Chapter 1 concepts and behavior of gas

• A hypothetical body with a relatively large thermal energy capacity mass x specific heat that can supply or absorb finite amounts of heat without undergoing any change in temperature

Dr Ngo Thanh An

PHYSICAL CHEMISTRY 1

1

• The principal goal of physical chemistry is to understand the properties and behaviour of material systems and to apply this understanding in useful ways.

Introduction

2

Textbook

3

Or: The study of heat and its transformation into mechanical energy is called thermodynamics

4

5

6

• Macroscopic system: A large system containing many atoms or molecules

• Microscopic system: a system consisting of a single atom or molecule

system and are properties of the whole system.

Definitions

7

A body or system whose condition

is altered without gaining heat from

or losing heat to the surroundings (energy is transferred only as work.)

Definitions

8

Thermodynamic definition of work: It is a kind of interaction that would occur at the system boundaries It can be positive or negative.

Heat: Heat is a mode of energy transfer that takes place between the system and the surroundings solely due to the temperature difference Thus, heat is a

transient phenomenon It can be recognized only during a process.

Energy exists in many forms, such as mechanical energy, heat, light, chemical energy, and electrical energy Energy is the ability to bring about change or to do work

Definitions

A thermodynamic process is a passage of a

thermodynamic system from an initial state

to a final state 10

When a gas is compressed or expanded so that no heat enters or

leaves a system, the process is said to be adiabatic

Adiabatic changes of volume can be achieved by performing the process rapidly so that heat has little time to enter or leave or by thermally insulating a system from its surroundings.

Do work on a pump by pressing

down on the piston and the air is

warmed.

Definitions

11

When a gas adiabatically expands, it does work on its surroundings and gives up internal energy, and thus becomes cooler

Blow warm air onto your hand from your wide-open mouth Now reduce the opening between your lips so the air expands as you blow Adiabatic expansion—the air is cooled.

Definitions

12

A source supplies

energy in the form

of heat, and a sink

absorbs it

• A hypothetical body with a relatively large thermal energy capacity (mass x specific

heat) that can supply or absorb finite amounts of heat without undergoing any change in temperature is called a thermal energy reservoir, or just a reservoir

• In practice, large bodies of water such as oceans, lakes, and rivers as well as the

atmospheric air can be modeled accurately as thermal energy reservoirs because of their large thermal energy storage capabilities or thermal masses

Bodies with relatively large thermal

masses can be modeled as thermal

energy reservoirs

Definitions

• system quantity whose value is dependent on the manner

in which the transformation is carried out.

Definitions

14

An intensive property is a bulk property, meaning that it is a physical property of

a system that does not depend on the system size or the amount of material in the system Ex: Temperature, Pressure, density, specific heat, …

By contrast, an extensive property is additive for independent, non-interacting

subsystems.The property is proportional to the amount of material in the system Ex: volume, mole number, mass, length, entropy, enthalpy, Gibbs free energy …

variables)

State

function

• State functions: Can we find the exact form of functions?

 We don’t need to know the functions because we just pay attention to the initial and final state

• State 1 or state 2 is completely determined by the value of its state functions at a certain set of state variables 15

State variables:

Describe equilibrium state of thermodynamic system uniquely.

Intensive: homogeneous of degree 0, independent of system size

Extensive: homogeneous of degree 1, proportional to system

size

Note: Intensive state variables serves as equilibrium parameters

Ex: temperature (T), pressure (P) and chemical potential ( µ )

Definitions

-Euler's Theorem: Let f(x1,…,xn) be a function such that

Then f is said to be a homogeneous function of degree n

Intensive and extensive variables

Definitions

17

Definitions

• Gas - a substance that is characterised by widely separated molecules in rapid motion

• Mixtures of gases are uniform Gases will expand to fill containers.

• Ex:

- Common gases include - O2 and N2, the major components of "air"

- Other common gases - F2, Cl2, H2, He, and N2O (laughing gas)

Definitions

19

• The pressure of a gas is best defined as the forces exerted by gas on the walls of the container

Some state variables

21

• How do we measure gas pressure?

