5.2 Ideal Gas Law

2026-05-20 17:43

Status: #new

Tags: #chemistry #gasses

5.2 Ideal Gas Law

NOTE: Only applies when a gas behaves accordingly with KMT

Formula

P V = n R T $ $ w h e r e R i s a p r o p o r t i o n a l i t y c o n s t a n t - M o l e s i s d e f i n e d a s $ n $ - D e f i n i n g " R " $ $ * R = 8.134 \frac{k P a \cdot L}{m o l \cdot K} Or R = 0.08206 \frac{a t m \cdot L}{m o l \cdot K}

NOTE: Pressure and Temperature are implied to be CONSTANT, where the volume ratio is EQUAL to the mole ratio (for all gas mixtures)

Applications of the Ideal Gas Law

Molar Volume

Molar Volume (MV) = $\frac{V}{n} = \frac{R T}{P} = M V$

Molar Mass

$M = \frac{m}{n}$ $\to$ $M = \frac{m R T}{P V}$
This is because $n = \frac{P V}{R T}$ $\to$ Take the inverses and you can solve for Molar Mass

Mass

$m = n M$ $\to$ substitute this property into Ideal gas law
$\to$ $m = \frac{P V}{R T} M$

Density

$ρ = d = \frac{m}{v} = \frac{n \cdot M}{v}$ , where $ρ \land d$ rep. Density
$\to$ $\frac{n}{v} = \frac{P}{R T}$ $\to$ $ρ = \frac{P M}{R T}$

Key Ideas

Molar Volume depends on environmental conditions only...
Molar mass depends on the identity of the substance
Density is proportional to Molar Mass
Mass is proportional to Molar Mass
Molar mass is proportional to mass

STP and SATP MV

STP: 22.4l/mol
SATP: 24.8l/mol

Some takeaways

When trying to find volume given moles, and STP or SATP, we can simply substitute moles directly and solve...

References

5.1 Gas Pressure and Volume
5.2 Ideal Gas Law