Quick wins for a faster PC:
Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →Repair Windows errors before they cause bigger problemsFix Now →Scan for outdated or missing drivers - takes under a minuteDriver Scan →iTechGuides is reader-supported. When you buy through links on our site, we may earn an affiliate commission. As an Amazon Associate I earn from qualifying purchases. Learn more
For oxygen evolution, Faradaic efficiency (FE) is the measured amount of O2 divided by the amount that the passed charge should produce, multiplied by 100. Calculate charge first, convert it to theoretical oxygen with the four-electron oxygen-evolution stoichiometry, convert your oxygen measurement to moles, and compare the two over the same time interval:
Q = ∫ I(t) dtn(O2, theoretical) = Q/(4F)FE(O2) = 100 × n(O2, measured)/n(O2, theoretical)
Here, F = 96,485 C mol−1. The difficult part is usually not the arithmetic: it is converting a gas volume, flow-stream concentration, or chromatographic signal into a calibrated amount of oxygen and synchronizing that amount with the electrochemical charge.
What oxygen Faradaic efficiency measures
Faradaic efficiency answers a specific question: what fraction of the electrons supplied to the electrode resulted in the oxygen product being measured? In oxygen evolution from water, the anodic half-reaction requires four electrons for every molecule of O2. In acidic notation, the reaction is commonly written as 2H2O → O2 + 4H+ + 4e−.
#1 Best Overall
- Read Before You Buy — No Video Output: These adapters support charging and USB 2.0 data transfer, but cannot transmit video signals. Except for standard USB webcams (which use USB data only), they are not compatible with HDMI/DisplayPort cables, video-capable USB-C hubs, or docking stations with video output.
- Convert USB-A Ports to USB-C: Designed to connect USB-C earphones, cables, flash drives, card readers, and other USB-C accessories to standard USB-A ports. Plug-and-play with no drivers or software required.
- Aluminum Alloy Housing: Built with a sturdy aluminum alloy shell that aids in heat dissipation and protects against daily wear and scratches. Designed to maintain a stable and secure connection.
- Compact & Travel-Friendly: The ultra-compact design allows the adapter to stay plugged into your device without blocking adjacent ports or adding bulk, reducing wear and tear on your original USB ports.
- 12-Month Warranty: Backed by a 12-month manufacturer warranty for peace of mind. Designed to meet strict quality control standards for reliable everyday performance.
That stoichiometry makes the theoretical oxygen amount proportional to charge, not simply to current or to the oxygen concentration displayed by an instrument. A concentration or volume becomes useful only after it has been converted to moles on a defined pressure, temperature, composition, flow, and time basis.
The core equations
- Charge:
Q = ∫ I(t) dt. For a genuinely constant current, this simplifies toQ = I × t. - Theoretical oxygen:
n(O2, theoretical) = Q/(4F). - Faradaic efficiency:
FE(O2) = 100 × n(O2, measured) / n(O2, theoretical).
Use amperes and seconds so charge is in coulombs. Keep the gas-law units consistent, use absolute pressure, and express temperature in kelvin. The measured and theoretical oxygen quantities must cover the same interval.
Step 1: Determine the charge passed
Constant-current electrolysis
For a stable galvanostatic experiment, multiply current by elapsed time. Convert milliamperes to amperes and minutes or hours to seconds before calculating:
Recommended Free Tools
Q (C) = I (A) × t (s)
Do not use the current value alone. A 10 mA experiment lasting 10 seconds and one lasting 10 minutes have very different theoretical oxygen yields.
Variable-current or potentiostatic electrolysis
When current changes with time, integrate the recorded current trace over the exact oxygen-measurement window:
Q = ∫t1t2 I(t) dt
In spreadsheet or analysis software, numerical integration can be performed by summing each interval’s average current multiplied by its duration. State whether the instrument reports signed current and use the anodic charge corresponding to the oxygen-producing reaction. Include or exclude startup, shutdown, and equilibration periods consistently with the gas data.
