Zero-order concentration calculator
Starting at 1 mol/L with k of 0.1 mol/L per second, half the reactant is left after 5 seconds. Enter the initial concentration, the zero-order rate constant and the elapsed time to see how much remains and whether it has run out. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Initial concentration
- 1
- K
- 0.1
- Time
- 5
- Concentration
- 0.5
- Remaining fraction
- 0.5
- Product k t
- 0.5
- Amount consumed
- 0.5
Zero-order chemical kinetics with rate equal to a constant k independent of reactant concentration appears in enzyme-saturated catalytic regimes, certain catalytic surface reactions, and controlled-release or photochemical systems taught in general and physical chemistry. The integrated form links initial concentration, the observed zero-order rate constant, and elapsed time to the amount of reactant that remains, so students and process chemists can answer how much is left without re-deriving the linear decay equation every time.
What zero-order remaining concentration means and how to choose inputs
For a reaction that follows rate equals k with no concentration dependence, the differential equation integrates to concentration of A at time t equals the initial concentration minus k times t. That identity is the heart of this calculator: send a strictly positive initial concentration in the same units you use for the rate law, a non-negative zero-order rate constant in concentration per time, and a non-negative elapsed time in the matching time unit.
If k is in moles per liter per second and initial concentration is in moles per liter, time must be in seconds and the returned concentration is again in moles per liter. The engine does not convert units for you, which keeps the contract honest and free of silent scale mistakes. Negative time is invalid input because elapsed reaction time cannot run backward under this model; zero time correctly returns the initial concentration unchanged.
Zero rate constant freezes the concentration at the initial value, which is mathematically consistent even if it is rarely the physical case of interest. When k times t exceeds the initial concentration, the reactant is fully depleted and concentration is reported as zero rather than a negative unphysical value. Unlike first-order kinetics, the remaining amount for a zero-order process falls linearly with time, so half-life grows with larger starting concentration.
What you can do with it
Lab notebooks and batch planning
Process chemists paste fitted zero-order k and planned reaction time to estimate how much reactant remains without re-deriving the linear integrated rate law in each spreadsheet.
FAQ
How do I calculate remaining concentration for a zero-order reaction?
The response concentration is [A]_t = max(0, [A]_0 − k t).
What happens if time is negative?
Elapsed reaction time must be non-negative; negative time is rejected and not charged.
What units should I use for k and concentration?
Use any consistent set: if [A]_0 is in mol/L and time is in s, k must be in mol·L⁻¹·s⁻¹. Concentration units carry through unchanged. The calculator does not convert units automatically.
Is the zero-order concentration calculator free?
The browser tool runs free on your device.
What happens when k times t is larger than the starting concentration?
The reactant is fully used up, so the remaining concentration is shown as zero instead of a negative number. The result also flags that the reaction has reached its end.
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/zero-order-concentration \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"initial_concentration":1,"k":0.1,"time":5}'const res = await fetch("https://api.kit.forhosting.com/chem/zero-order-concentration", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"initial_concentration": 1,
"k": 0.1,
"time": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/zero-order-concentration",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"initial_concentration": 1,
"k": 0.1,
"time": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/zero-order-concentration", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"initial_concentration":1,"k":0.1,"time":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"initial_concentration":1,"k":0.1,"time":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/zero-order-concentration", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"initial_concentration": 1,
"k": 0.1,
"time": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.zero_order_concentration",
"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 applies the textbook relation concentration of A at time t equals initial concentration minus k times t, floors at zero when the reactant is fully depleted, rejects negative time with a clear invalid input error, and returns structured JSON that homework checkers, lab notebooks, and lightweight process tools can pin in automated tests.
What zero-order remaining concentration means and how to choose inputs
Missing fields, non-finite numbers, empty strings, non-positive initial concentration, and negative k all fail with invalid_input. Identical inputs always produce identical JSON because the path is pure arithmetic with no network, no random seed, and no wall clock.
Reading the response fields and common classroom workflows
Typical classroom drills include verifying that concentration falls linearly until it hits zero, computing remaining reactant after a given batch time, confirming that half the reactant remains when t equals half-life equal to initial concentration over two k, and contrasting this concentration-dependent half-life with first-order laws that keep a constant fractional half-life. The depleted boolean flags full consumption so UI layers can show a clear end-of-reaction state without re-checking inequalities. The formula field always restates concentration of A at t equals initial minus k times t, and method is always zero_order_integrated_rate_law for downstream branching. Pair this endpoint with zero-order half-life tools when the next question is t half, with first-order or second-order concentration calculators when you are comparing reaction orders, or with rate-law calculators when you still need an instantaneous rate. Validation failures never consume balance after the engine rejects the request, so exploratory calls with negative time or missing k stay free to fix.
API usage, pricing, lab pipelines, and practical limits
Call the free in-browser zero-order concentration calculator for lecture demos, homework checks, and quick mental verification without installing a kinetics package. Keep magnitudes within ordinary floating-point ranges; extremely large products of k and time drive remaining concentration to the zero floor in a controlled way, while tiny products leave concentration near the start. Send a JSON body with the required fields initial_concentration, k, and time; aliases a0, A0, c0, rate_constant, t, elapsed, and related names are accepted so pipelines can reuse field names from kinetic fits and spreadsheets. Authors shipping SDKs can map concentration and remaining_fraction into UI tables next to concentration–time plots so students see the same linear identity written in textbooks. This product does not estimate k from multi-point data, does not report half-life alone, does not solve for time given a target final concentration, and does not apply Arrhenius temperature corrections—those are different search intents served by sibling capabilities. When you already hold A zero, k, and t and only need remaining zero-order concentration, this endpoint is the direct, charge-transparent path from inputs to remaining amount.
Integration use cases
Homework and kinetics drills
Students compute remaining [A] after a stated batch time for rate = k, verify linear decay until depletion, and get a clear invalid_input error when they submit negative time.
Teaching platforms and CI fixtures
Tutoring apps and automated graders call a stable prepaid endpoint so worked examples and unit tests share one deterministic contract for zero-order remaining concentration.
Technical questions
How is this different from first-order remaining concentration?
Zero-order uses [A]_t = [A]_0 − k t (linear decay, floors at zero). First-order uses [A]_t = [A]_0 · e^(−k t) and the remaining fraction depends only on k and t, never hitting a hard zero in finite time.