Physical Chemistry

Dae Yong JEONG

Inha University

1

1.1 STATE OF A SYSTEM

Definitions System: the object of interest

Surrounding: rest of the space which gives an effect on system

Boundary: The surface dividing the TD system from the surroundings

Surrounding

system

Boundary • Insulation or heat conduction

• Or semipermeable (matter transfer)

Universe

2

surrounding

System

3

matter

energy

matter

energy

Open system

surrounding

energy energy

Closed system

matter

surrounding

Isolated system

matter energy

Depending on the property of the boundary, the TD system can be classified into; Open system: mass and energy can transfer bw

System & Surrounding

Closed system: energy can be transfer bw System & Surrounding, but NOT mass

Isolated system: neither mass nor energy can transfer bw system & surrounding

Homogeneous: its properties are uniform throughout

For example: single phase

Heterogeneous: contains more than one phase:

For example: water + ice at 0 oC

Physical state (참고)

Two meanings of “State”

State of matter (물질의 상)

Gas

Liquid

Solid

Plasma

Physical state: P, V, T, n (이와 같은 변수로 표현될 수 있음)

개념적으로 서술 가능한 상태

4

How to describe the TD system macroscopically? How to describe the energy state (change) in TD system?

What kind of variables can be used to describe the TD system? As possible as, simple and small # of variables.

Can give an information on energy and physical state!!

A few macroscopic properties: T, P, V, n, m Follow all of the rules of calculus

모든 수학계산이 가능하며, 수학계산을 통하여 여러 물성을 계산해 낼 수 있다.

The state of a system at Equilibrium; Can be described by state variables (ex, T, P, V, n1..) being

independent of the history of the system.

State of a system = f (state variable) : state function

모든 state variables이 주어지면, 원칙적으로 동일한 system을 복사할 수 있다.

최종 state만을 알 수 있으며, 어떤 과정을 겪어서 복사 하였는지 알 수 없음.

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Classification of TD Variables

Extensive variables: (ex) V, mass, S, n1… Only have values for a system as a whole

Intensive variables: (ex) P, T, density… Independent of the size of the system.

They can be either intensities or densities.

Densities: obtained from dividing a extensive variable by another extensive variable (ex. Per mole, per unit volume)

Intensive state of the system; described by intensive variables

Extensive state of the system: described by intensive variable and at least one extensive variable.

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Equilibrium state in TD

Equilibrium state: Properties independent of time and having no fluxes (e.g., no heat flowing through the system)

TD system in Eq. can be specified by a small number of state variables. No history information!!

For examples, For ideal gas: PV = nRT

Multi-components system: the information on composition should be given.

If a liquid system is in the form of small droplets, the surface area has to be given.

If a system is in an electric or magnetic field, this may have an effect on its properties, and then electric field strength and magnetic field strength become state variables.

In general, gravitational field is ignored.

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Change of state

It is difficult to know the absolute value of energy.

We could just know the energy change (ΔE) involved in the change of state.

To know the change, we could be able to define the initial and final states.

However, the change is sometimes dependent on the path which is determined by the process.

Path: sequence of intermediate states Process: describe the path

Reversible: always in eq.

Irreversible: defines direction of time

Adiabatic: no heat transfer bw system and surrounding

Isobaric: constant pressure

Isothermal: constant temp.

Constant volume

If we could define the initial and final state and know the process, then energy change can be known.

(열역학 문제를 풀 때, 항상 초기, 최종 상태가 어떤 조건인지, 그리고 어떤 과정을 거쳐서 진행되었는지 살펴보아야 한다.)

P (

bar)

T (K)

Initial

state

final

state

8

Reversible & Irreversible process

Reversible process A process that takes place through a series of eq. states

However, an infinitesimal change in the external conditions will cause a change in the direction of process. (아주 조금 조금씩은 어느 한쪽 방향으로 변화시킬 수 있음.)

Irreversible process: the direction of a process cannot be changed by an infinitesimal change in external conditions

자연현상에서 진짜로 가역반응이 있을 수 있을까? Although actual processes in nature are never reversible, the consideration of reversible

processes permit changes in the state functions to be calculated.

Since changes in state functions depends only on the initial & final states, we can imagine for computational purposes that a reversible process connects these two states.

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1.2 The 0th Law of TDs

0th law (A & C: thermal eq.) and (B & C: thermal eq.) A & B: thermal eq.

Give the definition of Temp. At thermal eq., T is the same.

Measure the temp. (experimental) Temp. is same. Two state are in thermal eq.

