{rxn}°$)

Heat change for a reaction with all substances in standard states.

Calculating ΔH from $\Delta H_f°$

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

Example

Calculate $\Delta H°$ for: $\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l)$

$\Delta H_f°$ values:

• $\text{CH}_4(g) = -74.8$ kJ/mol
• $\text{O}_2(g) = 0$ kJ/mol
• $\text{CO}_2(g) = -393.5$ kJ/mol
• $\text{H}_2\text{O}(l) = -285.8$ kJ/mol

$$\Delta H° = [(-393.5) + 2(-285.8)] - [(-74.8) + 2(0)]$$ $$\Delta H° = [-393.5 - 571.6] - [-74.8] = -890.3 \text{ kJ/mol}$$

Thermochemical Equations

Rules

1. $\Delta H$ is proportional to amount of reactants/products
2. Reversing reaction changes sign of $\Delta H$
3. $\Delta H$ depends on states of matter

Example

$$\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l) \quad \Delta H = -285.8 \text{ kJ}$$ $$2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l) \quad \Delta H = -571.6 \text{ kJ (doubled)}$$ $$\text{H}_2\text{O}(l) \rightarrow \text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \quad \Delta H = +285.8 \text{ kJ (reversed)}$$

Enthalpy of Phase Changes

Change	Name	$\Delta H$ Sign
Solid → Liquid	Fusion (melting)	+
Liquid → Solid	Freezing	-
Liquid → Gas	Vaporization	+
Gas → Liquid	Condensation	-
Solid → Gas	Sublimation	+
Gas → Solid	Deposition	-

Relationship

$$\Delta H_{\text{sublimation}} = \Delta H_{\text{fusion}} + \Delta H_{\text{vaporization}}$$

Example: Water

$$\Delta H_{fus} = 6.01 \text{ kJ/mol}$$ $$\Delta H_{vap} = 40.7 \text{ kJ/mol}$$ $$\Delta H_{sub} = 46.7 \text{ kJ/mol}$$

Heat Capacity and Specific Heat

Heat Capacity (C)

Heat needed to raise temperature by 1°C.

Specific Heat Capacity (c)

Heat needed to raise 1 gram by 1°C.

$$q = mc\Delta T$$

Molar Heat Capacity

Heat needed to raise 1 mole by 1°C.

$$q = nC_m\Delta T$$

Common Specific Heat Values

Substance	c (J/g·°C)
Water (l)	4.184
Water (s)	2.09
Water (g)	2.01
Aluminum	0.897
Copper	0.385

Energy Level Diagrams

Exothermic Reaction

Energy
  ↑
  |   Reactants ────────
  |                      \
  |                       \  ΔH < 0 (heat released)
  |                        \
  |   Products ─────────────
  |_________________________→ Reaction Progress

Endothermic Reaction

Energy
  ↑
  |   Products ─────────────
  |                        /
  |                       /  ΔH > 0 (heat absorbed)
  |                      /
  |   Reactants ────────
  |_________________________→ Reaction Progress

System and Surroundings

Term	Definition
System	The reaction or process being studied
Surroundings	Everything outside the system
Universe	System + Surroundings

Sign Conventions

$$q > 0: \text{ System gains heat (endothermic)}$$ $$q < 0: \text{ System loses heat (exothermic)}$$ $$q_{\text{system}} = -q_{\text{surroundings}}$$