1.5.3—Molar volume

Molar volume is the volume occupied by one mole of gas at a specified temperature and pressure. At STP as used by the current IB data context (273.15 K and 100 kPa), Vₘ is approximately 22.7 dm³ mol⁻¹; a different condition requires its own value.

$For fixed amount and temperature: P ∝ 1/V$

Read pressure–volume graphs as an inverse relationship, not simply as one quantity increasing while the other decreases. At STP, use the stated molar volume with the balanced-equation mole ratio.

Attach conditions to every molar volume. Once Vₘ is valid for the stated temperature and pressure, convert gas volume to moles, apply the balanced-equation ratio, then convert back if needed. Do not carry one tabulated Vₘ into a different set of conditions.

Fixed amount of gas; held constant	Relationship	Graph/interpretation check
temperature	P ∝ 1/V	P–V is inverse, not a straight decreasing line
pressure	V ∝ T	V–T is linear only with T in kelvin
volume	P ∝ T	P–T is linear only with T in kelvin

State the fixed variable and use absolute temperature before interpreting a gas graph.

How it is assessed

Questions calculate a gas volume from amount at STP or deduce the pressure–volume relationship for a fixed gas sample.

Command terms

determine / deduce

What earns marks

Use the stated molar volume and reaction ratio for the calculation, or state inverse proportionality explicitly for the graph relationship.

Watch for

Calling the pressure–volume relationship merely negative rather than inverse, or using the wrong molar-volume condition.

Representative question

[Maximum number: 1]

Deduce the relationship between the pressure and volume of the sample of carbon dioxide gas.

inversely proportional / V $\alpha \frac{1}{\mathrm{p}} / \mathrm{P} \alpha \frac{1}{\mathrm{~V}}$ ;

Marking guidance:

Accept inverse/negative correlation/relationship.
Do not accept $\mathrm{V}=\frac{1}{\mathrm{p}}, \mathrm{P}=\frac{1}{\mathrm{~V}}$ or descriptions like "one goes up as other goes down" / OWTTE.

Retrieve the model: ideal particles have negligible volume and forces with elastic collisions; low temperature and high pressure expose real-gas limits; molar volume and PV=nRT then connect amount, pressure, volume, and temperature.

Before calculating, check whether the question uses STP molar volume or PV=nRT, identify the fixed conditions, convert temperature to kelvin, and align pressure and volume units.

1.5.3—Molar volume

Molar Volume and Gas Relationships

Applying Molar Volume

Assessment in practice

Ideal Gases Summary

Question 1