States of Matter (Gases and Liquids)

States of Matter (Gases and Liquids)NEET Chemistry · Class 11 · NCERT Chapter 13

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3 interactive concept widgets for States of Matter (Gases and Liquids). Drag any slider, change any number, and watch the formula and the answer update live. Built so you understand how each NEET problem actually works, not just the final number.

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Boyle's, Charles's, Gay-Lussac's law live graph

Maxwell speed distribution: u_mp, u_avg, u_rms vs T and M

Van der Waals Z = PV/nRT: real vs ideal gas (4 gases)

Gas laws simulator

Interactive Boyle's, Charles's, and Gay-Lussac's law visualizer. Drag the slider to see P, V, or T update live with a real-time graph.

States of matter

Gas laws simulator

Interactive Boyle's, Charles's, and Gay-Lussac's law visualizer. Drag the slider to see P, V, or T update live with a real-time graph.

Select a gas law and drag the slider to see how one variable changes when another is varied. All based on PV = nRT.

Boyle's Law (1662)

At constant temperature, the volume of a given amount of gas is inversely proportional to its pressure: V ∝ 1/P. Graph: hyperbola (P vs V).

P₁V₁ = P₂V₂ (constant T, n)

Pressure

At T = 298 K: P = 2.75 atm → V = 8.89 L

PV = nRT: 2.75 × 8.89 ≈ 24.45 L·atm (n=1, R=0.08206)

Try this

Boyle's Law: P×V = constant at fixed T. Hyperbola on P-V graph. Straight line on P vs 1/V graph.
Charles's Law: V/T = constant at fixed P. Straight line V vs T — extrapolates to V=0 at T=0 K (−273°C), defining absolute zero.
All three laws merge into ideal gas law: PV = nRT. R = 8.314 J/mol·K = 0.08206 L·atm/mol·K.

Maxwell speed distribution

See how the Maxwell-Boltzmann speed distribution shifts with temperature and molar mass. u_mp, u_avg, and u_rms are marked on the curve.

States of matter

Maxwell speed distribution

See how the Maxwell-Boltzmann speed distribution changes with temperature and gas molar mass. u_mp, u_avg, and u_rms are marked on the curve.

The Maxwell speed distribution shows the fraction of gas molecules having each speed. Adjust temperature and select a gas to see the curve shift.

H₂

N₂

O₂

CO₂

Temperature

300 K (27°C)

u_mp

1579 m/s

u_avg

1782 m/s

u_rms

1934 m/s

Formulas

u_mp = √(2RT/M) = 1579 m/s
u_avg = √(8RT/πM) = 1782 m/s
u_rms = √(3RT/M) = 1934 m/s

Order: u_mp < u_avg < u_rms (always, for any gas at any T)
Ratio: u_mp : u_avg : u_rms = 1 : 1.128 : 1.225
Higher T → broader, shorter curve (peak shifts right).
Higher M → narrower, taller curve (peak shifts left).

Try this

Compare H₂ vs CO₂ at same T: H₂ has much higher speeds (lower M). u_rms ∝ 1/√M.
At higher T, the peak moves right (higher most probable speed) and the curve broadens.
u_rms is used in KE calculations: (1/2)Mu_rms² = (3/2)RT.

Van der Waals and real gases

Compare real gas vs ideal gas behaviour via compressibility factor Z = PV/nRT. Adjust P and T for H₂, N₂, CO₂, He and see the Z vs P curve.

States of matter

Van der Waals and real gases

Compare real gas vs ideal gas behaviour via compressibility factor Z = PV/nRT. Adjust P and T for H₂, N₂, CO₂, He and see the Z vs P curve.

The compressibility factor Z = PV/nRT measures how much a real gas deviates from ideal behaviour. Z = 1 for an ideal gas.

H₂

N₂

CO₂

Pressure

1 atm

Temperature

300 K

Z (real)

0.996

V_real

24.514 L/mol

V_ideal

24.618 L/mol

Z ≈ 1: Near-ideal behaviour

CO₂: Large a (strong intermolecular attraction). Significant dip Z < 1 at moderate P.

Van der Waals equation

(P + an²/V²)(V − nb) = nRT
a corrects for intermolecular attractions. b corrects for finite molecular volume.
At high P: b term dominates → V_real > V_ideal → Z > 1 (repulsive).
At moderate P: a term dominates → V_real < V_ideal → Z < 1 (attractive).
At low P (→ 0): Z → 1 (all gases approach ideal behaviour).

Try this

CO₂ has large a (3.59) — strong attraction. At moderate pressures it shows strong negative deviation (Z < 1).
H₂ and He have very small a. They show mostly positive deviation (Z > 1) because repulsive volume effects dominate.
Boyle temperature: the temperature at which Z = 1 at all pressures (attractive and repulsive effects cancel). T_B = a/(Rb).

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