No thermal change temp. is same.

Why temp.?

Temp. gives on information on thermal energy.

Let’s consider the fluid first. Fluid: either a gas or a compressible liquid.

Why fluid first? From our experiences, At const. P V changes

At const. V P changes

P and V are independent variables.

Quite simple to specify the physical state with P and V for a given composition!!

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Boyle’s law

For gas state, Thermal energy (T) vs physical state (P, V)

PV=constant at a specific T

11

gas ofamount the:

constant gas :

state ofequation gas ideal The :

or 1

11

2

22

1

2

11

22

n

R

nRT

PV

T

VP

T

VP

T

T

VP

VP

1.3 The ideal gas temp. scale

Let’s define the temp. with variables for physical state

12

R

VP

nR

PVT

PP 00limlim

The unit of TD temp, Kelvin or 1K is defined as the fraction 1/273.16 of the temperature of the triple point of water.

0 K: absolute zero

05.273// KTCt o

Pressure (P) = Force/Unit area

SI unit: Pascal, Pa = 1N/m2

1 bar = 105 Pa

1 atm = 101325 Pa = 1.01325 bar

mole (n) is the number of 12C atom for 0.012 kg.

1 mole 6.02214 x 1023 #/mole : Avogadro number (NA)

Number of molecules = n x NA

Molar mass (M) = NA m (kg/mol)

m: the mass of a single molecule

Gas constant (R) R = 8.31451 J/(K-mol)

R = kB x NA

= (Boltzmann constant = 1.3802 x 10-23 J/K) x (Abogadro Number = 6.02214 x 1023 #/mole)

Here, 1 J = 1 Pa x m3 (energy) = (Pressure x volume)

Example 1.2

Volume (V) For an ideal gas, at 0 oC (273.15 K) and 1 atm 1 mole of ideal gas has 22.414 liters

RconstT

VP

0

00

Temperature

열이 흐르는 지표 물질의 팽창하는 지표 분자나 원자의 활발한 움직임 정도 개체의 에너지 분포 지표

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Pressure

수은의 높이

• Microscopic: 기체분자가 container의 벽을 부딪히는 힘에 의해 발생

15

1.4 Ideal gas mixtures and Dalton’s law

Mixture of ideal gas n = n1 + n2 + n3 + ….

i

iPPPVRTnnP

2121/) (

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Pressure (microscopically)

Atom (molecule) hits the wall of vessel. pressure

# of atoms (for the same temp. and volume) high pressure

Temp. increases pressure increases.

1.5. Real Gases and the Virial Equation

What is ideal gas? What are the properties of real gas?

기체자체가 특정 부피를 가지고 있으며 기체간의 상호 작용하는 힘을 고려. (Liquid/solid: 상호 작용하는 힘이 매우 크다.) Real gases behave like ideal gas in the limits of low pressures and high temp., but

they deviate significantly at high P and low T.

How to modify the ideal gas’s equation for the real gas?

Virial (force) Equation Compressibility factor

B: 2nd virial coefficient B = 0 at Boyle Temp. (TB) B changes with temp.

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...12

V

C

V

B

RT

VPZ

Low P Z < 1 가능 (분자간 인력영향) High P Z > 1 (실제기체 분자크기 영향)

At Low T 압력에 따라 Z 감소 (분자간 접근 인력증가) At High P 압력에 따라 직선적 변화 (분자크기영향), Z > 1

In fact, it is more convenient to use P as the experimental variable than V.

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...1 2'' PCPBRT

VPZ

..2

...

...1

2

2

3

2

2

2

2

32

2

V

BRT

V

RT

V

CRT

V

BRT

V

RTP

V

CRT

V

BRT

V

RTP

V

C

V

B

RT

VPZ

...12

22'

2

''

V

TRC

V

BRTB

V

RTBZ

22''

'

TRCBRTBC

RTBB

1.6 P-V-T surface for a 1-component system

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Triple point

The state where Gas-liquid-solid co-exist

1.7 critical phenomena

For a pure substance, there is a critical point (Pc, Tc) End point for Liquid-Gas coexistence (Fig. 1.12)

Tc: highest temp. at which condensation of a gas is possible

Pc: highest pressure at which a liquid will boil when heated.

At Tc, 수학적으로

Tc에서 가지는 물리적 특성: Isothermal compressibility

압력을 가했을 때 부피가 얼마나 줄어드는가?

어디에 이용될까?

