deltaU = q + w
Internal energy changes by heat and work transferred to the system.
First law of thermodynamics in the Chemistry sign convention.
- q
- heat transferred to the system (J)
- w
- work done on the system (J)
Use when — q and w are positive when energy enters the system, under the Chemistry sign convention.
Common trap — Importing the Physics work-by-system sign convention without noting the switch.
w = -P_ext * deltaV
Expansion does work on the surroundings, so system work is negative under constant external pressure.
Pressure-volume work for a one-step process against constant external pressure.
- P_ext
- constant external pressure (Pa)
- deltaV
- volume change (m^3)
Use when — The process occurs against a constant external pressure.
Common trap — Replacing P_ext with the gas's own pressure in an irreversible step.
w_rev = -integral of P_ext dV
Work depends on the path through the external pressure.
Reversible pressure-volume work along a quasistatic path.
- P_ext
- external pressure, matching internal pressure at every step (Pa)
Use when — The path is quasistatic and reversible.
Common trap — Calling every slow-looking process reversible without checking the quasistatic condition.
H = U + PV
Enthalpy combines internal energy with the pressure-volume term.
Definition of enthalpy for a macroscopic thermodynamic state.
- H
- enthalpy (J)
- U
- internal energy (J)
- P
- pressure (Pa)
- V
- volume (m^3)
Use when — A macroscopic thermodynamic state is defined.
Common trap — Calling enthalpy the same as heat under all conditions.
q_p = deltaH
Under these limits, constant-pressure heat measures enthalpy change.
Heat exchanged at constant pressure equals the enthalpy change.
- q_p
- heat at constant pressure (J)
Use when — The system is closed, pressure is constant, and only pressure-volume work occurs.
Common trap — Applying it when electrical or other non-pressure-volume work also acts.
deltaH = deltaU + deltaN_g * R * T
Gas expansion changes the pressure-volume contribution between internal energy and enthalpy.
Relation between reaction enthalpy and internal-energy change for gas-phase stoichiometric change.
- deltaN_g
- change in gaseous stoichiometric moles only (mol)
- R
- gas constant (J/(mol K))
- T
- temperature (K)
Use when — Ideal gases at one temperature, with deltaN_g counting only gaseous species.
Common trap — Counting liquids and solids in deltaN_g.
deltaH_rxn(standard) = sum(v * deltaHf(products)) - sum(v * deltaHf(reactants))
Build the reaction enthalpy from standard formation steps.
Standard reaction enthalpy computed from standard formation enthalpies.
- v
- stoichiometric coefficient (dimensionless)
Use when — The same standard-state convention applies and the reaction is balanced.
Common trap — Omitting stoichiometric coefficients when summing formation enthalpies.
deltaG = deltaH - T * deltaS
Enthalpy and entropy compete through temperature.
Gibbs energy change at fixed temperature for the compared states.
- deltaS
- entropy change (J/(mol K))
Use when — Temperature is consistent, and the criterion is used at constant temperature and pressure.
Common trap — Using Celsius, or ignoring the units of entropy relative to enthalpy.
deltaG = deltaG(standard) + R * T * ln(Q)
Composition changes the current driving force away from the standard value.
Gibbs energy change away from standard composition.
- Q
- reaction quotient at the current composition (dimensionless)
Use when — Activities are defined and the temperature matches the standard-state reference.
Common trap — Using the equilibrium constant in place of the current reaction quotient.
deltaG(standard) = -R * T * ln(K)
Standard tendency determines the equilibrium position, but the reaction's own Gibbs change is zero at equilibrium, not the standard one.
Relation between standard Gibbs energy change and the equilibrium constant.
- K
- dimensionless thermodynamic equilibrium constant (dimensionless)
Use when — Equilibrium is established at temperature T with a properly defined dimensionless K.
Common trap — Saying deltaG(standard) becomes zero once an equilibrium mixture forms.