1. Physical Chemistry (TKK-2446)
16/17 Semester 2
Physical Chemistry (TKK-2446)
Instructor: Rama Oktavian
Office Hr.: M. 10 – 12, T. 10 – 12, W. 09 – 10, F.10 – 15

2. Outlines 1. Kinetic theory of gas 2. Condensed phase
3. Properties of liquids
4. Solid structure

3. Learning check Molar mass of gas
In an experiment to measure the molar mass of a gas, 250 cm3
of the gas was confined in a glass vessel. The pressure was 152 Torr at 298 K and, after correcting for buoyancy effects, the mass of the gas was 33.5 mg. What is the molar mass of the gas?

4. Learning check Dalton’s partial pressure
A gas mixture consists of 320 mg of methane, 175 mg of argon, and 225 mg of neon. The partial pressure of neon at 300 K is 8.87 kPa. Calculate
(a) the volume and (b) the total pressure of the mixture.

5. Learning check Dalton’s partial pressure
A vessel of volume 22.4 dm3 contains 2.0 mol H2and 1.0 mol N2 at K initially. All the H2 reacted with sufficient N2 to form NH3. Calculate
the partial pressures and the total pressure of the final mixture.

6. Kinetic theory of gases
Kinetic theory of gas observes molecular motion in gases
In the kinetic model of gases we assume that the only contribution to the energy of the gas is from the kinetic energies of the molecules
The pressure that a gas exerts is caused by the collisions of its molecules with the walls of the container.

7. Kinetic theory of gases
Pressure and molecular speed relation
(1)
Where M = mNA, the molar mass of the molecules, and c is the root mean square speed of the molecules, the square root of the mean of the squares of the speeds, v, of the molecules:
(2)

8. Kinetic theory of gases
Pressure and molecular speed relation
Justification
Consider the movement of gas
the momentum before collision is
the momentum after collision is
the change in momentum is the difference between final and initial momentum

9. Kinetic theory of gases
Pressure and molecular speed relation
Justification
The distance that molecule can travel along the x-axis in an interval ∆t is written as
if the wall has area A, then all the particles in a volume
will reach the wall

10. Kinetic theory of gases
Pressure and molecular speed relation
Justification
The number density of particles is
where n is the total amount of molecules in the container of volume V and NA is Avogadro’s constant
The number of molecules in the volume x

11. Kinetic theory of gases
Pressure and molecular speed relation
Justification
At any instant, half the particles are moving to the right and half are moving to the left
Therefore the number of molecules will become
The total momentum change within interval Δt is x

12. Kinetic theory of gases
Pressure and molecular speed relation
Justification
The total momentum change within interval Δt is x
Where M = mNA

13. Kinetic theory of gases
Pressure and molecular speed relation
Justification
Rate of change of momentum can be written as total momentum divided by time interval
rate of change of momentum is equal to the force (by Newton’s second law of motion)

14. Kinetic theory of gases
Pressure and molecular speed relation
Justification
the pressure, the force divided by the area, is
rate of change of momentum is equal to the force (by Newton’s second law of motion)
Not all the molecules travel with the same velocity, so the detected pressure, p, is the average (denoted ) of the quantity just calculated

15. Kinetic theory of gases
Pressure and molecular speed relation
Justification
To write an expression of the pressure in terms of the root mean square speed, c, we begin by writing the speed of a single molecule, v, as
because the molecules are moving randomly, all three averages are the same, it follows

16. Kinetic theory of gases
Pressure and molecular speed relation
Justification

17. Kinetic theory of gases
Pressure and molecular speed relation
Using Boyle’s Law and ideal gas Law
the root mean square speed of the molecules in a gas at a temperature T must be
the higher the temperature, the higher the root mean square speed of the molecules, and, at a given temperature, heavy molecules travel more slowly than light molecules

18. Kinetic theory of gases
Pressure and kinetic energy relation
Kinetic energy of molecule is defined as
M = mNA
N = nNA

19. Kinetic theory of gases
Pressure and kinetic energy relation
Using Boyle’s Law and ideal gas Law
k is Boltzmann constant
k = × m2 kg s-2 K-1

20. Condensed Phase The definition of “condensed”
1. reduced in volume, area, length, or scope; shortened: a condensed version of the book.
2. made denser, especially reduced from a gaseous to a liquid state.
3. thickened by distillation or evaporation; concentrated: condensed lemon juice.

21. Condensed Phase The definition of “condensed phase”
Solid and Liquid are condensed phase because the particles are very close together.
There are strong intermolecular forces

22. Condensed Phase The definition of “condensed phase”
made denser, especially reduced from a gaseous to a liquid state.

23. Liquid state
Structure of liquids

24. Liquid state Structure of liquids
Substances that can flow are referred as fluids. Both gases and liquids are fluid

25. Liquid state Structure of liquids
The particles that form a liquid are relatively close together, but not as close together as the particles in the corresponding solid.
The particles in a liquid have more kinetic energy than the particles in the corresponding solid.
As a result, the particles in a liquid move faster in terms of vibration, rotation, and translation.
Because they are moving faster, the particles in the liquid occupy more space, and the liquid is less dense than the corresponding solid.

