Chemistry Tools

K_p Simulator

N₂O₄ ⇌ 2 NO₂ · Endothermic (ΔH° = +57.2 kJ/mol)
Only temperature changes K_p. Changing pressure (volume) or concentration shifts the equilibrium position but the K_p calculation always gives the same answer.

N₂O₄ ⇌ 2 NO₂

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Temperature changes K_p

298 K

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Volume K_p unchanged ✓

30.0 L

⚗

Initial N₂O₄ K_p unchanged ✓

1.00 mol

Equilibrium gas mixture — mole fraction (bar width) shifts with volume & concentration; Kp computed below stays constant

N₂O₄ colorless

NO₂ brown

Live K_p derivation — updates with every slider move

① Equilibrium concentrations (mol/L)

[N₂O₄]_eq = 0.0271 [NO₂]_eq = 0.0125

↓ P = [c] × RT (R = 0.08206 L·atm·mol⁻¹·K⁻¹, RT = 24.45 L·atm·mol⁻¹)

② Partial pressures (atm)

P(N₂O₄) = 0.0271 × 24.45 = 0.6621

P(NO₂) = 0.0125 × 24.45 = 0.3059

↓ K_p = P(NO₂)² / P(N₂O₄)

③ K_p (atm)

K_p = (0.3059)² / 0.6621 = 0.09357 / 0.6621 = 0.1414 atm ← only T can shift this

④ Verify via K_c

K_c = [NO₂]² / [N₂O₄] = 0.005782 mol/L → K_p = K_c × RT = 0.005782 × 24.45 = 0.1414 atm ✓

Equilibrium Constant

K_p = 0.1414

atm

temperature-dependent only

Partial Pressures at Equilibrium

N₂O₄

0.662 atm

NO₂

0.306 atm

P_total = 0.968 atm

Dissociation α

18.8%

of N₂O₄ converted to NO₂

Drag the sliders — only temperature changes K_p; volume and concentration just shift the equilibrium position.

Electron Orbital Viewer

Point cloud weighted by |ψ(r)|² — denser regions have higher electron probability.
Hydrogen atom s-orbitals (a₀ = 1). Drag to rotate · scroll to zoom.

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1s orbital — lowest-energy state, spherically symmetric. Electron density peaks at the nucleus and decays exponentially outward. No radial nodes.

Electron Configuration Builder

Add electrons one at a time · Aufbau principle · Hund's rule applied within each sublevel
Covers elements H → Zn (Z = 1–30) · 4s fills before 3d per Aufbau order

— Z = 0

0 / 30 electrons

Electron Configuration

—

Chromium & Copper: Aufbau Exceptions

Cr (Z=24) and Cu (Z=29) deviate from the Aufbau principle because half-filled and fully-filled d subshells are extra stable.

Chromium Z = 24

Group 6 · Period 4 · [Ar] core = 1s² 2s² 2p⁶ 3s² 3p⁶

Aufbau predicts

[Ar] 4s² 3d⁴

↑↓

↑

→

Actual

[Ar] 4s¹ 3d⁵

↑

⚡ The 3d subshell is half-filled (3d⁵ — one electron per orbital, all spin-up). This maximises exchange energy and minimises electron-electron repulsion, making 4s¹ 3d⁵ lower in energy than the predicted 4s² 3d⁴. One electron is effectively "promoted" from 4s into the empty 3d orbital.

Copper Z = 29

Group 11 · Period 4 · [Ar] core = 1s² 2s² 2p⁶ 3s² 3p⁶

Aufbau predicts

[Ar] 4s² 3d⁹

↑↓

↑

→

Actual

[Ar] 4s¹ 3d¹⁰

↑

↑↓

⚡ The 3d subshell is fully filled (3d¹⁰). A completely filled d subshell is particularly stable. The atom reaches it by promoting one 4s electron into the last 3d orbital, giving 4s¹ 3d¹⁰ instead of the predicted 4s² 3d⁹.

Key takeaway

Both exceptions involve a one-electron shift from 4s → 3d to achieve an especially stable d subshell (half-filled 3d⁵ for Cr, fully-filled 3d¹⁰ for Cu). The same pattern recurs across the periodic table: Mo (Z=42), Ag (Z=47), Au (Z=79), and others. These exceptions are a frequent exam topic in AP, IB, and university chemistry.

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