• We use an instrument called the barometer - invented by Torricelli

• Gas pressure conversion factors

Definition: Temperature measures the degree of hotness of a body (“how

hot”) It doesn’t depend on the mass or the material of an object It can be thought of as a measure of the average kinetic energy of the atoms or

molecules in a body

Some state variables

23

If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

Some state variables

24

As thermal motion of atoms increases, temperature increases There seems to

be no upper limit of temperature but there is a definite limit at the other end of the temperature scale If we continually decrease the thermal motion of atoms

in a substance, the temperature will drop

Absolute zero is the temperature at which no more energy can be extracted

from a substance

At absolute zero, no further lowering of its temperature is possible This temperature is 273 degrees below zero on the Celsius scale Absolute zero corresponds to zero degrees on the Kelvin, or thermodynamic, scale and is written 0 K (short for “zero Kelvin”)

Unlike the Celsius scale, there are no negative numbers on the thermodynamic scale Degrees on the Kelvin scale are the same size as those on the Celsius scale Ice melts at 0°C, or 273 K, and water boils at 100°C, or 373 K

Some state variables

25

P versus T plots of the

experimental data obtained

from a constant-volume gas

thermometer using four

different gases at different (but

nR

→

=

(for ideal gas)

Some state variables

26

Some state variables

27

Consider thermodynamic system described by state variables {Z1, Z2,…, Zn}Subspace of equilibrium states: f(Z1, Z2,…, Zn) = 0  This is the equation of state (EOS)

Ideal gas: {T, P, V}  thermodynamics EOS: pV = nRT

Equation of state

28

• Experiments with a wide variety of gases revealed that four variables were sufficient to fully describe the state of a gas

• Pressure (P)

• Volume (V)

• Temperature (T)

• The amount of the gas in moles (n)

Ideal gas law

29

Ideal gas lawPV=nRT

Ideal gas law

30

• Combine these relationships into a single fundamental equation of state - the ideal gas equation of state

mole K

atm 08206

0 314

.

mole K

J R

nRT PV

• The pressure exerted by gas #1: P1 = n1 RT / V

nT represents the total number of moles of gas present in the mixture

P1 and P2 are the partial pressures of gas 1 and gas 2, respectively

• PT = P1 + P2 = nT (RT/V)

• PT = P1 + P2 + P3 = Σ Pi

Ideal gas law

32

• Gaseous mixtures - gases exert the same pressure as if they were alone and occupied the same volume.

• The partial pressure of each gas, Pi, is related to the total pressure by Pi = Xi PT

• Xj is the mole fraction of gas i.

• Xj= nj / nT

Ideal gas law

33

• An ideal gas is a gas that obeys totally the ideal gas law over its entire P-V-T range

• Ideal gases – molecules have negligible intermolecular attractive forces and they occupy a negligible volume compared with the container volume

Ideal gas

34

Ideal gas

35

Ideal gas

36

Real gas

PvT diagram for real gases

37

Real gas

38

Real gas

39

Several equations have been proposed to represent the P-v-T behavior of substances

accurately over a larger region with no limitations

Critical isotherm

of a pure substance has an inflection point

at the critical

state

This model includes two effects not considered in the

ideal-gas model: the intermolecular attraction forces and

accuracy of the van der Waals equation of state is often

inadequate

Real gas

41

critical point is defined as the point at which the saturated liquid and saturated vapor

states are identical.

At the critical point, only one phase exists There is an inflection point in the

constant-temperature line (critical isotherm) on a PV diagram This means that at the critical point:

Real gas

42

Real gas

43

Real gas

44

Real gas

45

Compressibility factor Z A factor

that accounts for the deviation

of real gases from ideal-gas

behavior at a given temperature

and pressure

The farther away Z is from unity, the more the gas

deviates from ideal-gas behavior

Gases behave as an ideal gas at low densities (i.e., low pressure, high temperature).

Question: What is the criteria for low pressure and

high temperature?

Answer: The pressure or temperature of a gas is high

or low relative to its critical temperature or pressure

Real gas

All substances obey the same equation of state in terms of reduced variables

Real gas

47

Comparison of Z factors for various gases.

Reduced temperature

49

Real gas

51

Real gas

52

Real gas

53

Real gas

54