Ethylene from carbon dioxide, with less voltage

Carbon dioxide and water are converted to ethylene and oxygen in one cell, at a rate and a full-cell energy efficiency that are both high for a full day, with the carbon in the ethylene coming from the carbon dioxide.

Ethylene is the largest organic feedstock. Making it from CO₂ and water, instead of from steam cracking, only changes the energy balance if the cell voltage and the selectivity are both good. A high faradaic efficiency at an unstated full-cell voltage, or a low voltage held for a few minutes, does not answer that. The grade is the two numbers on the same electrode, averaged over a day, with the voltage taken between the anode and the cathode.

Li and co-workers define the full-cell energy efficiency for 2 CO₂ + 2 H₂O → C₂H₄ + 3 O₂ as

energy efficiency = (1.15 V × faradaic efficiency to ethylene) / full-cell voltage,

with 1.15 V the equilibrium cell potential they give for that reaction. In a membrane-electrode assembly they held a full-cell voltage of 3.65 V for 190 hours with an ethylene selectivity of 64%, and they report the efficiency of that system as 20%. The arithmetic 1.15 × 0.64 / 3.65 is 20%.

Fang and co-workers, in a 2026 membrane-electrode paper, report a full-cell energy efficiency of 29.2% at an ethylene partial current density of 401 mA cm⁻². Their methods write

energy efficiency = [1.23 V + (−E°_A)] × faradaic efficiency / full-cell voltage,

where E°_A is the thermodynamic potential of CO₂ to the product, from the standard Gibbs energy at 298.15 K, and the full-cell voltage is measured without ohmic correction. The main text does not print the value of E°_A used for ethylene. The Li expression and this expression are the same arithmetic when E°_A = 0.08 V, because 1.23 − 0.08 = 1.15. This problem does not assert that the 2026 experiment used 0.08 V. It cites 29.2% as that paper’s reported number and grades only with 1.15 V.

The same paper’s long run is a different operating point. For 1020 hours at 200 mA cm⁻² in 0.1 M KHCO₃ they report a full-cell voltage of approximately 3.5 V and an ethylene faradaic efficiency around 68%, and they replaced the anion-exchange membrane periodically. Applied to those approximate figures, the Li formula gives 1.15 × 0.68 / 3.5 ≈ 22%, and 200 × 0.68 ≈ 136 mA cm⁻² of ethylene partial current. That 22% is computed here. It is not a number the paper prints. A half-cell ethylene energy efficiency of 38.5% at −0.98 V versus RHE, also in that paper, is not a full-cell result and does not enter the grade.

The cell is a two-electrode device. The anode reaction is water oxidation. The cathode reduces CO₂. The full-cell voltage is the measured voltage between anode and cathode, with no ohmic-drop correction. Ethylene is quantified by gas chromatography against a calibration mixture. Liquid products are quantified and included in the balance, but the graded product is ethylene.

Energy efficiency is computed only with the Li formula above, using 1.15 V. The partial current density is the total geometric current density multiplied by the faradaic efficiency to ethylene. Both numbers are averages over 24 hours of continuous operation, not peak values, and neither the membrane nor the cathode is replaced in that window. A ¹³CO₂ feed, run as a separate experiment of at least 1 hour in the same cell, must show ¹³C-ethylene consistent with the enrichment of the feed.

A polycrystalline copper foil is run in the same cell hardware, the same day, as an instrument control. It must make detectable ethylene, so that a dead cell cannot pass on a calibration error.

The gas is at 1 bar of CO₂. Elevated pressure is allowed only if every compressor’s electrical energy is added to the denominator of the efficiency as an equivalent voltage, energy divided by the charge passed. The simpler experiment, and the one that keeps the grade inside a normal lab, is 1 bar with no compressor term.

The 24-hour averages are an energy efficiency of at least 40% and an ethylene partial current density of at least 200 mA cm⁻², together, on one electrode in one cell, with no membrane or cathode replacement. The isotope experiment passes, the copper foil control makes ethylene, and the carbon balance below closes. Carbonate and bicarbonate are not counted as ethylene.

Forty percent and 200 mA cm⁻² are a joint pass mark defined here. Forty percent is above the reported 29.2% point and above the 20% point, and it is above the roughly 22% figure computed here for the 1020-hour run. Two hundred milliamperes per square centimetre of partial current, held as a 24-hour average together with that efficiency, is the other half of the mark. Matching either cited paper is not the task.

• ¹³CO₂ labeling as above. Unlabeled ethylene during that experiment fails the attempt.
• An argon feed in place of CO₂, same current, produces no ethylene above the chromatographic baseline.
• The copper foil control produces ethylene and is reported, including its faradaic efficiency and voltage, but the candidate does not have to beat the foil on every axis. The foil checks the apparatus.
• The outlet flow is measured, not assumed equal to the inlet, so that a change in gas volume does not inflate the faradaic efficiency. Fang and co-workers already record inlet and outlet flow for this reason.
• Liquid products that cross the membrane are counted in the balance. They do not have to be zero. They must not be omitted.
• Carbonate and bicarbonate are quantified on both sides of the membrane. The sum of carbon in outlet CO₂, ethylene, other identified carbon products, and carbonate plus bicarbonate closes to within 10% relative of the CO₂ fed over the same window. That 10% is a pass mark for analytical closure, the same kind of tolerance problem 06 uses, not a figure taken from a paper. A cell that posts a high ethylene faradaic efficiency while most of the consumed CO₂ is carbonate fails.

Any cathode catalyst, ionomer, or membrane. Neutral, acidic, or alkaline electrolytes. A gas-diffusion electrode. The compressor term above, if pressure is used.

A sacrificial anode. Stoichiometric chemical reductants. Reporting a cathode potential against a reference electrode in place of the full-cell voltage. iR-corrected voltages in the efficiency formula. A peak efficiency held for minutes. Purchased ethylene. A 24-hour average assembled by discarding intervals. Replacing the membrane, the cathode, or the electrolyte during the graded 24 hours and continuing the average. Using a numerator other than 1.15 V. Counting carbonate or bicarbonate as the ethylene product. Omitting them from the carbon balance.

The 24-hour average energy efficiency, on the Li formula, is at least 25% at an ethylene partial current density of at least 100 mA cm⁻², with the isotope and argon controls passing, and with no membrane or cathode replacement. Twenty-five percent and 100 mA cm⁻² are pass marks for this lesser bar. Twenty-five percent sits above the reported 20% and above the roughly 22% computed here for the long run, and below the reported 29.2% peak. Partial success is not a solution.

Definition, equilibrium potential 1.15 V, and the 20% full-cell result at 3.65 V and 64% ethylene selectivity: Li and co-workers, Nature, 2020, 577, 509–513, doi:10.1038/s41586-019-1782-2 (opens in a new tab). The 29.2% figure at 401 mA cm⁻², the methods formula, the 1020-hour point at about 3.5 V and about 68% faradaic efficiency, the periodic membrane replacement, and the half-cell 38.5% figure: Fang, Huang, Wang, Wang, Feng, Ma, Dai, Zhu, and Jiang, Nature Communications, 2026, 17, 984, doi:10.1038/s41467-025-67719-z (opens in a new tab). The 22% and 136 mA cm⁻² figures are computed here from that paper’s approximate long-run voltage and faradaic efficiency; they are not printed by the paper. The 40%, 24-hour, and 200 mA cm⁻² joint requirement, and the 25% and 100 mA cm⁻² partial bar, are pass marks defined here. Open point: the main text does not state whether 29.2% was held for 24 hours, and it does not print E°_A, so this problem does not treat 29.2% as a 24-hour Li-formula result.