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Catalytic selectivity concerns which reaction products form when competing reaction mechanisms are available. Faster conversion is valuable when a process would otherwise be impractically slow; a suitable catalyst can also favour a useful product within the available time. In an illustrative pair of irreversible first-order reactions A to B and A to D, the initial fraction of converted A going to B is $k_B/(k_B+k_D)$. Multiplying both rate constants by the same factor changes speed but leaves this fraction unchanged; changing their relative values changes the kinetic product split. This is a finite-time kinetic illustration, not a new equilibrium constant.

A catalyst need not accelerate every competing chemical reaction equally. Enzymes, for example, can distinguish substrates through their active sites.^[ref] If every relevant reversible channel eventually equilibrates in a closed system, its final chemical equilibrium still obeys the endpoint thermodynamics. Selective acceleration, product removal, or external driving can make an observed product distribution depend on time and operating conditions. A claim of improved yield must specify those conditions.

In chain-growth polymerization, each growth step joins a monomer to a reactive site on a polymer chain and regenerates that reactive site. This is the precise mechanistic restriction in IUPAC's definition: growth occurs exclusively through these monomer–chain-site reactions. The word chain refers to the succession of site-regenerating chemical reactions. It does not merely mean that the product looks like a long chain. Chain-growth initiation starts this succession; chain-growth propagation continues it; chain-growth termination and chain transfer in chain polymerization can change its fate.^[ref]

The contrast with step-growth polymerization concerns the permitted joining partners. There, suitable reactive groups can join two existing chains, for example a two-unit chain and a three-unit chain. In chain-growth propagation, a free monomer adds to a polymerization-active site. Release of a small byproduct is a separate classification question: IUPAC explicitly allows condensative chain polymerization.^[ref] The useful consequence is that a few growing chains can incorporate many monomer molecules while much of the feed remains unreacted. Their degree of polymerization depends on how those units are shared among chains, as finite chain-growth bookkeeping makes explicit.

A chemical equation represents a chemical reaction using chemical formulas, with reactants on the left and reaction products on the right. A balanced chemical equation has the same number of chemical atoms of each chemical element on both sides. For molecular hydrogen and molecular oxygen forming water,The coefficients $2,1,2$ give the relative numbers of molecules; the coefficient $1$ is normally omitted. Count hydrogen as $2\times 2=4$ on the left and $2\times 2=4$ on the right, and oxygen as $1\times 2=2$ on the left and $2\times 1=2$ on the right. See Flowers et al., Chemistry 2e, §4.1: writing and balancing chemical equations.

To balance the initial expression ${\mathrm{H}}_2+{\mathrm{O}}_2⟶{\mathrm{H}}_2\mathrm{O}$, first put $2$ before water to match the two oxygen chemical atoms. This creates four hydrogen chemical atoms on the right, so put $2$ before molecular hydrogen. Changing a coefficient multiplies the entire chemical formula. Changing a subscript changes composition and usually the chemical substance: $2{\mathrm{H}}_2\mathrm{O}$ is two water molecules, whereas ${\mathrm{H}}_2{\mathrm{O}}_2$ is one hydrogen peroxide molecule. Never balance a chemical equation by changing its subscripts.

The bookkeeping follows from conservation of the atomic nuclei in ordinary, non-nuclear chemical reactions; chemical bonds and the distribution of Electrons can change. For a chemical equation involving ions, total electric charge must also match. For example, the existing self-ionization of water equation has zero total electric charge on each side, since the $+1$ of hydronium cancels the $-1$ of hydroxide. See 2.6 Ionic and Molecular Compounds (§2.6: nuclei and ions).

The same $2:1:2$ ratio relates changes in amount of substance: two moles of molecular hydrogen consumed per mole of molecular oxygen correspond to two moles of water formed. A mole is a defined unit, not one molecule; the little whole-number picture is an abstract counting model, not a claim that a macroscopic sample contains just five molecules. See molecular count and amount of substance for the exact conversion and BIPM, SI base unit: mole for the definition.

This is why a balanced chemical equation is useful: stoichiometry turns the same atom accounting into relations between measurable quantities. It does not determine reaction rate, the final conversion set by chemical equilibrium, or the actual yield of recovered reaction products. The limiting reagent gives an upper bound under the specified chemical reaction.