화력발전소 고압이 필요 우리 주변이 중앙난방 시스템 (먼 곳까지 열용량이 큰 물(steam)을 보

내야 할 때) 화공열역학 참고

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0 and 02

2

CC TTTT V

P

V

P

TP

V

V

1

21

Solid Liquid

Vapor

compressionat const. T

coolingat const. P

Expansionat const. T

Temperature

Pre

ssure

Sublimation temp.

Freezing temp.

Boiling temp.

Triple point

S-Vaporcoexistence curve

S-L

coexi

ste

nce c

urv

e

L-V

apor co

exi

stence

curv

e

Criticalpoint

3 step process to liquefy gaswithout phase transition

임계 온도(TC) 및 임계 압력(PC) 이상 : 상전이 없이 상변화

Critical Point

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1.8 The Van Der Waals Equation

Real gas Real gas is not a point particle but has a certain volume. So, the (empty) volume in ideal gas Eq.

should be replaced.

b: the volume of one mole of real gas

Always, Compressibility > 1

Attraction force bw gases (Van der Waal force!!) How to modify the ideal gas Eq.? Which variable should be modified?

실제 관찰되는 압력보다 큰 압력이 존재한다고 생각.(약간의 압력이 기체간의 인력에 의해 감소되었기 때문에)

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RTbVP )(

2

V

aPP

1.8 The Van Der Waals Equation van der Waals Equation

Molar volume is large, b is negligible ideal gas behavior

Useful for gas-liquid phase separation

(Math)

Compressibility factor for van der Waals gas

Calculate the van der Waals constant from the critical constants for a gas

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RTbVV

aP

)(

2

...1

1

...1

1

1for

1

1

2

PRT

ab

RTZ

V

b

VRT

abZ

Vb

VRT

a

VbVRT

a

bV

V

RT

VPZ

Analysis

• At low temp. a is relatively more

important (~ force bw gases)

• At high temp. b is relatively more

important (~ gas volume)

Van der Waals constant

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1.9 Description of the state of a system w/o chemical reactions

Number of degree of freedom (F) # of independent variables required

For one-phase system w/o chemical rnx, Independent Intensive variable, F = Ns + 1

Ex: one component F = 2

Gas상태인 A를 결정하려면 T1, P1을 알아야 함. Ns: # of species

For two-phase w/o chemical rxn Ex: one component F = 1

Liquid-solid 가 공존하며, 온도 T2만 결정되면 바로 P2이 결정됨

For three-phase w/o chemical rxn Ex: one component F = 0

G-L-S가 공존하는 점은 T3, P3가 결정됨.

Ns+2 variables are required to describe the extensive state of a homogeneous one-phase system.

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P

T

S

L

G

A

T1

P1

T2

P2

T3

P3

1.10 Partial molar properties

For the mixtures of gases and mixtures of liquids

Partial molar volume:

: The change in V when an infinitesimal

amount (dni) of this substance is added to the

solution at constant T, P, and all other nj.

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nnnVnVnVV ...2211

}{,, ijnPTi

i

n

VV

iidnV

nndnVdnVdnVdnVdV ....332211

nnxVxVxVV ...2211

Next class

First Law of Thermodynamics

에너지 보존 법칙

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질문들?

영구기관은 가능한가? 불가능하다면, 왜?

Is it possible to design a ship that is purely powered by the heat of the ocean? Take water from the ocean, absorb the heat from water and turn

water into ice, then drop the ice balls behind?

강의실 구석에서 방귀를 뀌면, 다른 쪽 사람이 냄새를 맡을 수 있을까?

왜 철은 녹이 슬까?

…

우리 주변에 있는 모든 현상?

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Q: Real Gases and the Virial Equation

Virial Equation

30

...12

V

C

V

B

RT

VPZ

Q: 200 oC의 이소프로판올 (isopropanol) 증기에 대한 비리알 계수들은 다음과 같이 주어진다. B = - 388 cm3/mol C = -26,000 cm6/mol2

200 oC, 10 bar에서 다음 식들을 이용하여 이소프로판올 증기에 대한 V와 Z를 계산하시오. (1) 이상기체 (2) 비리알 공식

A) 이상기체

1 ,/ 934,310

15.47314.83 3 ZmolcmP

RTV

비이랄 21

V

C

V

B

RT

VPZ V = 3,488 cm3/mol

Z = 0.8866

이상기체보다 약 13% 적게 나타남.

위 계산을 통하여, 200 oC, 10 bar에서 필요한 이소프로판올 가스통 크기가 결정될 수 있을 것임.