1. Physical Chemistry I (TKK-2246)
14/15 Semester 2
Physical Chemistry I (TKK-2246)
Instructor: Rama Oktavian
Office Hr.: M-F 13-15

2. Outlines 1. Gas: Properties 2. Gas laws: Boyle and Charles law
3. Ideal gas law
4. Equation of state

3. Gas state
State of matter
There are 4 states of matter

4. Gas state State of matter
retains a fixed volume and shape rigid - particles locked into place
Properties of solid
not easily compressible little free space between particles
Microscopic view of a solid
does not flow easily rigid - particles cannot move/slide past one another

5. Gas state State of matter
assumes the shape of the part of the container which it occupies particles can move/slide past one another
Properties of liquid
not easily compressible little free space between particles
Microscopic view of a solid
flows easily particles can move/slide past one another

6. Gas state State of matter Microscopic properties
assumes the shape and volume of its container particles can move past one another
Properties of gas
compressible lots of free space between particles
Microscopic view of a solid
flows easily particles can move past one another

7. Gas state State of matter Macroscopic properties
Properties that can be observed and measured
Properties of gas
Properties of bulk gases
• Observable
– Pressure, volume, mass, temperature..
Microscopic view of a solid
How to make relation between those macroscopic properties of gas??
The general form of an equation of state is
p=f(T,V,n)

8. Gas state

9. Gas properties Gases Exert Pressure: What is Pressure?
Pressure is defined as the force exerted divided by the area it acts over
Pressure = Force/Area
The SI unit of pressure, the pascal(Pa), is defined as 1 newton per metre-squared:
1 Pa =1 N m−2
1 Pa =1 kg m−1s−2
1 atm = ×105Pa exactly 1 bar =105Pa

10. Gas properties Gases Exert Pressure: What is Pressure?
Pressure is defined as the force exerted divided by the area it acts over
Pressure = Force/Area
Self-test 1.1 Calculate the pressure (in pascals and atmospheres) exerted by a mass of 1.0 kg pressing through the point of a pin of area 1.0 ×10−2 mm2 at the surface of the Earth.

11. Gas properties Pressure measurement
Barometer – device that measures atmospheric pressure
Invented by Evangelista Torricelli in 1643
the height of the mercury column is proportional to the external pressure

12. Gas properties Pressure measurement
Derive an equation for the pressure at the base of a column of liquid of mass density ρ(rho) and height h at the surface of the Earth.
p=F/A
F = mg
m = ρV
V = Ah
m = ρAh
F = mg = ρAhg
the pressure is independent of the shape and cross-sectional area of the column.

13. Gas properties
Pressure measurement

14. Gas properties Pressure measurement
A manometer measures the pressure of a gas in a container
Gas pressure is the force exerted by the collisions of gas particles with a surface

15. Gas properties Pressure measurement Atmospheric pressure
By definition the average pressure at sea level will support a column of 760 mm of mercury. (760 torr)
g = 9.81 m.s-2 h = 0.76 m
ρ = 13.6 g.cm-3 = 13.6 kg.L-1 = 13.6x103kg.m-3
P = 9.81x0.76x13.6x103 = 1.013x105 Pa (N.m-2)

16. Gas properties Pressure measurement Atmospheric pressure problem
If we made a barometer out of water, what would be the height of the water column if the pressure is 745 torr?

17. Gas properties Pressure measurement Changing weather conditions
Variation in atmospheric pressure
Changing weather conditions

18. Gas properties Pressure measurement Changing altitude
Variation in atmospheric pressure
Changing altitude

19. Gas laws
Boyle’s law
Boyle’s Law is one of the laws in physics that concern the behaviour of gases
When a gas is under pressure it takes up less space:
The higher the pressure, the smaller the volume
Boyles Law tells us about the relationship between the volume of a gas and its pressure at a constant temperature
The law states that pressure is inversely proportional to the volume

20. Gas laws Boyle’s law Pressure-volume relationship
pressure-volume behavior of gases were made by Robert Boyle in 1662
P a 1/V
P x V = constant
P1 x V1 = P2 x V2

21. Gas laws Pressure and Volume: Boyle’s Law
Volume and pressure are inversely proportional.
If one increases the other decreases.

