كيف يحسب الرقم الهيدروجيني pH للمحاليل؟ How to calculate pH and pOH?

يحسب الرقم الهيدروجيني بالعلاقة: pH = -log[H⁺]، وللمحاليل المائية عند 25°C: pH + pOH = 14. إذا كان pH 7 فالمحلول قاعدي. [الصيغة الرمزية الموزونة: pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴]

S1.3Structure 1 — Models of the particulate nature of matter

Electron configurations — IB Chemistry HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 3 of 6 1 quiz

📚 IB Chemistry HL Hub / Topical Revision

Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution

pH = -log[H⁺]  |  pOH = -log[OH⁻]  |  pH + pOH = 14  |  [H⁺][OH⁻] = 10⁻¹⁴

Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14

Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.

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Lesson summary

S1.3 Electron configurations — IB CHEMISTRY HL notes: Explain line spectra, describe shells, subshells and orbitals, write electron configurations, and use ionisation energies (HL).Spectrum — the range of frequencies of electromagnetic radiation, divided into regions and importan…

High-energy radiation
Inverse link
Photon energy
What the symbols mean
Continuous spectrum
Line spectrum

Part 1 of 9The electromagnetic spectrum

Spectrum

Spectrum the range of frequencies of electromagnetic radiation, divided into regions and important in analytical chemistry.

Order

Order radio, microwave, infrared, visible, ultraviolet, X-ray, gamma, from low to high frequency and energy.

High-energy radiation

High-energy radiation gamma rays, X-rays and UV have high frequency and can damage cells.

Equation

Equation c = fλ, where c = 3.00 × 10⁸ m s⁻¹ is the same for all waves in a vacuum.

Inverse link

Inverse link higher frequency means shorter wavelength and the reverse.

Photon energy

E = hf, with h = 6.63 × 10⁻³⁴ J s; these equations are in the Data Booklet.
What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10⁻³⁴ J s) · f = frequency (Hz)

Part 2 of 9Continuous and line spectra

Continuous spectrum

Continuous spectrum contains all frequencies, blending smoothly with no gaps, as in white light through a prism.

Line spectrum

Line spectrum shows only certain frequencies, as in the helium spectrum.

Quantised energy

Quantised energy the fixed frequencies show that electrons can have only certain amounts of energy.

Quanta

"little packets" of energy.

Unique spectrum

Unique spectrum each element has its own line spectrum, so spectra identify elements.

Part 3 of 9Emission and the hydrogen spectrum

Excitation

Excitation energy promotes an electron to a higher energy level.
- (heat or electricity)

Emission

Emission the electron falls to a lower level and emits a photon with energy equal to the difference, ΔE = hf.

Hydrogen series

Hydrogen series the spectrum has families of lines.
Falls to n = 1 give ultraviolet lines (high energy, Lyman).
Falls to n = 2 give visible lines (medium energy, Balmer).
Falls to n = 3 give infrared lines (low energy).

Convergence

Convergence lines get closer together towards high energy because the energy levels get closer together.

Evidence

Evidence the hydrogen line spectrum supports Bohr's model of fixed energy levels, which followed Planck's quantum theory.

Visible light

Visible light emission in the visible region is analysed with a diffraction grating.

Part 4 of 9Energy levels, subshells and orbitals

Principal quantum number (n)

Principal quantum number (n) numbers the shells; a lower n is closer to the nucleus and lower in energy.

Electron capacity

Electron capacity a shell holds at most 2n² electrons, so n = 1, 2, 3, 4 hold 2, 8, 18, 32.

Subshells

Subshells labelled s, p, d and f; shell n contains n subshells.

Energy order

Energy order s < p < d < f, with the 4s subshell filling before 3d.

Orbitals

Orbitals each subshell holds 1 (s), 3 (p), 5 (d) or 7 (f) orbitals, and each orbital holds a maximum of two electrons.

Subshell capacity

Subshell capacity s 2, p 6, d 10, f 14 electrons.

Degenerate

Degenerate orbitals in the same subshell have the same energy.

Shapes

Shapes s orbitals are spherical and grow larger with n;
- p orbitals are dumbbell shaped along the x, y and z axes at right angles.

