= Homogeneous catalysis
{wiki}
In <homogeneous catalysis>, the <catalyst> and <reactants> occupy the same <thermodynamic phase>.
For a liquid example, specify <hydrogen peroxide> as the <reactant>, dissolved <iodide> as the <catalyst>, and <water> as the <solvent>. If both reacting <chemical species> remain dissolved in that one liquid <thermodynamic phase>, this is <homogeneous catalysis>. The University of Wisconsin–Madison's https://www2.chem.wisc.edu/deptfiles/genchem/sstutorial/Text13/Tx133/tx133.html[The Rate of a Reaction] identifies <iodide>-catalysed <hydrogen peroxide> decomposition in its final example; the aqueous setting here makes the phase roles explicit.<The Rate of a Reaction by University of Wisconsin–Madison Department of Chemistry>[The Rate of a Reaction, final Example: iodide-catalysed decomposition of hydrogen peroxide]{ref} Its net <chemical equation> is
$$
2\mathrm{H_2O_2}(aq)\longrightarrow2\mathrm{H_2O}(l)+\mathrm{O_2}(g).
$$
The <molecular oxygen> is a <reaction product>: its bubbles do not make the dissolved catalytic route <heterogeneous catalysis>. The classification compares the participating <catalyst> and <reactants>, rather than demanding that everything in the vessel share a phase.<Chemistry 2e by Paul Flowers and others/12.7 Catalysis>[Chemistry 2e by Paul Flowers and others; §12.7, Homogeneous Catalysts: catalyst in the same phase as the reactants]{ref}
\Image[/catalyst-phase-and-contact.png]
{title=The same <hydrogen peroxide> <reactant> can meet a dissolved <catalyst> or a separate <solid> <catalyst>}
{id=image-catalyst-phase-and-contact}
{description=Original schematic phase comparison with <water> as the <solvent>. Left: dissolved <iodide> and <hydrogen peroxide> share a liquid <thermodynamic phase>. Right: <manganese dioxide> remains a separate <solid> in contact with the liquid <chemical solution>. Symbols indicate phase roles, not molecular structure, a measured distribution, or a common microscopic <reaction mechanism>. The <molecular oxygen> product is omitted to keep the comparison focused on <reactants> and <catalysts>.}
Being in the same <thermodynamic phase> describes where the <chemical species> are; it does not specify their <reaction mechanism>. A uniform-looking liquid can contain unresolved <solid> particles, so appearance alone is insufficient. Conversely, suspended <solid> particles do not establish that their surfaces supply the observed <catalysis>: dissolved material released from them could contribute. Phase identification and catalytic participation need separate evidence.
The bookkeeping of a <catalyst> in <homogeneous catalysis> is particularly transparent in the schematic <catalytic cycle> A plus C forming AC, followed by AC releasing B plus C. This is the generic model in <catalyst>, not an asserted <iodide> <reaction mechanism>. Suppose a fixed <volume (thermodynamics)> initially contains $1.00\,\mathrm{mmol}$ of A and $0.20\,\mathrm{mmol}$ of C. At a chosen snapshot, let $0.60\,\mathrm{mmol}$ of B and $0.12\,\mathrm{mmol}$ of AC be present, with no other <chemical reactions>. Each AC contains one A unit and one C unit, so
$$
n_{\mathrm A}+n_{\mathrm{AC}}+n_{\mathrm B}=1.00\,\mathrm{mmol},\qquad
n_{\mathrm C}+n_{\mathrm{AC}}=0.20\,\mathrm{mmol}.
$$
Thus free A is $0.28\,\mathrm{mmol}$ and free C is $0.08\,\mathrm{mmol}$. B formation already exceeds the initial <amount of substance> of C by a factor of three, while the total C inventory remains $0.20\,\mathrm{mmol}$. Adding the two steps cancels C and AC, giving the net A-to-B <chemical reaction>; counting their constituents proves these balances. Conserved total <catalyst> does not mean constant free <catalyst> <concentration>.
Dissolved contact is useful because <reactants> can encounter the catalytic <chemical species> throughout the mixed liquid, without first reaching a macroscopic <solid> surface. Recovering a dissolved <catalyst> from the same <chemical solution> can instead require a separation. Neither ease of contact nor phase classification determines an <activation energy> or an <equilibrium constant>; those depend on the relevant <chemical kinetics> and endpoint <thermodynamics>.
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