# Osmotic Pressure Calculator

π = i·M·R·T with van't Hoff factor, multi-unit readout and a molar-mass inversion mode.

> Canonical page: https://elysiatools.com/en/tools/osmotic-pressure-calculator

- **Category:** Science & Education

- **Keywords:** osmotic pressure, pi equals imrt, van't hoff factor, molar mass, membrane, colligative property

## Overview

The Osmotic Pressure Calculator computes osmotic pressure using the van 't Hoff equation (π = i·M·R·T) and offers a reverse mode to determine unknown molar mass from experimental osmometry measurements.

## Inputs

- **Mode** (select)
- **Molarity M (mol/L)** (number): e.g. 0.1 for a sucrose solution
- **Temperature T** (number): e.g. 298.15
- **Temperature unit** (select)
- **van't Hoff factor i (particles per formula unit)** (number): 1 for sucrose, 2 for NaCl, 3 for CaCl₂
- **Measured osmotic pressure π** (number): e.g. 1 (torr, for the molar-mass mode)
- **Pressure unit** (select)
- **Mass concentration c (g/L)** (number): e.g. 1 g/L of protein

## When to use

- Predicting osmotic pressure for electrolyte or non-electrolyte aqueous solutions across various temperatures.
- Determining the molar mass of polymers or proteins from membrane osmometry data.
- Converting calculated osmotic pressure values across standard units including atm, kPa, bar, and torr (mmHg).

## How it works

- Select your calculation mode: direct osmotic pressure from molarity or inverse molar mass calculation from experimental pressure.
- Input solute molarity or mass concentration alongside the van 't Hoff dissociation factor (i).
- Specify temperature in Kelvin or Celsius and configure pressure units (atm, torr, or kPa).
- Calculate to obtain step-by-step thermodynamic derivations and multi-unit pressure or molar mass results.

## Use cases

- General chemistry coursework verifying colligative property problem sets and osmotic pressure calculations.
- Biochemistry laboratories determining molecular weights of purified proteins via membrane osmometry.
- Process formulation estimating osmotic pressures required for reverse osmosis or filtration systems.

## Frequently asked questions

### What is the van 't Hoff factor (i)?

It represents the number of discrete particles formed per formula unit in solution, such as i = 1 for non-electrolytes like sucrose or i = 2 for NaCl.

### Which formula is used for calculating osmotic pressure?

The calculator uses the standard colligative formula π = i·M·R·T, where R is the ideal gas constant (0.082057 L·atm/(mol·K)).

### How is molar mass calculated in reverse mode?

It solves for molarity M = π / (i·R·T) from the observed osmotic pressure and temperature, then computes molar mass via MW = c / M using the mass concentration.

### What temperature units are accepted?

The tool accepts temperature inputs in either Kelvin (K) or degrees Celsius (°C), automatically converting Celsius to absolute temperature.

### Which pressure units can be input or displayed?

Inputs support atm, torr (mmHg), and kPa, while calculated outputs display values across atm, kPa, bar, and mmHg.

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