Pseudo-first-order rate constant calculator
A second-order constant of 0.05 M⁻¹ s⁻¹ with a 0.5 M excess gives an observed constant k′ of 0.025 s⁻¹, simply k times the excess concentration. Use it to check a measured first-order decay against published k values. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- K
- 0.05
- Concentration
- 0.5
- K pseudo
- 0.025
Many bimolecular reactions are studied under pseudo-first-order conditions so that the observed decay of the limiting reactant looks first-order while the true elementary step remains second-order. The shortcut is simple but easy to mis-handle by hand: multiply the second-order rate constant k by the nearly constant excess concentration to obtain the observed constant k prime.
What pseudo-first-order kinetics means and which numbers to send
Start from a second-order rate law rate equals k times the product of two reactant concentrations. When one reactant is present in large excess, its concentration barely changes while the other is consumed, so you can fold that nearly constant concentration into the rate constant. The observed first-order constant is then k prime equals k times the excess concentration.
Send the required field k as a finite non-negative number in concentration to the minus one times time to the minus one units, for example molar inverse seconds, and send concentration as the excess reactant level in matching concentration units. Negative concentration is invalid input because a physical concentration cannot be negative; the engine fails fast with a readable message rather than inventing a signed kinetic constant. Zero excess is mathematically allowed and yields k prime equals zero, but experimentally it means you are not actually running pseudo-first-order conditions.
What you can do with it
Homework and lab report checks
Students convert a literature second-order k and a stated excess concentration into k', then compare against their integrated first-order fit of absorbance or concentration–time data.
Stopped-flow and excess-reagent experiments
Instrument scripts compute the expected pseudo-first-order constant from calibrated k2 and the large reagent stock before a kinetic run, flagging negative concentration typos early.
FAQ
Which units should I use for k and concentration?
Keep them consistent. If k is in M⁻¹ s⁻¹, use concentration in M so that k' is in s⁻¹. The calculator multiplies the numbers as given and does not convert units.
Is the pseudo-first-order rate constant calculator free?
The browser tool runs free on your device.
How is this different from a first-order half-life calculator?
This tool builds the observed first-order constant k' from second-order k and excess concentration. A half-life calculator starts from an already first-order k and returns t½ = ln(2)/k; they answer different search and lab intents.
When can a second-order reaction be treated as pseudo-first-order?
When one reactant is present in large excess. Its concentration barely changes while the other is consumed, so the decay of the limiting reactant looks first-order even though the real step is still second-order.
What does an excess concentration of zero mean?
The calculator accepts it and returns a k′ of zero, which is mathematically sound. In practice it means you are not running pseudo-first-order conditions at all, because nothing is present in excess.
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/pseudo-first-order \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k":0.05,"concentration":0.5}'const res = await fetch("https://api.kit.forhosting.com/chem/pseudo-first-order", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k": 0.05,
"concentration": 0.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/pseudo-first-order",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k": 0.05,
"concentration": 0.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/pseudo-first-order", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k":0.05,"concentration":0.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k":0.05,"concentration":0.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/pseudo-first-order", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"k": 0.05,
"concentration": 0.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.pseudo_first_order",
"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.
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
This capability does that multiplication deterministically, rejects negative concentrations with a clear invalid input error, and returns structured JSON that lab notebooks, kinetics tutorials, and automated homework checkers can pin in tests. Students preparing SN2 or enzyme-kinetics demos, process chemists sizing continuous stirred tanks, and data pipelines that normalize literature k2 values into observed first-order constants all get the same contract whether they use the free in-browser tool or the prepaid API at $0.002 per successful item.
What pseudo-first-order kinetics means and which numbers to send
Aliases such as rate_constant, k2, k_second for the constant and excess, excess_concentration, or B for the concentration are accepted so scripts written against different naming conventions still work. The path is pure arithmetic with no network, no random seed, and no wall clock, so identical inputs always produce identical JSON.
Reading k_pseudo, units, formula, and validation errors
Prefer consistent unit systems end to end; the calculator does not convert millimolar to molar or minutes to seconds, because silent unit conversion would hide the most common source of order-of-magnitude errors in kinetics homework and lab notebooks. On success the response echoes k and concentration, returns k_pseudo as the rounded product k times concentration, and labels the method pseudo_first_order with the formula string k prime equals k times open bracket excess close bracket. The units_note field reminds you that k_pseudo has reciprocal-time units: if k is in molar inverse seconds and concentration is in molar, k prime is in reciprocal seconds, ready for first-order half-life or integrated rate-law tools. Use k_pseudo alone when a pipeline only needs the observed constant; use the echoed inputs when a report must show both the microscopic k2 and the experimental excess level side by side. Missing k, missing concentration, non-finite numbers, negative k, and negative concentration all fail with invalid_input and are not charged after the engine rejects the request.
API usage, pricing, lab workflows, and practical limits
Call the free in-browser pseudo-first-order rate constant calculator for lecture demos, pre-lab checks, and quick mental-math verification without installing a symbolic algebra package. Send a JSON body with the required second-order rate constant k and the excess reactant concentration. Pair this endpoint with a first-order half-life calculator when the next step is t half from k prime, or with a rate-law evaluator when you still need the full power-form rate at a given composition. Authors shipping SDKs can map k_pseudo directly into decay models, stopped-flow analyses, and teaching dashboards that contrast second-order elementary constants with the observed first-order constants students actually fit from absorbance traces.
Integration use cases
Teaching and curriculum generators
Lesson builders produce worked pseudo-first-order examples with structured JSON for auto-graded drills without reimplementing unit-aware multiplication in every language.
Technical questions
How do I compute a pseudo-first-order rate constant?
Send JSON with k set to the second-order rate constant and concentration set to the large excess reactant concentration. The response field k_pseudo equals k times concentration.
What happens if concentration is negative?
The request fails with invalid_input. Negative excess reactant concentration is not allowed; the error message states that negative concentration is rejected and the call is not charged.