CHEMICAL THERMODYNAMICS
                           |
          ┌────────────────┼────────────────┐
          |                |                |
      ENERGY            ENTROPY         SPONTANEITY
      CHANGES           (S)              ($\Delta G$)
          |                |                |
    ┌─────┴─────┐    ┌─────┴─────┐    ┌────┴────┐
    |           |    |           |    |         |
   $\Delta U$          $\Delta H$   $\Delta S$>0      $\Delta S$<0  $\Delta G$<0    $\Delta G$>0
    |           |  (disorder↑)(disorder↓)(spont)(non-spont)
  First     Hess's              |         |
   Law       Law         $\Delta G$ = $\Delta H$ - T$\Delta S$  $\Delta G$°=-RTlnK
    |           |                |
  q+w    $\Delta U$+$\Delta n$gRT          4 Cases:
          |              (1) $\Delta H$-,$\Delta S$+: Always
      Bond     Formation  (2) $\Delta H$+,$\Delta S$-: Never
    Enthalpy   Enthalpy   (3) $\Delta H$-,$\Delta S$-: Low T
                          (4) $\Delta H$+,$\Delta S$+: High T
                                |
                         T_cross = $\Delta H$/$\Delta S$

Central connections:

• First law links $q$ and $w$ to $\Delta U$
• Enthalpy derived from first law: $\Delta H = \Delta U + \Delta n_g RT$
• Gibbs equation combines $\Delta H$ and $\Delta S$: $\Delta G = \Delta H - T\Delta S$
• Equilibrium constant $K$ connects to $\Delta G^\circ$: $\Delta G^\circ = -RT\ln K$