Electrode potential vs pH calculator
Find the reversible potential of a hydrogen electrode from the solution's pH and the hydrogen pressure; at pH 7 and 1 bar it sits at −0.414 V. The Nernst equation at 25 °C is applied and every step is shown. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Ph
- 7
- Pressure
- 1
- PH
- 7
- P h2
- 1
- Partial pressure
- 1
- Temperature k
- 298.15
An electrode potential versus pH calculator turns the acidity of a solution and the partial pressure of hydrogen gas into the reversible potential of the hydrogen half-cell. Enter pH and P(H2); the tool applies the Nernst equation at twenty-five degrees Celsius with E-zero equal to zero by definition for the standard hydrogen electrode, returning E in volts, the decade slope factors, a readable equation string, and step-by-step substitution. Corrosion labs, Pourbaix sketches, battery teaching, and coding kata expected values all need that same deterministic E(pH, P) check without opening a spreadsheet of constants.
What the hydrogen electrode potential means versus pH
The standard hydrogen electrode defines the zero of the electrochemical potential scale: the half-reaction two H-plus plus two electrons in equilibrium with dihydrogen gas has E-zero equal to zero volts under unit activity of H-plus and unit pressure of H2. Away from those standard conditions the reversible potential shifts with both the hydrogen-ion activity and the hydrogen partial pressure.
The decade slope is RT times the natural log of ten divided by the Faraday constant, about fifty-nine millivolts per pH unit at room temperature, which is why many textbooks quote E approximately equal to minus zero point zero five nine times pH when P is one bar.
Teachers and automated graders care about the non-positive pressure rejection as much as the numeric answer: a student who plugs P equals zero into a log term has left the domain of the model, and a silent clamp to a tiny epsilon would hide that mistake. The check path recomputes the same fixed R, F, and T used for published fields, so a successful response always ships with steps you can assert in tests or lab notebooks.
Practical tips, limits, and related searches
Keep pH and pressure inside the published absolute range so the log term and multiplications cannot overflow into a non-finite potential that the solver must reject. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. Use bar or atmosphere for P_H2 interchangeably in the ideal forms taught in most general chemistry courses—the numerical Nernst expression is the same when both are treated as the dimensionless pressure ratio relative to one bar.
Prefer this capability when you already have pH and P_H2 and only need the hydrogen half-cell potential; if your source is a word problem, extract those two quantities first. Round-trip checks are easy: recompute minus the decade slope times pH minus half that slope times log ten of pressure by hand and confirm it equals the published potential within the same twelve-decimal rounding.
What you can do with it
Homework checks for SHE Nernst problems
Students enter pH and hydrogen pressure from textbook half-cell questions and compare hand-written E and slope terms against a deterministic result before submitting.
Corrosion and Pourbaix sketch prep
Labs map the hydrogen line E versus pH at a chosen P_H2 before drawing stability domains, using the same fixed twenty-five degree Celsius constants every run.
FAQ
What equation does this calculator use?
The Nernst equation for the hydrogen half-cell at 25 °C with E° = 0 V: E = −(RT ln(10)/F)·pH − (RT ln(10)/(2F))·log10(P_H2).
Why is E zero when pH is zero and P is one?
That is the standard hydrogen electrode definition: unit H+ activity (pH 0) and unit H2 pressure give E = E° = 0 V by convention.
Can I change the temperature?
Not in this capability. Temperature is fixed at 298.15 K so goldens and browser results stay identical; use a variable-T Nernst tool if you need other temperatures.
Is the electrode potential vs pH calculator free?
The browser tool is free and runs locally.
What happens if the hydrogen pressure is zero?
The calculation is refused with a clear message, because the logarithm of zero is undefined. A zero pressure means the inputs have left the model, and quietly swapping it for a tiny number would only hide the mistake.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/chem/electrode-potential-ph \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"ph":7,"pressure":1}'const res = await fetch("https://api.kit.forhosting.com/chem/electrode-potential-ph", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"ph": 7,
"pressure": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/electrode-potential-ph",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"ph": 7,
"pressure": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/electrode-potential-ph", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"ph":7,"pressure":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"ph":7,"pressure":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/electrode-potential-ph", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"ph": 7,
"pressure": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.electrode_potential_ph",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
When pressure is zero or negative the logarithm is undefined, so the API returns a clear invalid_input error instead of inventing a potential.
What the hydrogen electrode potential means versus pH
Writing the Nernst equation at fixed temperature twenty-five degrees Celsius and converting activity of H-plus into pH yields a linear dependence on pH plus a logarithmic correction for pressure: E equals minus the decade slope times pH minus half that slope times the base-ten log of P of H2.
How to call the API and what comes back
Pressure must be strictly positive; values at or below one times ten to the minus fifteen are treated as non-positive and rejected. Send a JSON body with two required finite numbers: ph (aliases pH, p_h, and acidity) and pressure (aliases p_h2, P_H2, partial_pressure, pH2, and hydrogen_pressure). Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded ph and pressure fields under several common names, sets temperature_k to two hundred ninety-eight point one five, exposes the fixed gas constant and Faraday constant used, publishes nernst_slope as the full RT ln ten over F decade factor in volts, sets potential, e, and e_volts to the same rounded electrode potential, formula to the Nernst string with E-zero equal to zero, equation to a filled substitution line ending in volts, message to a short English summary, and steps to an ordered array of calculation lines. Failed validation—missing fields, non-finite numbers, values outside absolute limits, non-positive pressure, or a non-finite potential—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
When teaching, pair examples: pH seven with one bar hydrogen yields a potential near minus zero point four one four volts; pH zero with one bar recovers E near zero as expected for the SHE reference; and a zero or negative pressure demonstrates the hard invalid_input path. This landing targets people searching for an electrode potential versus pH calculator, hydrogen electrode Nernst tool, or SHE potential online; it is not a full multi-species Pourbaix generator, not a temperature-variable Nernst solver for arbitrary redox couples, and not a battery pack OCV model. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set pressure to zero.
Integration use cases
Unit tests for electrochemistry code
Generate known-good E(pH, P) cases plus deliberate non-positive pressure rejections for coding kata expected values and continuous-integration fixtures.
Technical questions
What happens when pressure is zero or negative?
log10(P_H2) is undefined for non-positive pressure. This tool returns invalid_input instead of inventing a potential.