Convert every peak to moles, then multiply by the electron count: 2 for CO and formate, 6 for methanol, 8 for methane, 12 for ethylene. A 20 µmol/h CO rate under 2 W of 365 nm light, which is 22 mmol photons/h, gives an apparent quantum yield of 0.18 %. Publish the carbon balance and the dissolved fraction alongside it.
Every number downstream inherits this step's error, so do it explicitly. At 101.3 kPa and 298 K one millilitre of ideal gas holds 40.9 µmol, so a 1 mL loop at 1,000 ppm CO delivers 40.9 nmol and a 1 % standard delivers 409 nmol. Fit in nanomoles, not peak-area-per-ppm, and the curve survives a loop or instrument change.
Then scale to the reactor using free volume — the gas space after subtracting the liquid and immersed hardware, not the nominal vessel size. A 300 mL vessel holding 100 mL of slurry has 200 mL of gas, so a reading of 815 ppm is 6.7 µmol, not 10 µmol. That 33 % difference is larger than most of the effects people argue about.
Two independent counters must agree: electrons to products and carbon atoms to products. Assign the electron count from the balanced half-reaction first, because it is not proportional to carbon number.
| Product | Electrons per molecule | Carbon per molecule | Where it ends up | Quantification |
|---|---|---|---|---|
| CO | 2 | 1 | Gas phase, with a dissolved pool near 100 µmol in 100 mL | TCD, or FID with methanizer |
| CH4 | 8 | 1 | Gas phase almost entirely | FID |
| CH3OH | 6 | 1 | Split between liquid and headspace | HPLC or GC-FID, both phases summed |
| HCOOH / HCOO− | 2 | 1 | Liquid only above pH 4 | HPLC, ion chromatography or 1H NMR |
| C2H4 | 12 | 2 | Gas phase | FID |
| C2H5OH | 12 | 2 | Liquid, partly volatile | GC-FID with a polar column |
| H2 | 2 | 0 | Gas phase | TCD — not a CO2 product, count separately |
State whether hydrogen sits in the selectivity denominator: 20 µmol/h of CO plus 20 µmol/h of H2 is 50 % selective on an electron basis and 100 % on a carbon basis. Quote the electron figure — it is the one that reflects the competing proton reduction.
Faradaic efficiency needs a denominator: charge passed. A photon-only slurry reactor has no external circuit, so FE is undefined there and the honest metric is quantum yield. FE belongs to photoelectrochemical and electrocatalytic cells, where FE = n × z × F / Q, with F = 96,485 C/mol.
Worked example: a cell held at 10 mA for one hour passes 36 C. If the headspace gains 149 µmol of CO, the charge attributable to CO is 149 × 10−6 × 2 × 96,485 = 28.8 C, so FECO = 80 %. An FE sum below 90 % means a product is missing from the method, not that the catalyst is poor.
Apparent quantum yield is AQY = (nproduct × z) / nphotons. Compute the photon count from measured irradiance and illuminated area, not from lamp power. At 365 nm a photon carries 1240/365 = 3.40 eV, or 5.44 × 10−19 J, so 100 mW/cm² over 20 cm² delivers 2.0 W and therefore 3.68 × 1018 photons/s — 22 mmol/h.
Two rules keep the number defensible. AQY at a stated wavelength needs monochromatic light or a spectral irradiance integrated over the emission band; an AQY for a full-spectrum 300 W xenon lamp is a different quantity and belongs under energy conversion. And state whether the denominator is incident or absorbed photons: for a film transmitting 60 %, incident-photon AQY understates the intrinsic value by 2.5×.
Not for a light-only slurry system, because there is no measurable charge to divide by. Use apparent quantum yield, or report a product distribution on an electron basis. FE becomes valid once the experiment includes an electrode and a measured current.
Almost always an unmeasured phase or an unmeasured product. Check the liquid for formate, acetate and methanol before assuming a leak, then check whether the run was long enough for dissolved CO to equilibrate with the headspace.
Either, as long as you say which. Incident-photon AQY is the number to use when comparing reactors, because it reflects what the hardware delivers; absorbed-photon AQY is the number to use when comparing catalysts at equal optical density.
Two, the same as CO, because the carbon stays at the +2 oxidation state. Formic acid and formate are the same product for bookkeeping purposes; only the pH-dependent phase distribution changes.