Rank #2
- 5-in-1 USB-C Hub: Experience comprehensive connectivity featuring a Power Delivery input, two USB-A 2.0 ports, a USB-A 3.0 port, and an HDMI port. (Note: The USB-C power delivery input port is only for connecting an external wall charger to power your laptop and cannot power peripheral devices.)
- 90W Pass-Through Charging: Achieve optimal charging with 90W pass-through power to your laptop, supported by a total input of 100W, with the hub reserving 10W for operational efficiency. (Note: Wall charger not included.)
- Quick Data Transfers: Accelerate your productivity with rapid data transfers using a high-speed 5Gbps USB 3.0 port and two 480Mbps USB 2.0 ports.
- 4K HDMI Display: Enhance your visual experience with a hub capable of delivering 4K resolution at 30Hz in both mirror and extend modes. Please note that this hub is compatible with MacBook (macOS 12 and newer), Windows 10 and 11, ChromeOS, and laptops equipped with DP Alt Mode and Power Delivery. Note: This device is not compatible with Linux.
- What You Get: Anker USB-C Hub (5-in-1, 4K HDMI), welcome guide, 18-month warranty, and our friendly customer service.
Step 2: Calculate the theoretical oxygen amount
Divide charge by four times the Faraday constant:
n(O2, theoretical) = Q/(4 × 96,485 C mol−1)
The factor of four is essential. Replacing it with one would overstate the predicted oxygen by a factor of four and make the resulting FE appear four times too small.
What’s actually slowing this PC down?
Pick the symptom - the matching free tool is one click away.
If you need a theoretical production rate at constant current, use:
dn(O2)/dt = I/(4F)
This rate is useful when comparing an oxygen flow from a carrier-gas system with the electrochemical prediction. It is still a molar rate; a sensor percentage by itself is not a rate.
Step 3: Convert the oxygen measurement to moles
Choose the conversion that matches how oxygen was measured. The three common routes are collected gas, an oxygen fraction in a flowing carrier gas, and calibrated gas chromatography.
Collected gas volume
For a measured oxygen volume, apply the ideal-gas law:
n(O2) = p(O2)V/(RT)
Use oxygen’s partial pressure, not automatically the total pressure. If the collection vessel contains essentially pure, dry oxygen, its oxygen partial pressure may be close to the measured absolute pressure. If the gas is mixed, multiply total pressure by the oxygen mole fraction. If collection occurs over water, subtract the water-vapor pressure at the measured temperature before calculating dry oxygen partial pressure.
Rank #3
- Sleek 7-in-1 USB-C Hub: Features an HDMI port, two USB-A 3.0 ports, and a USB-C data port, each providing 5Gbps transfer speeds. It also includes a USB-C PD input port for charging up to 100W and dual SD and TF card slots, all in a compact design.
- Flawless 4K@60Hz Video with HDMI: Delivers exceptional clarity and smoothness with its 4K@60Hz HDMI port, making it ideal for high-definition presentations and entertainment. (Note: Only the HDMI port supports video projection; the USB-C port is for data transfer only.)
- Double Up on Efficiency: The two USB-A 3.0 ports and a USB-C port support a fast 5Gbps data rate, significantly boosting your transfer speeds and improving productivity.
- Fast and Reliable 85W Charging: Offers high-capacity, speedy charging for laptops up to 85W, so you spend less time tethered to an outlet and more time being productive.
- What You Get: Anker USB-C Hub (7-in-1), welcome guide, 18-month warranty, and our friendly customer service.
- Measure the collected volume at the same temperature and pressure used in the calculation, or correct it to a stated reference condition.
- Use absolute pressure; gauge pressure is not suitable without conversion.
- Keep the volume and gas constant in compatible units. Liters can be used when the selected gas constant is expressed in pressure-liter units.
- Subtract a documented background or initial gas contribution when the vessel already contained oxygen.
Collection efficiency matters. Leaks, dissolved oxygen, bubbles that bypass the collector, and oxygen remaining in tubing or headspace can all make recovered gas differ from generated gas.
