Chemical Thermodynamics

Chemical Thermodynamics deals with energy changes in chemical reactions and determines whether a reaction is spontaneous.

Overview

graph TD
    A[Chemical Thermodynamics] --> B[First Law]
    A --> C[Enthalpy]
    A --> D[Second Law]
    A --> E[Gibbs Energy]
    C --> C1[Hess's Law]
    C --> C2[Types of ΔH]
    D --> D1[Entropy]
    E --> E1[Spontaneity]

System and Surroundings

Types of Systems

Type	Matter Exchange	Energy Exchange
Open	Yes	Yes
Closed	No	Yes
Isolated	No	No

State Functions

Properties that depend only on state, not path:

• Internal Energy (U)
• Enthalpy (H)
• Entropy (S)
• Gibbs Energy (G)

Path functions: Work (W), Heat (Q)

First Law of Thermodynamics

$$\boxed{\Delta U = q + w}$$

For processes at constant volume:

$$\Delta U = q_V$$

For processes at constant pressure:

$$\Delta H = q_P$$

Work Done

Expansion work:

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

Reversible isothermal:

$$w = -nRT\ln\frac{V_2}{V_1} = -2.303nRT\log\frac{V_2}{V_1}$$

Enthalpy (H)

$$H = U + PV$$

At constant pressure:

$$\boxed{\Delta H = \Delta U + P\Delta V = \Delta U + \Delta n_g RT}$$

where $\Delta n_g$ = (moles of gaseous products) - (moles of gaseous reactants)

Heat Capacity

At constant volume: $C_V = \frac{dU}{dT}$

At constant pressure: $C_P = \frac{dH}{dT}$

$$\boxed{C_P - C_V = R}$$

(for ideal gas)

Types of Enthalpy Changes

Type	Symbol	Definition
Formation	$\Delta_f H°$	1 mole of compound from elements
Combustion	$\Delta_c H°$	Complete burning with O₂
Atomization	$\Delta_a H°$	Conversion to gaseous atoms
Sublimation	$\Delta_{sub} H°$	Solid to gas
Ionization	$\Delta_{ion} H$	Removal of electron
Bond dissociation	$\Delta_{bond} H°$	Breaking one mole of bonds
Neutralization	$\Delta_{neut} H°$	Acid + Base → Salt + Water

Standard States

• Gases: 1 bar pressure
• Solutions: 1 M concentration
• Temperature: 298 K (unless specified)

Hess’s Law

Enthalpy change is independent of path:

$$\Delta H_{overall} = \sum \Delta H_{steps}$$

Applications

1. Calculate ΔH for reactions that can’t be measured directly
2. Add equations to get desired equation

Bond Enthalpy

$$\Delta H_{rxn} = \sum(\text{Bond energies of reactants}) - \sum(\text{Bond energies of products})$$

or

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

Entropy (S)

Measure of disorder or randomness.

$$\Delta S = \frac{q_{rev}}{T}$$

Second Law of Thermodynamics

$$\boxed{\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} \geq 0}$$

• Spontaneous: $\Delta S_{universe} > 0$
• Equilibrium: $\Delta S_{universe} = 0$
• Non-spontaneous: $\Delta S_{universe} < 0$

Factors Increasing Entropy

1. Solid → Liquid → Gas
2. Increase in temperature
3. Increase in volume
4. Increase in number of moles
5. Dissolving (usually)

Gibbs Energy (G)

$$G = H - TS$$ $$\boxed{\Delta G = \Delta H - T\Delta S}$$

Spontaneity Criterion

ΔH	ΔS	ΔG	Spontaneity
-	+	Always -	Always spontaneous
+	-	Always +	Never spontaneous
-	-	- at low T	Spontaneous at low T
+	+	- at high T	Spontaneous at high T

At Equilibrium

$$\Delta G = 0$$ $$T_{eq} = \frac{\Delta H}{\Delta S}$$

Standard Gibbs Energy

$$\boxed{\Delta G° = -RT\ln K = -2.303RT\log K}$$ $$\Delta G = \Delta G° + RT\ln Q$$

where Q = reaction quotient, K = equilibrium constant

At Equilibrium (Q = K)

$$\Delta G = 0$$ $$\Delta G° = -RT\ln K$$

Practice Problems

1. Calculate ΔU when ΔH = -280 kJ and Δn_g = -2 at 300 K.

2. For a reaction, ΔH = -200 kJ/mol and ΔS = -50 J/mol·K. At what temperature will it become non-spontaneous?

3. Given: $\Delta G° = -30$ kJ/mol at 300 K. Calculate the equilibrium constant.

4. Calculate ΔS for the universe when 1 mol of ice melts at 273 K. (ΔH_fus = 6 kJ/mol)

Further Reading

• Equilibrium
• Solutions