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]

Theme B — The Particulate Nature of Matter

B.4.3 Entropy — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 35 of 53 1 quiz

📚 IB Physics 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

B.4.3 Entropy — IB PHYSICS HL notes: Define entropy through microstates, S = kB ln Ω, and explain how entropy changes in physical processes and why natural processes are irreversible.Limitation — the first law would allow a hot coffee to get hotter by taking energy from the coole…

Missing idea
Macrostate
Multiplicity Ω
Coin model
Large numbers
Additivity

Part 1 of 7Why energy conservation is not enough

Limitation

Limitation the first law would allow a hot coffee to get hotter by taking energy from the cooler room, but this never happens

Missing idea

Missing idea entropy decides which processes occur naturally

Meaning

Meaning entropy measures how widely energy and particles are spread among the available arrangements

Part 2 of 7Macrostates and microstates

Macrostate

Macrostate a description of a system by large-scale variables such as p, V, T and U

Microstate

Microstate a complete specification of the positions and energies of every particle

Multiplicity Ω

Multiplicity Ω the number of microstates that correspond to a given macrostate

Coin model

Coin model with four coins, 2 heads and 2 tails occurs in 6 ways while 4 heads occurs in 1 way
The most probable macrostate has the most microstates

Large numbers

Large numbers for a mole of molecules the evenly spread arrangements are so overwhelmingly more numerous that other macrostates are never seen

Part 3 of 7Boltzmann's definition of entropy

Equation

S = kB ln Ω

Symbols

S in J K⁻¹, kB = 1.38 × 10⁻²³ J K⁻¹, Ω the number of microstates, ln the natural logarithm

Trend

Trend entropy increases as the number of microstates increases

Additivity

Additivity independent systems have Ω₁Ω₂ microstates
S = kB ln Ω₁ + kB ln Ω₂ = S₁ + S₂

Disorder

Disorder entropy is often called disorder, but the number of ways to arrange particles and energy is more precise

Part 4 of 7Entropy change in a two-compartment container

Entropy change in a two-compartment container

Start

N distinguishable particles are all in one compartment so Ω₁ = 1^N = 1

After removing the partition

After removing the partition each particle may be in either compartment so Ω₂ = 2^N

Entropy change

ΔS = kB ln(Ω₂/Ω₁) = kB ln(2^N) = NkB ln 2

Volume form

Volume form doubling the volume from V to 2V gives ΔS = NkB ln(2V/V) = NkB ln 2

Reversal

Reversal the probability of all particles returning to one half is 2^−N, effectively zero

Part 5 of 7Examples of entropy change

States of matter

States of matter entropy increases in the order solid, liquid, gas
Melting and boiling increase entropy while freezing and condensing decrease it

Heating

Heating raising the temperature gives particles more ways to share the energy so entropy rises

Dissolving

Dissolving a solid dissolving in a solvent spreads out its particles and raises entropy

Diffusion

Diffusion a gas filling a whole container has more ways to arrange its particles and energy

Mixing

Mixing two different gases mixed have more arrangements than when separate

Local decrease

Local decrease entropy can fall in one system, such as freezing water, if the surroundings gain more entropy

Part 6 of 7Entropy and irreversibility

1Irreversible process

Irreversible process one that cannot be undone without leaving changes elsewhere

2Cause

Cause natural processes lead from less probable macrostates to more probable ones

3Heat flow

Heat flow heat passes from hot to cold because there are far more ways to share energy evenly

4Arrow of time

Arrow of time the direction of increasing entropy gives time its direction

Part 7 of 7More from the specification

Second Law of Thermodynamics and Entropy

In any spontaneous cyclic or natural thermodynamic process, the total entropy of the universe increases or remains constant, setting a fundamental limit on heat engine efficiency.

Thermal Efficiency of Heat Engines

A heat engine absorbs heat Q_H from a high-temperature reservoir, performs useful work W,
and expels waste heat Q_C to a cold reservoir, with thermal efficiency defined as eta = W / Q_H = 1 - (Q_C / Q_H).

Adiabatic and Isothermal Processes

In an ideal gas cycle, an adiabatic process occurs with zero heat exchange (Q = 0),
so work done changes internal energy directly (Delta U = -W),
while temperature remains constant during an isothermal process.

The Carnot Cycle as an Ideal Benchmark

The Carnot cycle consists of two reversible isothermal and two reversible adiabatic processes operating between two thermal reservoirs, establishing the theoretical maximum efficiency achievable at constant reservoir temperatures.

Compression

Decrease in length under a squashing force.

Piston

A moving part in a cylinder that applies or receives pressure.

Internal energy

Total random kinetic and potential energy of all particles.

Carnot cycle

A reversible cycle of two isothermal and two adiabatic processes between two reservoirs.

Kinetic energy

K = ½mv², energy of motion.

Isolated system

System with no external interaction.

Atmospheric pressure

Pressure of the air, about 1.01 × 10⁵ Pa at sea level.

Pressure

Force per unit area, P = F/A.
What the symbols mean: p = pressure (Pa = N m⁻²) · F = force acting at right angles to the surface (N) · A = area (m²)

Constant

Not changing.

Efficiency

Useful output divided by total input.

Reservoir

Artificial lake that stores water.

Adiabatic

With no thermal energy transfer

Thermal

A convection current in the air.

Isothermal

At constant temperature

Expansion

Increase in size on heating as particles move further apart.

Key terms

Term	Meaning
Entropy (S)	A measure of the number of microstates corresponding to a macrostate, S = kB ln Ω.
Microstate	A complete specification of the state of every particle in a system.
Macrostate	A description of a system by its large-scale variables.
Multiplicity (Ω)	The number of microstates corresponding to a macrostate.
Irreversible process	A process that cannot be reversed without leaving a net change in the universe.

Avoid these mistakes

Saying entropy is the same as energy — it is measured in J K⁻¹ and describes how energy is spread among microstates.

Defining entropy only as disorder — state that it depends on the number of microstates.

Thinking entropy can never decrease anywhere — a system can lose entropy if its surroundings gain more.

Using log₁₀ in S = kB ln Ω — the natural logarithm is required.

Confusing a microstate with a macrostate — a macrostate contains many microstates.

Last updated: 15 October 2026