Oxygen fraction in a carrier-gas stream
A calibrated oxygen sensor reports a fraction or concentration, while a flow controller or flow meter supplies the total carrier-gas flow. Convert both to an oxygen molar flow. If y(O2) is the oxygen mole fraction and ṅtotal is the total molar flow, then:
ṅ(O2) = y(O2) × ṅtotal
For a volumetric flow, convert that flow to molar flow with the ideal-gas law using the flow measurement’s absolute pressure and kelvin temperature. The oxygen amount over an interval is the integrated oxygen molar flow:
Do these 3 things before closing this tab:
1Fix the driver behind crashes, sound loss and screen glitches2Repair Windows errors before they cause bigger problems3Scan for outdated or missing drivers - takes under a minuten(O2) = ∫ ṅ(O2, t) dt
An inert carrier such as argon supplies the transport flow but not the oxygen product. Confirm that the reported concentration basis and flow basis match: a wet oxygen fraction must not be multiplied by a dry-gas flow without correcting for water vapor. Published oxygen-microsensor work used an argon carrier, calibrated the sensor in situ, and waited for a stable oxygen concentration before calculating efficiency.
Account for residence time. Oxygen leaving the cell may be delayed by tubing and headspace, so align the sensor trace with the electrolysis time window after establishing the system’s response time. A stable reading is not necessarily reached immediately after current starts.
Online gas chromatography
Gas chromatography converts a detector response, such as peak area, into oxygen content through calibration standards. A defensible calculation has four parts:
Rank #4
- Dual Converters, Infinite Potential：Includes 2× USB C male to USB A female adapters and 2× USB A male to USB C female adapters. Perfect for a wide range of uses—tablets with Bluetooth keyboards, expand USB ports on macbook, and more. Two different converters for all your daily needs
- Next-Level 10Gbps & 3A Charging: No more slow 480Mbps, this usb to usb c adapter has a transfer speed of up to 10Gbps, allowing you to do more transferring in less time. This usb adapter fits both USB A and USB C charger, supporting up to 3A fast charging
- Upgraded Exquisite Craftsmanship: With an aluminum alloy housing and metal connector, the usbc to usb adapter is extremely durable and sturdy. Rigorously tested to withstand more than 10,000 times of plugging and unplugging, ensuring long-lasting performance
- Broad Compatible: The usb c to usb adapter widely supports all USB C/ USB A devices like laptops, tablets, cellphones, car chargers, and phone chargers. Such as compatible with MacBook Pro/Air 2023/2022, Thunderbolt 4/3 Devices,Apple MagSafe Watch 9/8/7/SE/Ultra, iPad Pro 2022/2021, Samsung Galaxy S23/S20/S10, and iPhone 17/16/15 Pro. Plug and play
- Please Note: To reach 10Gbps speed, keep the cable under 3.3 ft. For USB A Male to USB C adapters, try flipping the USB C connector. USB C Male to USB A adapters support bidirectional 10Gbps transfer within 3.3 ft
- Run oxygen calibration gas concentrations spanning the expected sample range.
- Fit the detector response to oxygen amount or concentration and verify the calibration during the experiment.
- Use the known carrier flow and sample interval to convert each calibrated oxygen result into moles.
- Compare the oxygen accumulated in each interval with the charge passed during that same interval.
One reported method used a helium carrier, constant flow, and online oxygen calibration. It excluded the initial injection used for headspace equilibration from the average. That treatment illustrates why startup injections and headspace replacement must be identified rather than silently counted as product.
The Tool Desk
Outbyte PC Repair FREERepair Windows errors before they cause bigger problemsFix Now →Outbyte Driver Updater FREEScan for outdated or missing drivers - takes under a minuteDriver Scan →Worked calculation
Suppose a cell runs at a constant 10.0 mA for 30.0 minutes and the oxygen measurement gives 0.0400 mmol O2 over exactly those 30.0 minutes.
