Chemistry · Lesson

Catalytic, photochemical and electrochemical transformations

Compare catalyst productivity, absorbed-photon yield and product-assigned charge with their correct denominators. Separate a pathway’s rate effect from equilibrium and from overall energy or environmental performance.

Back to the Chemistry map

By the end, you can

Identify ideal catalyst regeneration without assuming indefinite activity.
Define the counted-site basis of TON and average TOF.
Distinguish absorbed-photon quantum yield from an incident-photon ratio.
Calculate ideal electron capacity and a stipulated current efficiency.

A catalytic pathway has a complete regeneration ledger

A catalyst participates in a pathway and is regenerated in its ideal cycle. It can change reaction rates and pathway selectivity; for the same closed equilibrium transformation at fixed conditions, it does not change the overall standard Gibbs difference or equilibrium constant. Practical activity can decline through deactivation or other loss, so regeneration in a drawn cycle does not prove indefinite reuse.

For an invented one-step isomer model at 298 K, let product G° be 5.00 kJ mol⁻¹ below reactant G°. Compare forward barriers 75.0 and 55.0 kJ mol⁻¹ with equal transition-state prefactors and transmission coefficients. Reverse barriers must be 80.0 and 60.0 kJ mol⁻¹ respectively. Both models give K=exp(5000/(R× 298))≈ 7.52321, although their conditional forward-rate ratio is exp(20000/(R× 298))≈ 3203.41.

Here R is the molar gas constant. These are stipulated illustrative paths rather than measured catalyst energies. A real catalytic network can involve several intermediates and different prefactors. A driven photochemical or electrochemical steady state is not automatically this closed equilibrium model.

Turnover metrics need an explicit site convention

Here define chemical turnover number, TON, as cumulative net product amount divided by the counted active-site amount. Define average turnover frequency, TOF, as that TON divided by the elapsed interval. TON is dimensionless; average TOF has inverse-time units. Historical and enzymological uses of turnover terminology differ, so state this convention whenever comparing values.

With invented net product amount 0.00250 mol, counted site amount 0.0000500 mol and interval 600 s, TON=50.0 and average TOF≈ 0.0833333 s⁻¹. These values do not determine instantaneous activity, an intrinsic surface-site rate or an enzyme’s saturated k_cat. A different site count changes the numerical denominator, and deactivation can make the average differ markedly from a current rate.

A quantum yield uses absorbed photons

A specified photochemical quantum yield compares the number of selected events with the number of absorbed photons at a stated excitation wavelength. Molar event amounts and molar photon amounts give the same ratio when their bases match. Incident photons that were not absorbed must not be silently included in that denominator. Reaction chains can generate multiple selected events per absorbed photon, so a universal yield ceiling of one is inappropriate for every photochemical event definition.

In an invented monochromatic 455 nm case, 0.000500 mol incident photons with absorbed fraction 0.400 give 0.000200 mol absorbed photons. A stipulated 0.0000500 mol product then gives Φ=0.250 per absorbed photon, while product/incident-photon amount is 0.100. The two ratios answer different questions.

Photon energy E=hc/λ≈ 4.36582× 10⁻¹⁹ J uses Planck’s constant h, light speed c and wavelength λ. With N_A denoting Avogadro’s constant, molar photon energy N_Ahc/λ≈ 262.916 kJ mol⁻¹ gives incident radiant energy approximately 131.458 J for this count. These values do not include source electrical losses, energy used elsewhere in the process or lifecycle impacts.

An absorbing sensitizer may induce an alteration in another molecular entity. Electron-transfer and energy-transfer paths are distinct; a photoredox proposal must account for electron exchange and sensitizer regeneration, rather than relying on a light symbol alone. Absorption does not establish suitable substrates, a particular mechanism or a practical yield.

Charge capacity requires electron stoichiometry

For constant current, passed charge Q=It; if current varies, use its time integral. Dividing by the Faraday constant F=N_A e, with e the elementary charge, gives the molar electron amount, and dividing again by the specified electron count z per product gives ideal product capacity. In an invented one-direction case I=0.500 A over 240 s gives Q=120 C, n(e⁻)≈ 0.00124371 mol and z=2 capacity approximately 0.000621856 mol product.

