Integrated rate law order checker
Decide the order of a reaction from your time and concentration readings: when ln[A] against time fits a perfect line with an R² of 1 and the plain concentration plot reaches only 0.859221709465, the reaction is first order. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Times
- 0, 10, 20, 30
- Concentrations
- 1, 0.3678794412, 0.1353352832, 0.0497870684
- N
- 4
- Order
- 1
- Order label
- first
- Best plot
- ln[A] vs t
An integrated rate law order checker turns a table of times and reactant concentrations into a clear zero-, first-, or second-order call without hand-drawing three graphs. You send parallel lists of t and [A]; the tool builds the classic integrated plots—concentration versus time, natural log of concentration versus time, and reciprocal concentration versus time—fits each with ordinary least squares, and ranks them by coefficient of determination R squared. The transform with the highest R squared is reported as the reaction order, together with slope, intercept, per-order fit diagnostics, and step strings you can paste into a lab notebook.
What integrated rate laws say about reaction order
Chemical kinetics classifies elementary and many observed processes by how the rate depends on concentration. For a single reactant A with rate equal to k times [A] to the power n, the differential rate law integrates to three classroom-standard linear forms when n is zero, one, or two. In the teaching lab you never assume the order; you collect (t, [A]) pairs, prepare all three plots, and ask which one is most linear.
That is exactly the decision this capability automates: ordinary least-squares slope, intercept, and R squared for each transform, then selection of the maximum R squared as the reported order. The method assumes constant volume, a single concentration series for one reactant (or excess conditions that collapse the rate law to that form), and data free of mechanism changes over the window you supply.
It does not replace residual analysis or residual plots for publication-grade work, but it gives the same first-pass order call students learn in general and physical chemistry when they compare which integrated graph is straightest.
Practical tips, limits, and related searches
Collect at least three well-spaced times spanning a meaningful fraction of the reaction; two points always define a perfect line on every transform and cannot discriminate order, which is why the gate rejects short series. Prefer concentrations that stay clearly positive so first-order and second-order candidates both compete; if any concentration is zero or negative, only the transforms that remain defined are ranked. Sort order is applied internally by increasing time so you can paste lab tables that are slightly out of order.
When two orders produce identical R squared within floating noise, the lower order wins the tie so the response stays deterministic. Round-trip checks are easy: generate exact zero-, first-, or second-order synthetic series from the closed integrated laws, confirm order and R squared near one, then flip a deliberate short series to assert the three-point error message.
What you can do with it
Teaching-lab kinetics order determination
Students paste spectrophotometer or titration (t, [A]) tables and see which integrated plot is most linear before writing the order in their report.
Homework checks for integrated rate laws
Compare hand-drawn [A], ln[A], and 1/[A] versus time conclusions against a deterministic order, R², and step list before submitting.
FAQ
How does the integrated rate law order checker work?
It fits [A] vs t (zero order), ln[A] vs t (first order), and 1/[A] vs t (second order) with ordinary least squares, then reports the order whose plot has the highest R².
Why do I need at least three data points?
Two points always lie on a perfect line for every transform, so they cannot discriminate order.
What if my concentrations include zero?
First-order needs positive [A] for ln[A], and second-order needs non-zero [A] for 1/[A]. Those transforms are skipped with a reason; zero-order may still win if [A] vs t is defined.
Does this return the rate constant k?
It returns slope and intercept for the winning plot. For zero and first order, k is typically the negative of the slope; for second order, k is the slope of 1/[A] vs t. Interpret units carefully.
Is the integrated rate law order checker free?
The browser tool is free and runs locally.
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/integrated-rate-order \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"times":[0,10,20,30],"concentrations":[1,0.367879441171,0.135335283237,0.049787068368]}'const res = await fetch("https://api.kit.forhosting.com/chem/integrated-rate-order", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"times": [
0,
10,
20,
30
],
"concentrations": [
1,
0.367879441171,
0.135335283237,
0.049787068368
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/integrated-rate-order",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"times": [
0,
10,
20,
30
],
"concentrations": [
1,
0.367879441171,
0.135335283237,
0.049787068368
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/integrated-rate-order", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"times":[0,10,20,30],"concentrations":[1,0.367879441171,0.135335283237,0.049787068368]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"times":[0,10,20,30],"concentrations":[1,0.367879441171,0.135335283237,0.049787068368]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/integrated-rate-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
{
"times": [
0,
10,
20,
30
],
"concentrations": [
1,
0.367879441171,
0.135335283237,
0.049787068368
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.integrated_rate_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.
Limits
max_abs | 1000000000000 |
max_points | 1000 |
min_points | 3 |
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
Fewer than three points is rejected with invalid_input because a line needs enough samples to be meaningful.
What integrated rate laws say about reaction order
Zero-order kinetics means rate is independent of [A], so concentration falls as a straight line against time: [A] equals [A] zero minus k t, and a plot of [A] versus t is linear with slope equal to minus k. First-order kinetics integrates to the natural logarithm of concentration linear in time: ln[A] equals ln[A] zero minus k t, so ln[A] versus t is the diagnostic line and half-life is concentration-independent. Second-order kinetics with rate equal to k [A] squared integrates to the reciprocal of concentration linear in time: one over [A] equals one over [A] zero plus k t, so 1/[A] versus t is linear and half-life grows as concentration falls.
How to call the API and what comes back
Each array must contain at least three finite numbers within the published absolute limit of one trillion, at most one thousand points, and both arrays must share the same length. Times may be in any consistent unit (seconds, minutes, hours); concentrations must share one concentration unit (for example mol per liter). For first-order and second-order transforms every concentration must be strictly positive and non-zero respectively, because the natural logarithm and the reciprocal are otherwise undefined; zero-order fitting still uses raw [A] and remains available when logs fail. Send a JSON body with two required parallel arrays: times (aliases t, time, x, time_values) and concentrations (aliases concentration, c, conc, y, values). On success the response echoes n, the time-sorted times and concentrations arrays after fixed twelve-decimal rounding, order as the integer 0, 1, or 2, order_label as zero, first, or second, best_plot as the winning axis label, r_squared, slope, and intercept for that winning fit, a fits object with zero_order, first_order, and second_order diagnostics (or an unavailable reason when a transform could not run), plus message and steps. Failed validation—missing fields, length mismatch, fewer than three points, all times identical, non-finite values, or out-of-range magnitudes—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
Absolute values of times and concentrations must stay within one trillion so products and sums in ordinary least squares remain finite in IEEE double precision. This landing targets people searching for an integrated rate law order checker, zero first second order plot linear, or concentration time kinetics online; it is not a full nonlinear rate-law fitter, not a half-life calculator by itself, and not a multi-reactant mechanism solver. Prefer chem.reaction_rate when you only need average rate from a single concentration change over one interval, and chem.second_order_half_life when you already know the process is second order and only need t half from k and [A] zero. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send two-point series.
Integration use cases
Unit tests for kinetics analysis code
Generate synthetic zero-, first-, and second-order series plus deliberate short inputs to lock expected order labels and invalid_input paths.