- Convert current and time, then calculate charge:
Q = 0.0100 A × 1,800 s = 18.0 C. - Calculate theoretical oxygen:
ntheoretical = 18.0/(4 × 96,485) mol = 4.66 × 10−5 mol = 0.0466 mmol. - Form the ratio:
FE = 100 × 0.0400/0.0466 = 85.8%.
The 85.8% value is an illustrative calculation, not a performance result for a particular catalyst or cell.
Choose a measurement route
| Route | Measured output | Time resolution | Key setup requirements | Typical failure modes | Selectivity considerations |
|---|---|---|---|---|---|
| Collected gas | Total or composition-resolved gas volume | Usually batch or end-point | Known volume, absolute pressure, temperature, gas composition, and leak-tight collection | Leaks, incomplete recovery, bubbles escaping collection, water vapor, and unaccounted headspace oxygen | Requires a way to distinguish oxygen from other gases if the collector contains a mixture |
| Carrier-gas oxygen sensor | Oxygen fraction or concentration in a flowing stream | Continuous after sensor and cell equilibration | Calibrated sensor, known carrier flow, controlled pressure and temperature, suitable headspace and tubing | Calibration drift, unstable concentration, residence-time mismatch, wet/dry basis mismatch, and background oxygen | Directly reports oxygen only when calibrated for oxygen and the carrier does not contribute oxygen |
| Online gas chromatography | Calibrated oxygen signal for each injection | Periodic injections | Calibration gas, carrier gas, constant or measured flow, sampling schedule, and headspace-equilibration treatment | Calibration error, missed intervals, sampling delay, carryover, and counting an equilibration injection as product | Can separate oxygen from other gases when the chromatographic method resolves them |
A rotating ring-disk electrode can provide an electrochemical detection route in suitable configurations, but collection efficiency, ring collection, and gas-bubble behavior must be evaluated for that geometry. It is not a substitute for checking the transport and collection assumptions.
Synchronize gas data and charge data
Most serious FE errors are interval errors rather than arithmetic errors. Use a shared clock or a clearly documented time offset for the electrochemical workstation, sensor, flow meter, and chromatograph.
- Define the interval: record the exact start and end times for the oxygen quantity to be used.
- Record current continuously: retain the raw current trace instead of only a set-point value.
- Measure flow, pressure, and temperature: record whether each value is wet or dry and where in the gas path it was measured.
- Establish the gas delay: determine how long oxygen takes to travel from the cell to a sensor or sampling loop.
- Handle startup explicitly: allow headspace and sensor equilibration when required, or quantify and correct the transient.
- Calibrate before quantifying: use a volume calibration for collection, a sensor calibration for concentration, or certified gas standards for GC.
- Convert each interval: calculate oxygen moles for the same interval used for charge integration.
- Report assumptions: state pressure basis, temperature, vapor correction, oxygen fraction basis, background subtraction, and any excluded startup period.
Common mistakes and how to fix them
| Observed problem | Why it happens | Correction |
|---|---|---|
| Using current as though it were charge | Current is a rate; oxygen prediction depends on accumulated charge. | Multiply constant current by seconds or integrate the measured current trace. |
| Efficiency about four times too low | The four-electron OER stoichiometry was omitted or replaced with one electron. | Use Q/(4F) for theoretical O2. |
| Concentration treated as an oxygen amount | A percentage or fraction contains no information about total gas flow or sampled volume. | Multiply fraction by total molar flow and integrate, or combine sampled concentration with a known sample volume. |
| Gas-law result is inconsistent | Pressure, volume, gas constant, and temperature use incompatible units, or pressure is gauge pressure. | Use one unit system, absolute pressure, and kelvin temperature. |
| Collected oxygen appears too high | Water vapor, initial headspace oxygen, atmospheric leaks, or an incorrect gas fraction has been counted as product. | Apply vapor-pressure and composition corrections, subtract background, and inspect seals and tubing. |
| Sensor result starts high or drifts | The sensor or headspace has not equilibrated, or calibration has shifted. | Allow stabilization, document the response delay, and verify calibration with a known gas. |
| GC average is unexpectedly high or low | An equilibration injection, sampling delay, carryover, or a bad calibration point was included. | Define which injections represent steady operation and calculate oxygen interval by interval. |
| FE is greater than 100% | The measured oxygen-to-charge ratio is inflated by calibration, background, pressure, vapor, leakage, integration, or time-window errors. | Audit those terms before interpreting the value as chemistry; apparent FE above 100% is a diagnostic signal, not evidence of extra Faradaic oxygen. |
Why current in an OER region is not automatically oxygen current
Total anodic current can include catalyst or support oxidation, oxidation of dissolved species, and other competing reactions. The EcoMat recommended-practice review states: “The current density observed in the OER region comprises the cumulative currents of all redox reactions transpiring at that potential.” Therefore, a current measured at an OER-like potential is not by itself proof that every electron produced O2.
