CHM-20

Osmotic pressure π = c RT

π = c R T. van 't Hoff osmotic law for a dilute nonelectrolyte.

Reading speed

Solutionsvan 't Hoff osmotic

Governing equation

\pi=cRT

$c \in \left[0.001, 2\right]$

where

c: Molarity (mol/L)
T: Temperature (K)
\pi: Osmotic pressure (kPa)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

\pi=cRT

$c \in \left[0.001, 2\right]$

$c = 0.001$ $\pi = 2.478$

Along the curve

②

Domain of the variable — blue

c_{\min} = 0.001,\quad c_{\max} = 2

$c \in \left[0.001, 2\right]$

$c = 0.001$ $c = 0.001$

Along the curve

③

Response curve — green

\pi=cRT

$c \in \left[0.001, 2\right]$

$c = 0.001$ $\pi = 2.478$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\pi}{\mathrm{d}c}

$c \in \left[0.001, 2\right]$

$c = 0.014$ $\pi^{\prime} = 2477.7$

Along the curve

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-20 — Osmotic pressure π = c RT) is the form associated with van 't Hoff osmotic. Working symbols: $c$ , $T$ $\rightarrow$ $\pi$ . The van 't Hoff factor i multiplies c for electrolytes. Ideal dilute limit of the osmotic virial.

Purpose

Purpose: compute

\pi

from

c

T

in Physical chemistry via

\pi=cRT

π = c R T. van 't Hoff osmotic law for a dilute nonelectrolyte. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

c = 0.100\,\mathrm{mol/L}

T = 298.000\,\mathrm{K}

, the governing relation

\pi=cRT

yields

\pi = 247.77\,\mathrm{kPa}

. Dilute nonelectrolyte, i = 1. c in mol/L. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Molarity c0.1 mol/LTemperature T298 K

Outputs

Osmotic pressure \pi247.77 kPa

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Dilute nonelectrolyte, i = 1. c in mol/L.

The van 't Hoff factor i multiplies c for electrolytes. Ideal dilute limit of the osmotic virial.

Reading speed

Watch on YouTube