Summary

Summary Thermodynamics

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Course
Thermodynamics (NWIMOL017)

Institution
Radboud Universiteit Nijmegen (RU)

Book
Atkins\\\' Physical Chemistry

This is a complete summary of the course Spectroscopic Techniques. Includes information from the lecture notes, the book and the student manual. The book used for this course is Physical Chemistry 10th edition from Atkins and De Paula. Chapters Physical Chemistry: 1 (A-C), 2 (A-C, E), 3 (A-D), 5(A...

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Summarized whole book? No
Which chapters are summarized? 1 (a, c), 2 (a-c, e), 3 (a-e), 5 (a, b, f), 6 (a-d)
Uploaded on September 11, 2019
Number of pages 13
Written in 2018/2019
Type Summary

gas
perfect gas
first law
thermodynamics
reversible
irreversible
process
entropy
second law
enthalpy
free energy
activity
chemical potential
mixture
colligative properties
thermochemistry
potential
eq

Book Title:Atkins\\\' Physical Chemistry

Author(s):Peter Atkins, Julio Depaula

Edition:Unknown
ISBN:9780198769866
Edition:Unknown

Exam (elaborations)
Atkins' PHYSICAL CHEMISTRY

Institution
Radboud Universiteit Nijmegen (RU)
Education
Chemistry
Course
Thermodynamics (NWIMOL017)

IsabeldeKiewit

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Thermodynamics
1. Properties of Gases

1.A The perfect gas

Definition

 Gas: consists of a collection of molecules that are in ceaseless motion and which interact
significantly with one another only when they collide

Variables of state

 Physical state: depends on the pressure (p), the amount of substance it contains (n) the
volume it occupies (V) and the temperature (T)
 Thermodynamic equilibrium: the state variables of the system do not change spontaneously
 Pressure: mechanical equilibrium is the condition of equality in pressure of two gasses →
standard pressure (pᶿ) is 1 bar) is 1 bar
 Temperature: a perfect-gas/thermodynamic temperature scale (in Kelvins) is independent of
the identity of the gas → K = °C + 273.15

Perfect gas

 Equation of state: interrelates the variables that define the state of a substance → the value
depends only on the current state of the system and is independent of how that state has
been prepared
 Limiting law: strictly true only in a certain limit
 pV = nRT = NkT → perfect gas law
 Perfect gas: obeys the perfect gas law exactly under all conditions
 Real gas: is described exactly by the perfect gas law in the limit of p→0
 R = NAk → molar gas constant

Processes

 Reversible process: the system is in thermodynamic equilibrium at every moment
 Irreversible process: is not necessarily reversible
 Isothermal process: at constant temperature
 Isobaric process: at constant pressure
 Isochoric process: at constant volume
 Adiabatic process: without heat exchange with the environment (dQ = 0)

Mixture of gases

 pJ = xJp → partial pressure (xJ = mole fraction)
 pA + pB + … = (xA + xB + …)p = p → for real and perfect gases
 Dalton’s law: the pressure exerted by a mixture of gases is the sum of the pressures that each

one would exert if it occupied the container alone

1.C Real gases

Intermolecular forces

 Intermolecular forces: important when distance between the molecules is very small and the
temperature is very low
 Repulsions: short-range interactions that assist expansion
 Attractions: long-range interactions that assist compression
 Vapour pressure: the pressure at which both liquid and vapour are present in equilibrium

1

, Compression factor
 Z = Vm / V°m → compression factor (ratio measured molar volume/perfect gas molar volume)
 Z > 1: due to repulsive forces the molar volume is larger than that of a perfect gas
 Z < 1: due to attractive forces the molar volume is smaller than that of a perfect gas

Virial coefficients
 pVm = RT(1 + B/Vm + C/V2m + …) → virial equation of state (summarizes the behaviour of real
gases over a range of conditions)
 Virial coefficients: depend on the temperature → second (B), third (C), … in the equation
 Boyle temperature (TB): the properties of a real gas coincide with those of a perfect gas as
p→0
 At TB: B = 0 & pVm = RTB
Critical constants
 Critical point: compression takes place at TC and a surface separating two phases does not
appear and the volumes at each end of the horizontal part of the isotherm have merged to a
single point
 Critical constants: critical temperature Tc, critical pressure pc and critical molar volume Vc
 Tc = 8a / 27Rb , pc = a / 27b2 , Vc = 3b
 Zc = pcVc / RTc = 3/8 → critical compression factor (for all gases that are described by the van
der Waals equation near the critical point)
 Supercritical fluid: gas that occupies the entire volume (container) at T ≥ T C → much denser
than normally considered typical of gases
Van der Waals equation
 p = (nRT / V – nb) – a(n2 / V2) → Van der Waals equation of state (real gases)
 Van der Waals coefficients: represent the strength of attractive (a) and the repulsive
interactions between the molecules (b) → characteristic for each gas but independent of the
temperature
 Van der Waals’ loops: the unrealistic oscillations below Tc → they suggest that under some
conditions an increase of pressure results in an increase of volume
 Maxwell construction: the oscillations are replaced by horizontal lines drawn so the loops
define equal areas above and below the lines
Principles van der Waals equation
 Perfect gas isotherms are obtained at high temperatures and large molar volumes → then the
perfect gas law applies (p = RT / Vm)
 Liquids and gases coexist when the attractive and repulsive effects are in balance
 The critical constants are related to the van der Waals coefficients → the extrema of the
oscillations converge as T→Tc and coincide at T=Tc (1st and 2nd derivatives are zero)
Corresponding states
 Reduced variables: dimensionless variables of a gas used to compare the properties of
objects
 Vr = Vm / Vc , pr = pm / pc , Tr = Tm / Tc → reduced variables
 Principle of corresponding states: real gases at the same reduced volume and reduced
temperature exert the same reduced pressure → approximation that works best for spherical
(globular) molecules
 Pr = (8Tr / 3Vr – 1) – (3 / V2r) → same equation but Van der Waals coefficients disappeared

2. The First Law
2

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