Best Value
- 5-in-1 Connectivity: Equipped with a 4K HDMI port, a 5 Gbps USB-C data port, two 5 Gbps USB-A ports, and a USB C 100W PD-IN port. Note: The USB C 100W PD-IN port supports only charging and does not support data transfer devices such as headphones or speakers.
- Powerful Pass-Through Charging: Supports up to 85W pass-through charging so you can power up your laptop while you use the hub. Note: Pass-through charging requires a charger (not included). Note: To achieve full power for iPad, we recommend using a 45W wall charger.
- Transfer Files in Seconds: Move files to and from your laptop at speeds of up to 5 Gbps via the USB-C and USB-A data ports. Note: The USB C 5Gbps Data port does not support video output.
- HD Display: Connect to the HDMI port to stream or mirror content to an external monitor in resolutions of up to 4K@30Hz. Note: The USB-C ports do not support video output.
- What You Get: Anker 332 USB-C Hub (5-in-1), welcome guide, our worry-free 18-month warranty, and friendly customer service.
This distinction explains why oxygen FE can be below 100% even when the current trace is stable. It also means that a catalyst comparison based only on current density can miss selectivity losses. Gas analysis, charge accounting, and controls for background oxygen should be interpreted together.
How to interpret a result
Values below 100%
A value below 100% can reflect genuine competing oxidation or incomplete oxygen recovery. Before assigning it to reaction selectivity, check collection efficiency, transport delay, oxygen dissolved in the electrolyte, sensor or GC calibration, and whether the oxygen interval matches the integrated charge.
Values above 100%
Because FE is defined as measured oxygen divided by theoretical oxygen, a value above 100% means one or more terms in that ratio is wrong or incomplete. Check background and headspace oxygen, water-vapor correction, oxygen fraction, absolute pressure, flow calibration, current integration, leaks that admit air, and mismatched time windows.
Free tools Windows power users keep installed
One-click scans. No signup required.
Potential-dependent behavior
There is no universal oxygen-FE benchmark that applies to every electrolyte, electrode, cell, and gas-analysis method. In one 2022 acidic-water-oxidation study, oxygen efficiency was reported near 100% above 1.40 VRHE and around 20% at 1.33 VRHE. Those values belong to that study’s experimental system and should not be presented as expected results for all catalysts or potentials.
Minimum reporting checklist
- Electrolysis mode, current or potential program, and the exact charge-integration interval.
- Current trace or the constant-current value and elapsed seconds.
- Faraday constant and the four-electron OER stoichiometry used.
- Oxygen measurement method and calibration procedure.
- Gas volume, flow, pressure, temperature, oxygen fraction, and wet/dry basis.
- Water-vapor, background, headspace, and atmospheric-oxygen corrections.
- Sensor or GC response delay and treatment of startup or equilibration data.
- Whether the reported oxygen amount is total, interval-integrated, or an average rate.
- Any evidence of competing anodic reactions or incomplete gas recovery.
With these details, another reader can reproduce the conversion from instrument output to oxygen moles, independently calculate Q/(4F), and determine whether the reported Faradaic efficiency reflects oxygen selectivity, measurement recovery, or both.
Quick Recap
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