Chemical kinetics studies how quickly chemical reactions proceed and how their reaction rates depend on composition and conditions. It connects a measured change in concentration to a rate law, then uses a rate equation to predict future concentrations. This makes it useful for choosing how long to wait for conversion and for testing a proposed reaction mechanism. Changing temperature, reactant concentrations, or the presence of a catalyst can change reaction rates; see Flowers et al., Chemistry 2e, §12.2: factors affecting reaction rates.

Chemical equilibrium specifies the eventual balance under given constraints; chemical kinetics determines how rapidly it is approached. At fixed temperature and pressure, a decrease in Gibbs free energy favours conversion but does not guarantee a fast chemical reaction: reaching a transition state can require crossing a substantial barrier. Thus a mixture can change imperceptibly over an observation period without being at chemical equilibrium. The distinction separates which direction is favoured from how long conversion takes. See 12.5 Collision Theory (§12.5: collision theory and reaction barriers) and Chemistry 2e, §16.1: spontaneity and speed.

A concrete laboratory route to an Arrhenius plot is to infer a rate constant at each controlled temperature from a changing electrical conductivity. The Technical University of Munich's Activation Energy of a First-Order Reaction supplies a teaching protocol, rather than a published set of measured rate constants.

The manual follows tertiary amylbromide conversion, which produces conducting ions. A measuring cell connects to a thermostat; an immersed electrical conductivity probe also measures solution temperature, and a magnetic stirrer mixes it. Use $80\mathrm{mL}$ of $80\%$ by volume ethanol in water, equilibrate, then add $0.5\mathrm{mL}$ of tertiary amylbromide. Record the baseline before addition and set time zero at addition. Repeat with fresh mixtures at $25$, $30$, and $35{}^{\circ }\mathrm{C}$, each within $\pm 0.5{}^{\circ }\mathrm{C}$; record for $30$ minutes at the first two temperatures and until completion at the last. Clean the cell between runs and keep the added volume fixed. The completed $35{}^{\circ }\mathrm{C}$ mixture supplies endpoint electrical conductivity measurements at the other temperatures: one endpoint reading cannot be used unchanged at every temperature.^[ref]

To see what is inferred from the readout, let ${\sigma }_0$, $\sigma (t)$, and ${\sigma }_{\infty }$ be the baseline, current, and completed-mixture electrical conductivities at the same temperature. Assume their baseline-subtracted changes are proportional to converted concentration. Combining that measurement model with a first-order reaction givesThus the electrical conductivity increases toward an endpoint, while the remaining reactant fraction decreases. Fit $-\ln f$ against time to obtain $k$; then fit $\ln (k/k_{\mathrm{ref}})$ against $1/T$ in kelvin to estimate an apparent activation energy. This baseline-aware derivation states the measurement assumptions explicitly; it does not infer a rate constant from the steepness of a raw conductivity trace alone.

The controls distinguish a faster chemical reaction from a larger instrumental response. Measure the actual solution temperature, retain the same solvent composition and initial reactant concentration, and compare endpoint and baseline at that temperature. As further diagnostic checks, repeat runs and inspect regression residuals for departure from a first-order reaction. These checks follow from the model: electrical conductivity also depends on how ions move, a baseline drift can mimic conversion, and a mixing delay can distort early points. Near completion, a small endpoint error produces a large relative error in $f$ and its natural logarithm. A successful fit supports an apparent rate model for this solvent and interval; it does not directly image a transition state or identify a unique reaction mechanism. No measured $k$ or $E_a$ is supplied here.

An elementary reaction is a single step in a reaction mechanism. The law of mass action models its directional reaction rate using reactant concentrations raised to the step's stoichiometric multiplicities. Applying that rule requires evidence that the step is elementary; a net chemical equation alone supplies no such evidence.

Energy coupling links an endergonic reaction to an exergonic reaction through a reaction mechanism, so that the combined transformation has a favourable change in Gibbs free energy. ATP hydrolysis is a common driving chemical reaction. A shared reaction intermediate, produced in one step and consumed in another, can physically connect the transformations; merely placing two independent chemical reactions in the same chemical solution does not establish energy coupling. See Alberts et al., Molecular Biology of the Cell: coupled reactions and activated intermediates.

