FAD1018 Thermochemistry — Formula Sheet & Intuition

1. Calorimetry — "How much heat?"

$$q = mc\Delta T$$

Symbol Meaning Unit
$q$ Heat absorbed/released J or kJ
$m$ Mass of substance g
$c$ Specific heat capacity J/g·K
$\Delta T$ Temperature change ($T_f - T_i$) °C or K

[!tip] $q$ is positive when heat is absorbed (system gets hotter), negative when released.

Bomb vs Coffee-Cup — Intuition

Coffee-cup (constant pressure) Bomb (constant volume)
Container Open to atmosphere Sealed, rigid
Measures $\Delta H$ directly $\Delta U$ (internal energy)
Formula $q_p = \Delta H$ $q_v = C_v \Delta T$
Can expand? Yes No

Why bomb measures $\Delta U$ not $\Delta H$: Enthalpy is $H = U + PV$. At constant pressure, $\Delta H = \Delta U + P\Delta V = q_p$. But in a sealed bomb, $\Delta V = 0$ and pressure changes instead — so $q_v = \Delta U$.

Why $\Delta H \approx \Delta U$ for burning graphite: $\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g)$. One mole gas in, one mole gas out → $\Delta n_g = 0$ → $\Delta H = \Delta U + \Delta n_g RT = \Delta U$.

The flow:

  1. Temp rises → calorimeter absorbed heat → $q_{cal} = C\Delta T$
  2. That heat came from the reaction → $q_{rxn} = -q_{cal}$ (conservation)
  3. Volume is fixed → $q_{rxn} = \Delta U_{rxn}$
  4. Divide by moles to get per mole

2. First Law — Conservation of Energy

$$\Delta U = q + w$$

  • $\Delta U$ = change in internal energy
  • $q$ = heat absorbed by system
  • $w$ = work done on system

3. Enthalpy Types — Exact Exam Definitions

Symbol Name Exact definition
$\Delta H^\circ_f$ Standard enthalpy of formation Enthalpy change when 1 mole of compound is formed from its elements in their standard states
$\Delta H^\circ_c$ Standard enthalpy of combustion Enthalpy change when 1 mole of substance is burned completely in oxygen
$\Delta H^\circ_{neut}$ Enthalpy of neutralisation Enthalpy change when acid and base neutralise to form 1 mole of water
$\Delta H^\circ_{sol}$ Enthalpy of solution Enthalpy change when 1 mole of solute dissolves in a solvent
$\Delta H^\circ_{vap}$ Enthalpy of vaporisation Enthalpy change when 1 mole of liquid changes to gas
$\Delta H^\circ_{fus}$ Enthalpy of fusion Enthalpy change when 1 mole of solid changes to liquid
$\Delta H^\circ_{sub}$ Enthalpy of sublimation Enthalpy change when 1 mole of solid changes directly to gas
$\Delta H^\circ_{at}$ Enthalpy of atomisation Enthalpy change when 1 mole of substance is converted to gaseous atoms
Lattice energy — Enthalpy change when gaseous ions form 1 mole of ionic solid

[!warning] Key phrasing traps

  • Every definition starts with "Enthalpy change when..."
  • $\Delta H_f^\circ$: must say "elements" and "standard states"
  • $\Delta H_c^\circ$: must say "1 mole" and "completely in oxygen"
  • $\Delta H_{neut}^\circ$: must say "1 mole of water"
  • Lattice energy: "gaseous ions" → "ionic solid" (opposite direction)

4. Hess's Law — "Path doesn't matter"

$\Delta H$ for a reaction is the same regardless of pathway.

From Formation Enthalpies (most common exam problem)

$$\Delta H^\circ_{rxn} = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants})$$

Procedure:

  1. Multiply each $\Delta H^\circ_f$ by its stoichiometric coefficient
  2. Sum products, subtract sum of reactants

[!warning] Watch the signs $\Delta H^\circ_f$ for elements in standard state = zero (e.g. O₂(g), C(graphite), H₂(g))

From Bond Enthalpies

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

Sign
Breaking bonds Endothermic (+)
Forming bonds Exothermic (-)

[!tip] Draw the Lewis structures to count bonds. The formula already handles the sign — broken − formed.

Enthalpy of Solution

$$\Delta H^\circ_{sol} = \Delta H^\circ_{lattice} + \Delta H^\circ_{hyd}$$

If Then dissolution is
$ \Delta H_{hyd}
$ \Delta H_{hyd}

5. Gibbs Free Energy — "Will it happen?"

$$\Delta G = \Delta H - T\Delta S$$

$\Delta G$ Meaning
$< 0$ Spontaneous (favourable)
$= 0$ Equilibrium
$> 0$ Non-spontaneous

Spontaneity Cheat Sheet

$\Delta H$ $\Delta S$ Spontaneous?
$-$(exo) $+$ (more disorder) Always
$-$(exo) $-$ (less disorder) At low T only
$+$(endo) $+$ (more disorder) At high T only
$+$(endo) $-$ (less disorder) Never

[!tip] Mnemonic Exothermic + disorder = always go. Endothermic - disorder = never go. Mixed ones depend on T.

Related: Connection to Other Topics

Formula Links To
$\Delta G^\circ = -RT \ln K$ Chemical Equilibrium
$\Delta G^\circ = -nFE^\circ_{cell}$ Electrochemistry

6. Lattice Energy

Energy required to separate 1 mol ionic solid into gaseous ions.

Factors:

Factor Higher charge Smaller ion
Effect on LE ↑ Higher LE ↑ Higher LE

Born-Haber Cycle (Hess's Law applied to ionic compounds): $$\Delta H^\circ_f = \Delta H_{at} + IE + \Delta H_{at} + EA + LE$$

7. Problem-Type Mapping

Question pattern Formula / method
"Calculate heat released when X g burns..." $q = mc\Delta T$ or $q_v = C_v \Delta T$
"Calculate $\Delta H$ using formation data..." $\Delta H^\circ_{rxn} = \sum \Delta H^\circ_f(\text{prod}) - \sum \Delta H^\circ_f(\text{react})$
"Calculate $\Delta H$ using bond enthalpies..." $\sum(\text{bonds broken}) - \sum(\text{bonds formed})$
"Determine if reaction is spontaneous at T..." $\Delta G = \Delta H - T\Delta S$, check sign
"At what T does reaction become spontaneous?" Set $\Delta G = 0$, solve $T = \Delta H / \Delta S$
"Calculate lattice energy / construct Born-Haber" Hess's Law cycle
"Define $\Delta H_f^\circ$ / $\Delta H_c^\circ$ / $\Delta H_{neut}^\circ$ / lattice energy" Exact definitions from section 3

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