22. Gas laws Pressure and Volume: Boyle’s Law
Boyle’s Law and Breathing: Inhalation
During inhalation,
the lungs expand
the pressure in the lungs decreases
air flows towards the lower pressure in the lungs

23. Gas laws Pressure and Volume: Boyle’s Law
Boyle’s Law and Breathing: Inhalation
During exhalation
lung volume decreases
pressure within the lungs increases
air flows from the higher pressure in the lungs to the outside

24. Gas laws Pressure and Volume: Boyle’s Law
A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?
P1 x V1 = P2 x V2
P1 = 726 mmHg
P2 = ?
V1 = 946 mL
V2 = 154 mL
P1 x V1 V2
726 mmHg x 946 mL
154 mL =
P2 =
= 4460 mmHg

25. Gas laws Pressure and Volume: Boyle’s Law
Guide to Calculations with Gas Laws

26. Gas laws Pressure and Volume: Boyle’s Law Problem
A deep sea diver is working at a depth where the pressure is 3.0 atmospheres. He is breathing out air bubbles. The volume of each air bubble is 2 cm2. At the surface the pressure is 1 atmosphere. What is the volume of each bubble when it reaches the surface?

27. Gas laws
Charles’s law
French chemist Jacques Charles discovered that the volume of a gas at constant pressure changes with temperature.
As the temperature of the gas increases, so does its volume, and as its temperature decreases, so does its volume.
The law says that at constant pressure, the volume of a fixed number of particles of gas is directly proportional to the absolute (Kelvin) temperature

28. Gas laws Charles’s law Volume-temperature relationship
Variation of gas volume with temperature
at constant pressure
V a T
V = constant x T
V1/T1 = V2/T2

29. Gas laws Charles’s law For two conditions, Charles’s law is written
Volume-temperature relationship
For two conditions, Charles’s law is written
V1 = V (P and n constant)
T T2
Rearranging Charles’s law to solve for V2 gives
T2 x V1 = V2 x T2
T T2
V2 = V1 x T2 T1

30. Gas laws
Charles’s law
Example problem
A balloon has a volume of 785 mL at 21 °C. If the
temperature drops to 0 °C, what is the new volume of
the balloon (P constant)?
STEP 1 Set up data table:
Conditions Conditions Know Predict
V1 = 785 mL V2 = ? V decreases
T1 = 21 °C T2 = 0 °C
= 294 K = 273 K T decreases
Be sure to use the Kelvin (K) temperature in gas
calculations.

31. Gas laws Charles’s law STEP 2 Solve Charles’s law for V2: V1 = V2
T T2
V2 = V1 x T2 T1
Temperature factor
decreases T
STEP 3 Set up calculation with data:
V2 = mL x K = 729 mL
294 K

32. Gas laws
Charles’s law
A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n constant)?
1) 443 °C
2) 170 °C
3) –82 °C

33. Gas laws Avogadro’s law Avogadro’s law states that
the volume of a gas is directly related to the number of moles (n) of gas
T and P are constant
V1 = V2
n n2

34. Ideal Gas law The combination of those laws gives Usually written as:
R is gas constant

35. Ideal Gas law R is known as universal gas constant
Using STP conditions

36. Ideal gas and Real gas
Ideal gas
The ideal gas law is used to describe the behavior of an ideal gas.
Ideal gas: hypothetical gas that obeys kinetic molecular theory and the ideal gas law

37. Ideal gas and Real gas
Ideal gas
The ideal gas law was useful in determining the properties of a specific sample of gas at constant T, P, V, and n.
We often need to know how a change in one (or more) properties impacts the other properties for a sample of a gas

38. Equation of state Equation of state
The general form of an equation of state is
p=f(T,V,n)
Ideal gas equation is equation of state

39. Equation of state Equation of state P, V, n, T are properties
Intensive properties – independent on the quantity of material
P, T
Extensive properties – dependent on the quantity of material
n, V
The ratio of any two extensive variables is always an intensive variable
Intensive properties

40. Equation of state Equation of state
Expressed in intensive properties gives

41. Ideal gas and Real gas Real gas
deviations from the perfect gas law because molecules interact with one another
Repulsive forces are significant only when molecules are almost in contact
Attractive intermolecular forces have a relatively long range and are effective over several molecular diameters

42. Ideal gas and Real gas P moderate Z < 1 Real gas
The compression factor
For ideal gas
P moderate Z < 1

43. Ideal gas and Real gas
Real gas
The compression factor

44. Ideal gas and Real gas Equation of state for Real gas
Virial equation of state
How to describe this P-V behavior?

45. Ideal gas and Real gas Equation of state for Real gas
Virial equation of state

46. Ideal gas and Real gas Equation of state for Real gas
Virial equation of state

47. Ideal gas and Real gas Equation of state for Real gas
Virial equation of state
The second virial coefficient B′ can be obtained from measurements of the density ρ of a gas at a series of pressures. Show that the graph of p/ρ against p should be a straight line with slope proportional to B′.

48. Thank You !