Relative vapor pressure lowering calculator
Pure water at 23.8 torr and a solution at 20.23 torr give a lowering of 3.57 torr, a relative lowering of 0.15 or 15 %. Enter the two vapor pressures in any shared unit to get the absolute, relative and percent forms. Free in your browser.
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Worked example
- Pure vapor pressure
- 23.8
- Solution vapor pressure
- 20.23
- Vapor pressure lowering
- 3.57
- Relative vapor pressure lowering
- 0.15
- Relative vapor pressure lowering percent
- 15
Relative vapor-pressure lowering is the classic colligative ratio that compares how much a solution’s vapor pressure drops against the pure solvent at the same temperature. The definition is simple and unit-free: relative lowering equals Delta P over P degree, which expands to (P degree minus P) divided by P degree, where P degree is the pure-solvent vapor pressure and P is the solution vapor pressure. For an ideal solution of a non-volatile solute, Raoult’s law makes this ratio equal to the solute mole fraction, so the same number bridges manometer readings, mole-fraction homework, and first-pass process checks. Students use it when textbooks ask for relative lowering from tabulated pure and mixture pressures; lab instructors compare experimental Delta P to the ideal prediction; engineers screen how dilute non-volatile loads reduce solvent vapor pressure before opening a full thermo package. This calculator accepts pure and solution vapor pressures in any consistent unit, returns absolute lowering, dimensionless relative lowering, percent form, unit labels, and the formula string for audit, and rejects a pure vapor pressure of zero so division by P degree never becomes a silent infinity.
How relative vapor-pressure lowering is defined
Start from two pressures measured or tabulated at the same temperature: the pure-solvent vapor pressure P degree and the solution vapor pressure P. Absolute vapor-pressure lowering is the difference Delta P equals P degree minus P, which still carries the original pressure unit such as torr, millimeters of mercury, kilopascals, bar, or atmospheres. Relative vapor-pressure lowering removes that unit by dividing the difference by the pure value: (P degree minus P) divided by P degree.
The result is dimensionless and, for many ideal non-volatile-solute problems, equals the solute mole fraction x solute under Raoult’s law, because P equals x solvent times P degree implies (P degree minus P) over P degree equals one minus x solvent. That identity is why textbooks often ask for relative lowering even when the experimental table only lists pressures. Negative pressures are rejected as non-physical.
Solution vapor pressure may equal P degree (relative lowering zero, pure solvent) or fall below it (positive lowering); if a volatile solute raises total pressure above P degree the ratio can be negative, which the engine still reports honestly so you can catch bad data or non-ideal elevation cases. The capability does not look up Antoine pure pressures from temperature, convert between torr and kilopascals, compute boiling-point elevation, or solve multi-component Raoult sums; those remain separate search intents with their own landings.
Where relative vapor-pressure lowering calculators show up in real work
Secondary-school and introductory university chemistry courses assign colligative-property drills that start from two vapor pressures and ask for relative lowering or the implied solute mole fraction; a single trusted oracle speeds grading and demo setup without hand-waving floating-point noise. Laboratory courses measure solution vapor pressure with manometers or dynamic methods and compare experimental relative lowering to the ideal Raoult prediction, so students need the same closed form their report cites.
Process and formulation engineers estimate how much a non-volatile additive reduces solvent vapor pressure when designing drying, distillation, or emission-control steps, and the dimensionless ratio is convenient for comparing solvents that report pressures in different absolute units. Environmental and occupational-hygiene workflows convert liquid composition assumptions into expected relative lowering as a first-order screen before detailed activity models.
If you later need Raoult’s law vapor pressure from mole fraction, multi-component Raoult sums, Antoine pure vapor pressures from temperature, or boiling-point elevation, treat those as separate search intents and landings rather than overloading this relative vapor pressure lowering calculator page.
What you can do with it
Homework and exam answer keys
Compute (P° − P)/P° and ΔP from textbook pure and solution vapor pressures so students and auto-graders share one colligative ground truth.