For a computed example, stipulate an endergonic reaction $\mathrm{A}⟶\mathrm{B}$ with $\Delta G_1^{\circ \prime }=+20\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ under precisely the same biochemical standard state conditions as the quoted ATP hydrolysis value. Assume a reaction mechanism couples one ATP hydrolysis to each A-to-B conversion. The formal sum isThe sum $+20+(-30.5)=-10.5$ gives an exergonic reaction. The $+20$ is a chosen teaching value, not a measured property of an identified substance. Outside these reference conditions, add the actual $\Delta G_1$ and $\Delta G_2$, each evaluated using consistent thermodynamic activities; mixing a standard value for one chemical reaction with an unrelated cellular value for the other gives no justified prediction.

Why do the changes in Gibbs free energy add? Gibbs free energy is a state function. Adding consistent reaction changes cancels any shared reaction intermediate and leaves the difference between the combined reactants and combined reaction products. This explains the thermodynamic accounting; it does not construct the reaction mechanism. In many ATP-dependent routes, phosphorylation transfers a phosphate group to a substrate or an enzyme, and subsequent transformation consumes that modified material. The shared material is what connects the steps. Other reaction mechanisms use ATP differently. See Alberts et al., Molecular Biology of the Cell: ATP-driven biosynthesis.

The useful achievement is that a common regenerated nucleotide can connect many different processes in metabolism. The net negative change in Gibbs free energy permits the coupled conversion, but supplies no reaction rate: enzymes can lower activation energy barriers without changing the endpoint difference. Energy coupling changes which overall chemical reaction is being considered; catalysis accelerates an available route. See OpenStax Biology 2e, 6.2: free-energy changes and reaction barriers.

A historical landmark is Fritz Lipmann's ^[ref]. Its sections on the phosphate cycle, generation and utilization of phosphate-bond energy, and group transfer organized these processes around a reusable chemical carrier. The historical terminology should be read with the modern distinction between net hydrolysis and the cost of breaking a chemical bond.

The defining idealization of living polymerization excludes chain-growth termination and irreversible chain transfer in chain polymerization. Fast, effective chain-growth initiation is an additional condition behind a nearly fixed growing-chain population, not a guarantee contained in the name alone.^[ref] If all four chains in finite chain-growth bookkeeping remain active, completing the feed keeps $C=A=4$ and gives $X_n=10$. Stipulate six further additions to each chain, obtaining $(10,10,10,10)$. Other allocations with the same total also satisfy $X_n=10$: living does not mean identical lengths.

Alternatively, stipulate that the first two length-four chains undergo chain-growth termination without joining, while the other two each receive twelve more monomer molecules. The final lengths are $(4,4,16,16)$, with $(C,A,S)=(4,2,40)$. The mean degree of polymerization is still $10$, but two chains have stopped and two carry the remaining growth. The population variance of lengths is $36$, compared with zero in the deliberately equal living allocation. These are synthetic populations, not measured molecular distributions and not a claim that all terminating processes are broader than all living processes. Indeed, assigning all twenty-four remaining additions to one still-active chain gives the living allocation $(28,4,4,4)$, with the same mean but variance $108$. Comparable start times and opportunities for chain-growth propagation are extra assumptions behind an expectation of more uniform lengths.

If the two terminated length-four chains instead join, their inactive product has length eight; with the same remaining additions the final lengths are $(8,16,16)$. Now $C=3$, $A=2$, $S=40$ and $X_n=40/3$. Thus chain-growth termination can change both which chains grow and which chains enter the denominator. Continuing chain-growth initiation, inefficient initiation, chain transfer in chain polymerization, and reactivation require their own counts. Predicting an entire length distribution additionally needs a specified reaction mechanism and growth statistics. A measured mean alone cannot establish living polymerization.

A simple route to deuterated polystyrene block copolymers by reverse iodine transfer polymerisation by Trevor Gavin Wright and Harald Pasch (2015, Experimental section, pp. 3237–3238) provides a concrete study of consumption and chain products. The authors used a valve-sealed J Young tube, freeze–pump–thaw preparation and argon. NMR monitoring of chain polymerization compared a $25{}^{\circ }\mathrm{C}$ reference with spectra acquired at $70{}^{\circ }\mathrm{C}$ every fifteen minutes for twenty-four hours. Their formulation contained an azo initiating reagent, molecular iodine and a vinyl monomer. Companion flask syntheses used stirring and a heated silicone-oil bath.

