CHM-01

Ideal gas law

p V = n R T. The pedagogical thermal equation of state.

Reading speed

Equation of stateClapeyron 1834

Governing equation

pV=nRT

$T \in \left[200, 800\right]$

where

n: Amount (mol)
T: Temperature (K)
V: Volume (L)
p: 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

pV=nRT

$T \in \left[200, 800\right]$

$T = 200$ $p = 69.29$

Along the curve

②

Domain of the variable — blue

T_{\min} = 200,\quad T_{\max} = 800

$T \in \left[200, 800\right]$

$T = 200$ $T = 200$

Along the curve

③

Response curve — green

pV=nRT

$T \in \left[200, 800\right]$

$T = 200$ $p = 69.29$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}p}{\mathrm{d}T}

$T \in \left[200, 800\right]$

$T = 203.8$ $p^{\prime} = 0.346$

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-01 — Ideal gas law) is the form associated with Clapeyron 1834. Working symbols: $n$ , $T$ , $V$ $\rightarrow$ $p$ . Point masses with no interactions. Real gases recover this limit at low density.

Purpose

Purpose: compute

p

from

n

T

V

in Physical chemistry via

pV=nRT

p V = n R T. The pedagogical thermal equation of state. 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

n = 1.000\,\mathrm{mol}

T = 298.000\,\mathrm{K}

V = 24.000\,\mathrm{L}

, the governing relation

pV=nRT

yields

p = 103.24\,\mathrm{kPa}

. Closed sample; R = 8.314 J/(mol·K). Volume in litres gives p in kPa. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Amount n1 molTemperature T298 KVolume V24 L

Outputs

Pressure p103.24 kPa

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Closed sample; R = 8.314 J/(mol·K). Volume in litres gives p in kPa.

Point masses with no interactions. Real gases recover this limit at low density.

Reading speed

Watch on YouTube