If stipulated net product is 0.000400 mol and no subsequent chemistry generates or consumes that product, its assigned charge is zFn_product≈ 77.1883 C. The current-efficiency fraction is 77.1883/120≈ 0.643236. This ordinary one-direction toy assumes compatible product accounting; definitions involving opposing partial currents or consecutive chemistry require care.

No initial limiting-substrate amount or voltage was provided. Therefore neither overall synthetic yield nor energy efficiency follows from the 64.3236% charge fraction. Energy requires an electrical work model and other inputs. Electrochemical, photochemical and catalytic labels do not by themselves establish a more sustainable transformation.

Each productivity or efficiency ratio has a different denominator

Selected quantity	Numerator	Denominator or comparison	Toy result
Chemical TON convention	0.00250 mol net product	0.0000500 mol counted sites	50.0
Average TOF	TON 50.0	600 s	0.0833333 s⁻¹
Quantum yield at 455 nm	0.0000500 mol selected product	0.000200 mol absorbed photons	0.250
Incident-photon product ratio	0.0000500 mol selected product	0.000500 mol incident photons	0.100
Current-efficiency fraction, selected z=2	77.1883 C product-assigned charge	120 C passed charge	0.643236
Closed-model equilibrium K at 298 K	Same endpoint ΔG°=−5.00 kJ mol⁻¹	Consistent forward/reverse barriers	7.52321 for both illustrative paths

Original arithmetic ledger for four separate invented teaching comparisons. The site, photon, charge and equilibrium inputs are not interchangeable and are not real process measurements.

Worked examples

State the site basis before calculating productivity

Use 2.50 mmol net product, 0.0500 mmol counted sites and 600 s.

TON = 2.50 / 0.0500 = 50.0.
Average TOF = 50.0 / 600 ≈ 0.0833333 s⁻¹.

TON 50.0 and average TOF 0.0833333 s⁻¹ under the declared convention; no instantaneous or enzyme saturation rate was inferred.

Remove the unabsorbed photons from the quantum-yield denominator

Use incident 0.500 mmol photons, absorption 40.0% and product 0.0500 mmol.

Absorbed photon amount = 0.500 × 0.400 = 0.200 mmol.
Φ = 0.0500 / 0.200 = 0.250.
Product/incident amount = 0.0500 / 0.500 = 0.100.

Quantum yield 0.250 and a distinct incident-photon ratio 0.100 in the invented 455 nm case.

Assign a two-electron product’s share of charge

Use I=0.500 A, t=240 s, z=2 and net product 0.000400 mol.

Q = 0.500 × 240 = 120 C.
Product-assigned charge = 2 × 96485.33212 × 0.000400 ≈ 77.1883 C.
Efficiency fraction = 77.1883 / 120 ≈ 0.643236.

64.3236% charge fraction under the stated one-direction product model; no voltage or synthetic-yield basis was supplied.

Measure reverse barriers from the product state

For the two invented paths, product lies 5.00 kJ mol⁻¹ below reactant and forward barriers are 75.0 and 55.0 kJ mol⁻¹.

Reverse barriers are 75.0−(−5.00)=80.0 and 55.0−(−5.00)=60.0 kJ mol⁻¹.
Each forward/reverse ratio is exp(5000/(R× 298))≈ 7.52321.
Equal-prefactor forward-rate comparison is exp(20000/(R× 298))≈ 3203.41.

The same K with different conditional rates in this fixed-temperature toy.

Try it yourself

Does chemical TON as defined here already have inverse-time units?
Show the answer and reasoning
No.
It is a cumulative product/site ratio; average TOF divides that ratio by the time interval.
Can the incident-photon product ratio be called the same absorbed-photon quantum yield when absorption is incomplete?
Show the answer and reasoning
No.
The photon denominators differ.
Does a known product charge fraction establish electrical energy efficiency without a voltage/work model?
Show the answer and reasoning
No.
Charge and energy are different quantities.
Does a catalyst change K for the same closed equilibrium transformation at fixed conditions?
Show the answer and reasoning
No.
The endpoint thermodynamics remain the same; rates and pathways can change.

What to carry forward

Track catalyst regeneration and possible deactivation.
State counted sites and turnover conventions.
Use absorbed photons for the specified quantum yield.
Include electron stoichiometry in product charge capacity.
Keep charge, synthetic yield and energy comparisons separate.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.