26. Liquid properties Thermal expansion Compressibility Vapor pressure
intermolecular forces will play a major role in explaining their physical properties.
Thermal expansion
Compressibility
Vapor pressure

27. Liquid properties How to describe P-V-T relationship in liquid state?
The dependence of the volume of a solid or liquid on temperature at constant pressure can be expressed by
where :
α is coefficient of thermal expansion
V0 is volume of liquid at 0 C
t is temperatur in Celcius

28. Liquid properties How to describe P-V-T relationship in liquid state?
V0 is function of pressure and expressed as
where :
is volume of liquid at 0 C and 1 atm
V0 is volume of liquid at 0 C
is coefficient of compressibility

29. Liquid properties General definition of and
Equation of state for liquid
V = V(p,T)
Take the partial derivative

30. Liquid properties General definition of and Volume expansivity
Isothermal compressibility
EoS for liquid can be written as:

31. Liquid properties General definition of and Volume expansivity
The value is usually small
Isothermal compressibility

32. Liquid properties
General definition of and

33. Liquid properties
The effect of pressure change to volume change of liquids
If we take atm-1 , then for a pressure of two atmospheres, the volume of the condensed phase is
The decrease in volume in going from 1 atm to 2 atm pressure is %
Liquid is incompressible fluid

34. Liquid properties EoS for liquids
Find the volume change when acetone is changed from K and 1 bar to K and 10 bar

35. Liquid properties Viscosity Surface tension Vapor pressure
Other properties of liquid
Viscosity
Surface tension
Vapor pressure

36. Liquid properties the resistance of a liquid to flow
Viscosity
the resistance of a liquid to flow
Intensive property of liquids
Viscosity depends on:
- The attractive forces between molecules
- Temperature - The viscosity of liquids decreases with increase the temperature

37. Liquid properties Effect of temperature
M.A. Mehrabian, M. Khoramabadi, (2007) "Application of numerical methods to study the effect of variable fluid viscosity on the performance of plate heat exchangers", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 Iss: 1, pp

38. Liquid properties Surface tension
the amount of energy required to increase the surface area of a liquid by a unit amount
Stronger intermolecular forces cause higher surface tension
Water has a high surface tension (H-bonding)

39. Liquid properties
Surface tension

40. Liquid properties
Phase change

41. Liquid properties Phase change
Energy Changes Accompanying Phase Changes
• melting or fusion:ΔHfus> 0 (endothermic)
• vaporization:ΔHvap> 0 (endothermic)
• sublimation:ΔHsub> 0 (endothermic).
•deposition: ΔHdep < 0 (exo). •condensation: ΔHcon < 0 (exo).
• freezing: ΔHfre < 0 (exo).
•The following sequence is endothermic: heat solid → melt → heat liquid → boil → heat gas
•The following sequence is exothermic: cool gas → condense → cool liquid → freeze → cool solid

42. Liquid properties
Heating curve

43. Liquid properties Vapor pressure Vapor pressure
the pressure exerted by its vapor when the liquid and vapor are in dynamic
equilibrium
Dynamic equilibrium is a condition in which two opposing processes occur simultaneously at equal rates
Some of the molecules on the surface of a liquid have enough energy to escape the attraction of the bulk liquid.
•These molecules move into the gas phase.
As the number of molecules in the gas phase increases, some of the gas phase molecules strike the surface and return to the liquid.

44. Liquid properties Vapor pressure as function of temperature

45. Liquid properties Evaporation vs boiling
evaporation is a surface phenomenon - some molecules have enough kinetic energy to escape
Boling point is the temperature at which the vapor pressure is equal to the external pressure, bubbles form

46. Liquid properties Normal boiling point
The temperature at which the vapor pressure is equal to 1 atm

47. Solids Crystalline solid
the units that make up the solid are arranged in a very regular, repeating pattern.
Amorphous solid
An amorphous solid lacks the long range order of a crystalline solid.
Most plastics are amorphous solids. (they are polymers)

48. Solids Covalent Network Solids
In a covalent network solid, all of the atoms in a crystal are held together by covalent bonds.
Some examples of covalent network solids are diamond (C), boron nitride (BN), and silicon dioxide (SiO2).

49. Solids
Ionic Solids
An ionic solid consists of oppositely charged ions, held together by strong electrostatic interactions.
Binary compounds made up of a metal and a nonmetal are in this category.
Example: NaCl

50. Problems EoS of liquids
Express the volume expansivity and theisothermal compressibility as functions of density p and its partial derivatives
For water at K (50°C) and 1 bar, K = x10-6 bar-1. To what pressure must water be compressed at K (50°C) to change its density by 1 %? Assume that K is independent of P.

51. Problems
Castellan prob 5.7

52. Thank You !