Lab manometer and vapor-pressure checks
Turn measured pure and mixture vapor pressures into relative lowering for ideal-solution comparisons in colligative lab reports.
Process screening of non-volatile loads
Convert estimated pure and solution vapor pressures into a dimensionless lowering ratio for drying, distillation, or emission first-pass sizing.
FAQ
What is relative vapor-pressure lowering?
It is the dimensionless ratio (P° − P) / P°, where P° is the pure-solvent vapor pressure and P is the solution vapor pressure at the same temperature. Absolute lowering is ΔP = P° − P.
What pressure units can I use?
Any consistent pressure unit—torr, mmHg, kPa, bar, or atm. Both inputs must use the same unit; the calculator does not convert units. Relative lowering is dimensionless.
What does it cost?
The browser tool is free and runs locally.
How does it relate to the solute mole fraction?
For an ideal solution of a non-volatile solute, Raoult's law makes the relative lowering equal to the solute mole fraction. A relative lowering of 0.15 therefore means a solute mole fraction of 0.15.
Can the relative lowering be negative?
Yes, if the solution's vapor pressure sits above the pure-solvent value, for instance with a volatile solute. The calculator still reports that negative ratio, which helps you spot bad data or a non-ideal mixture.
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/relative-vapor-lowering \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"pure_vapor_pressure":23.8,"solution_vapor_pressure":20.23}'const res = await fetch("https://api.kit.forhosting.com/chem/relative-vapor-lowering", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"pure_vapor_pressure": 23.8,
"solution_vapor_pressure": 20.23
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/relative-vapor-lowering",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"pure_vapor_pressure": 23.8,
"solution_vapor_pressure": 20.23
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/relative-vapor-lowering", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"pure_vapor_pressure":23.8,"solution_vapor_pressure":20.23}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"pure_vapor_pressure":23.8,"solution_vapor_pressure":20.23}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/relative-vapor-lowering", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"pure_vapor_pressure": 23.8,
"solution_vapor_pressure": 20.23
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.relative_vapor_lowering",
"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
How relative vapor-pressure lowering is defined
Pure vapor pressure must be strictly positive: if P degree is zero the ratio is undefined, and this capability fails with invalid_input rather than inventing infinity or NaN. The entire evaluation is deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical inputs always produce identical JSON.
What you send and what you get back
Classic textbook checks include pure water near twenty-three point eight torr with a solution at twenty point two three torr giving absolute lowering about three point five seven torr and relative lowering about zero point one five, pure solvent with P equal to P degree giving zero relative lowering, and a fully suppressed solution vapor pressure of zero giving relative lowering of one. Send two required finite numbers under the fields pure_vapor_pressure and solution_vapor_pressure. pure_vapor_pressure is P degree of the pure solvent at your temperature and must be strictly greater than zero; zero fails because relative lowering divides by P degree, and negative values fail as non-physical. solution_vapor_pressure is P of the solution in the same pressure unit and must be non-negative. Missing fields, non-numeric strings, NaN, Infinity, zero pure vapor pressure, and negative pressures fail with invalid_input and are not charged. On success the response echoes cleaned pure_vapor_pressure and solution_vapor_pressure, provides vapor_pressure_lowering as Delta P equals P degree minus P, relative_vapor_pressure_lowering as the dimensionless ratio (P degree minus P) over P degree, relative_vapor_pressure_lowering_percent as one hundred times that ratio, a units hint object, method relative_vapor_pressure_lowering, and formula (P degree minus P) over P degree so homework write-ups can cite the same expression. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where relative vapor-pressure lowering calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Technical questions
Why must pure vapor pressure be greater than zero?
Relative lowering divides by P°. When pure vapor pressure is zero the ratio is undefined, so the request fails with invalid_input instead of returning infinity or NaN.
How does this relate to Raoult's law and mole fraction?
For an ideal solution of a non-volatile solute, relative lowering equals the solute mole fraction: (P° − P)/P° = x_solute. This page computes the ratio from pressures; a separate Raoult landing computes P from mole fraction.