Part 5 of 9Rules for filling orbitals

1Aufbau principle

Aufbau principle fill the lowest energy subshells first.

2Order

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p.

3Pauli exclusion principle

Pauli exclusion principle an orbital holds a maximum of two electrons with opposite spins.

4Hund's rule

Hund's rule degenerate orbitals fill singly with parallel spins before pairing, which reduces repulsion.

5Spin-pair repulsion

Spin-pair repulsion electrons with the same spin repel, so single occupancy is preferred.

6Box notation

Box notation each orbital is a box with arrows in opposite directions for paired electrons.

Part 6 of 9Writing electron configurations

Full configuration

Full configuration lists all electrons from 1s onward.

Shorthand

Shorthand uses the previous noble gas core in brackets, for example Fe = [Ar] 4s² 3d⁶.

Anions

Anions electrons are added to the outer shell.

Cations

Cations electrons are removed from the outer shell, and from 4s before 3d in transition metals.

Exceptions

Cr is [Ar] 3d⁵ 4s¹ and Cu is [Ar] 3d¹⁰ 4s¹, because half-full and full d subshells are favourable.

Blocks

Blocks elements are grouped as s-, p-, d- or f-block by the subshell holding the valence electrons.

Part 7 of 9Ionisation energy from a spectrum (HL)

Limit of convergence

Limit of convergence the point where lines merge, corresponding to the energy to remove an electron.

Lyman series

Lyman series the convergence limit is the fall from n = ∞ to n = 1, which equals the first ionisation energy.

Calculation

Calculation find f from c = fλ, then E = hf per atom.

Per mole

Per mole multiply by the Avogadro constant (6.02 × 10²³) and divide by 1000 to give kJ mol⁻¹.

Rounding

Rounding keep the full calculator value until the end.

Bohr model limits

Bohr model limits it assumes fixed electron positions and only explains hydrogen, not atoms with more than one electron.

Part 8 of 9Successive ionisation energies (HL)

Increase

Increase successive ionisation energies increase because each electron is removed from an increasingly positive ion.

Cause

Cause shielding decreases and the proton-to-electron ratio increases, so attraction rises.

Large jump

Large jump shows the next electron comes from a shell closer to the nucleus, so the electrons before the jump are the valence electrons.

Smaller jump

Smaller jump shows a change of subshell within a shell.

Uses

Uses predict or confirm configuration, count outer electrons and find the group number.

Part 9 of 9First ionisation energy trends (HL)

1Factors

Factors nuclear charge, distance of outer electrons from the nucleus, shielding by inner electrons and spin-pair repulsion.

2Across a period

Across a period it generally increases because nuclear charge rises, radius falls and shielding stays about the same.

3Down a group

Down a group it decreases because of greater radius and more shielding.

4Between periods

Between periods a large decrease occurs because a new shell adds distance and shielding.

5Group 2 to 13 dip

Group 2 to 13 dip the outer electron in boron is in a higher-energy 2p subshell, further from the nucleus.

6Group 15 to 16 dip

Group 15 to 16 dip the electron removed from oxygen is in a doubly occupied p orbital, and spin-pair repulsion makes removal easier.

Key terms

Term	Meaning
Line spectrum	A spectrum of discrete frequencies produced by atoms.
Quantum	A fixed packet of energy.
Subshell	A division of a shell labelled s, p, d or f.
Orbital	A region holding at most two electrons.
Aufbau principle	Fill the lowest energy subshells first.
Hund's rule	Degenerate orbitals fill singly before pairing.
Limit of convergence	The point where spectral lines merge, giving the ionisation energy.
Successive ionisation energies	The energies needed to remove each electron in turn.

Avoid these mistakes

Filling 3d before 4s — 4s fills first but is also lost first when forming ions.

Forgetting the exceptions Cr and Cu — they promote a 4s electron to reach a half-full or full 3d subshell.

Writing electrons paired before every orbital in a subshell has one — Hund's rule fills singly first.

Leaving out the Avogadro constant when converting an energy per atom to ionisation energy per mole.

Last updated: 13 October 2026