Ideal Gas LawJEE Main

Concept

The ideal gas law $PV = nRT$ ties together pressure, volume, temperature and amount in one equation. The classic named laws are just special cases — hold two quantities fixed and the other two trade off.

Key formula

Derivation

Combining Boyle's law ($P \propto 1/V$ at fixed $T,n$), Charles's law ($V \propto T$ at fixed $P,n$) and Avogadro's ($V \propto n$) gives $PV = nRT$ with the universal gas constant $R = 0.0821$ L·atm·mol⁻¹·K⁻¹.

At STP (273 K, 1 atm) one mole occupies 22.4 L — a number worth memorising. At fixed $T$ and $n$, plotting $P$ against $V$ traces a hyperbola (an isotherm).

Scenarios to explore

• Ideal Gas Law — PV = nRT and Boyle's isotherm.

Real-world applications

• Stoichiometry of gaseous reactions (molar volumes).
• Predicting how tyres, balloons and engines respond to heating.
• Vapour-density and molar-mass determination.

JEE exam tips

• Combined gas law $\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}$ handles most two-state problems.
• Real gases deviate at high $P$ / low $T$ — that's where van der Waals corrections enter.

Common mistakes

• Using Celsius instead of Kelvin for $T$.
• Mismatched units of $R$ (use 0.0821 with L, atm, K).
• Forgetting the gas amount $n$ when comparing two states.

Exam traps to avoid

• An isotherm is a hyperbola, not a straight line — only $P$ vs $1/V$ is linear.
• Equal volumes of different gases at the same $T,P$ contain equal moles (Avogadro).