The system is the specific part of the universe under study; everything else is the surroundings. A boundary (real or imaginary) separates the two.
| Type of System | Exchanges with Surroundings | Example |
|---|---|---|
| Open | Both matter and energy | Hot tea in an open cup |
| Closed | Only energy, not matter | Sealed flask being heated |
| Isolated | Neither matter nor energy | An ideal thermos flask |
A state function depends only on the initial and final state of the system, not on the path taken between them — e.g., internal energy, enthalpy, entropy, Gibbs energy. A path function depends on the route taken — e.g., heat (q) and work (w).
The sum of all forms of kinetic and potential energy of the particles within a system. Only the change in internal energy ($\Delta U$) between two states can be measured, not its absolute value.
Energy can neither be created nor destroyed, only transformed from one form to another. Here $q$ = heat absorbed by the system (positive if absorbed, negative if released) and $w$ = work done on the system (positive if done on the system, negative if done by the system).
For work done against a constant external pressure. The negative sign reflects that work done by the system (during expansion, $\Delta V$ positive) reduces its internal energy.
A gas absorbs 200 J of heat and does 80 J of work on the surroundings during expansion. Calculate ΔU.
$q = +200\ \text{J}$ (absorbed). $w = -80\ \text{J}$ (work done by system, so work done on system is negative).
$\Delta U = 200 + (-80) = 120\ \text{J}$
Defined as $H = U + pV$. At constant pressure (the most common lab condition), the heat exchanged equals the change in enthalpy: $q_p = \Delta H$. This makes enthalpy more practically useful than internal energy for most reactions carried out in open vessels.
where $\Delta n_g$ = (moles of gaseous products) − (moles of gaseous reactants). If $\Delta n_g = 0$ (no change in gas moles), $\Delta H = \Delta U$.
The total enthalpy change for a reaction is the same whether it occurs in one step or through several intermediate steps — since enthalpy is a state function, only the initial and final states matter, not the path. This allows enthalpies of reactions that are hard to measure directly to be calculated by combining known enthalpies of other, related reactions.
Given $\text{C(s)} + \text{O}_2\text{(g)} \rightarrow \text{CO}_2\text{(g)}$, $\Delta H = -393.5$ kJ, and $\text{CO(g)} + \tfrac{1}{2}\text{O}_2\text{(g)} \rightarrow \text{CO}_2\text{(g)}$, $\Delta H = -283.0$ kJ, find $\Delta H$ for $\text{C(s)} + \tfrac{1}{2}\text{O}_2\text{(g)} \rightarrow \text{CO(g)}$.
Subtracting the second equation from the first: $\Delta H = -393.5 - (-283.0) = -110.5\ \text{kJ}$
| Type | Definition |
|---|---|
| Enthalpy of formation (ΔfH°) | Enthalpy change when 1 mole of a compound forms from its elements in their standard states |
| Enthalpy of combustion (ΔcH°) | Enthalpy change when 1 mole of a substance is completely burnt in oxygen |
| Enthalpy of atomization | Enthalpy change to break 1 mole of bonds to obtain atoms in the gas phase |
| Bond enthalpy | Average energy needed to break one mole of a specific bond in the gaseous state |
| Enthalpy of sublimation | Enthalpy change when 1 mole of a solid converts directly to gas |
| Enthalpy of solution | Enthalpy change when 1 mole of a solute dissolves completely in a specified amount of solvent |
| Lattice enthalpy | Enthalpy change when 1 mole of an ionic solid separates into its gaseous ions |
Energy is absorbed to break bonds (reactants) and released when new bonds form (products).
Heat capacity is the heat required to raise a system's temperature by 1°C (or 1 K). $C_v$ = heat capacity at constant volume; $C_p$ = heat capacity at constant pressure. $C_p$ is always greater than $C_v$ because at constant pressure, some of the added heat also does expansion work rather than only raising the temperature.
A process that occurs on its own, without continuous external intervention, once started (though it may need initial activation energy). Spontaneity is about the natural direction of a process, not its speed — a spontaneous reaction can still be very slow.
Entropy is a measure of the randomness or disorder of a system — a state function. Gases have higher entropy than liquids, which have higher entropy than solids, for the same substance.
The total entropy of the universe always increases for any spontaneous process.
Entropy change alone isn't a convenient spontaneity test because it requires tracking both system and surroundings. Gibbs energy (G) combines both effects into one system-only quantity: $G = H - TS$.
| ΔH | ΔS | ΔG | Spontaneity |
|---|---|---|---|
| − | + | Always − | Spontaneous at all temperatures |
| + | − | Always + | Non-spontaneous at all temperatures |
| − | − | − at low T, + at high T | Spontaneous only at low temperature |
| + | + | + at low T, − at high T | Spontaneous only at high temperature |
For a reaction, ΔH = −40 kJ/mol and ΔS = −100 J/K/mol at 300 K. Determine if the reaction is spontaneous.
$\Delta G = \Delta H - T \Delta S = -40{,}000 - (300)(-100) = -40{,}000 + 30{,}000 = -10{,}000\ \text{J} = -10\ \text{kJ}$
Since ΔG is negative, the reaction is spontaneous at 300 K.
Links the standard Gibbs energy change of a reaction to its equilibrium constant K — a large K (products favoured) corresponds to a large negative ΔG°.
The entropy of a perfectly crystalline substance is zero at absolute zero temperature (0 K) — at this point, there is no thermal disorder, and the particles are in a single, perfectly ordered arrangement. This law provides a reference point for calculating absolute entropy values at other temperatures.