The authors followed initiating and transfer-agent signals; Figure 3 reports a transfer-agent signal rising during induction and then falling as polymerization proceeds. Their size-exclusion characterization of chain polymers used porous columns, refractive-index detection and polystyrene calibration. These distinct consumption and size readouts concern transfer-mediated chemistry; they do not establish strict living polymerization. ^[ref]

Useful proposed controls, rather than reported measurements, are a matched mixture omitting the initiating reagent, an unheated mixture, and a repeat of the complete formulation. Keep monomer amount, solvent, tube preparation and acquisition conditions matched where possible. The unheated comparison needs a readout that does not itself initiate polymerization; placing it in the hot probe would defeat that control. A mixture omitting iodine asks a different question: it changes chain transfer in chain polymerization and induction chemistry, so it is not necessarily a no-polymerization control. Record the pre-reaction baseline and compare crude material with isolated product; isolation can selectively remove shorter chains. These comparisons help separate initiation-dependent monomer consumption from signal drift and unrelated chemical reactions.

The mechanistic inference is deliberately limited. Consumption plus independently characterized larger chain products supports polymerization; evidence of an induction stage helps test a proposed reaction mechanism. Neither readout directly counts stars in $P_j^{\ast }$, proves the absence of chain-growth termination, nor recovers every chain length. A chain-extension test would probe retained growth capability, but even a successful extension would not by itself establish that all original chains extended. No measured molecular distribution is reconstructed here. IUPAC cautions that reversible deactivation can produce living-like behaviour even when some termination occurs.^[ref]

Phosphorylation attaches a phosphate group to a molecule. Transfer from ATP to a substrate or enzyme can participate in energy coupling; the name alone does not specify the complete reaction mechanism. See OpenStax Biology 2e, 6.4: phosphorylation.

A polymerization-active site is the reactive location that enables the next chain-growth propagation step. In the schematic$M$ is one free monomer molecule, $j$ is the chain's degree of polymerization in incorporated monomeric units, and the star marks the polymerization-active site. The site's reactive character survives the growth step, although the chemical atoms carrying it can change. The star is not an extra unit, a literal particle, or necessarily a positive or negative electric charge. Actual reaction mechanisms can involve an unpaired Electron, a cation, an anion, or a metal-associated site; the abstract notation does not identify which. ^[ref]

For bookkeeping below, each linear active chain has exactly one polymerization-active site. This is a stipulated model, not a property of every chain polymerization: a chain can have several reactive sites, and a reversibly inactive chain can remain capable of future growth. Count currently active sites separately from all chains capable of later reactivation.

The pre-exponential factor multiplies the exponential function in the Arrhenius equation. It has the same units as the rate constant, so for a first-order reaction both have units ${\mathrm{s}}^{-1}$. Its physical interpretation depends on the reaction mechanism; an assumed constant $A$ should not be identified with a universal collision frequency. Comparing activation energies alone does not rank absolute rate constants when the pre-exponential factors differ. See the pre-exponential factor.

A rate law specifies how a reaction rate depends on concentrations under stated conditions. A common form iswhere $k$ is a rate constant and the exponents are partial orders of reaction. Determine them experimentally, or derive them from a justified reaction mechanism. Do not infer $\alpha =a$ and $\beta =b$ from the net chemical equation: its coefficients describe consumption ratios, whereas the exponents describe sensitivity to concentration. See IUPAC Gold Book: rate law and Flowers et al., Chemistry 2e, §12.3: rate laws.

A rate law becomes a prediction of time evolution when combined with stoichiometry in a rate equation, for example $d[\mathrm{A}]/dt=-av$. Agreement with a measured rate law is useful evidence for a reaction mechanism, but several routes can give the same dependence.

A reaction intermediate is formed in one step of a reaction mechanism and consumed in a later step, cancelling from the net chemical equation. A reaction intermediate can connect the transformations in energy coupling; it is distinct from a transition state. See the IUPAC Gold Book: intermediate.