The Empirical Gas Laws

1. The Empirical Gas Laws Lesson 2

2. The Empirical Gas Laws: Pressure Kinetic Molecular Theory states that all substances are made of tiny particles that are in constant motion. • Gases have the most amount of movement in the three states of matter. The movement of the particles is independent of each other as each particle travels in a straight line until it bumps into another particle or wall of its container.

3. The movement of the particle is referred to as kinetic energy. As the energy increases so does the movement of the particles.

4. Quantitative measurements on gases were first made by the English chemist Robert Boyle (1627 - 1691). Boyle used two instruments to measure pressure: the manometer, which measures differences in pressure, and the barometer, which measures the total pressure of the atmosphere

5. Units of Pressure • Units of pressure were originally all based on the length of the column of liquid, usually mercury, supported in a manometer or barometer. • By far the most common of these units was the mm Hg.

6. Units of Pressure • However, the modern SI unit of pressure is derived from the fundamental units of the SI. • Pressure is force per unit area, and force is the product of mass times acceleration, so the SI unit of pressure is the kg m s2/m2 or newton/m2, • which is called the pascal (Pa).

7. Units of Pressure • The standard temperature and pressure that gas experiments are done at is referred to as SATP. • Standard Ambient Temperature and Pressure is 25° C and 100kPa.

8. Units of Pressure • All of the older units of pressure have now been redefined in terms of the pascal. • One standard atmosphere, the pressure of the atmosphere at sea level, is by definition exactly 101,325 Pa. • The torr, named in honour of Torricelli, is defined as 1/760 of a standard atmosphere or as 101,325/760 Pa. • The mmHg can be considered identical to the torr. The term bar is used for 100,000 Pa, which is slightly below one standard atmosphere. 

9. Boyle’s Law

10. Boyle’s Law • Boyle used the manometer and barometer to study the pressures and volumes of different samples of different gases. The results of his studies can be summarized in a simple statement which has come to be known as Boyle's law: • At any constant temperature, the product of the pressure and the volume of any size sample of any gas is a constant.

11. Boyle’s Law • For a particular sample of any gas, Boyle's law can be shown graphically as done in the Figure below. It is more common to express it mathematically as  P1V1 =P2V2

12. Boyle’s Law • This means that the pressure and the volume vary inversely; as the pressure increases the volume of the sample gas must decrease and vice versa.

13. Boyle’s Law – Example 1 • A sample of gas occupies a volume of 47.3 cm3 at 25°C with a pressure of 30 mm of mercury. If the pressure is increased to 75 mm of mercury, what will the volume be at the new pressure?

14. Boyle’s Law – Example 1

15. Boyle’s Law – Example 2 • A student is trying to compress the gas in a cylinder that has an initial volume of 1000 cm3 and a pressure of 100 kPa. The student decreases the volume by 500 cm3. What is the pressure of the gas in the cylinder?

16. Boyle’s Law – Example 2

17. Questions: Page 335 # 1-5

18. Charles Law: The Relationship between the Volume and Temperature

19. Celsius and Kelvin Temperature • In SI Metric the temperature scale is defined as Kelvin temperature scale. • The degree unit is the Kelvin (K). The symbol for the unit is K, not o K.  • Kelvin temperatures must be used in many gas law equations in which temperature enters directly into the calculations. 

20. Celsius and Kelvin Temperature • The Celsius and Kelvin scale are related unit for unit. One degree unit on the Celsius scale is equivalent to one degree unit on the Kelvin scale. The only difference between these two scales is the zero point.  • The zero point on the Celsius scale was defined as the freezing point of water, which means that there are higher and lower temperatures around it. 

21. Celsius and Kelvin Temperature • The zero point on the Kelvin scale - calledabsolute zero– it corresponds to the lowest temperature that is possible.  It is 273.15 units lower than the zero point on the Celsius scale.

22. Celsius and Kelvin Temperature • So this means that 0 K equals -273.15 oC and 0oC equals 273.15 K. Thermometers are never marked in the Kelvin scale. • If we need degrees in Kelvin the following relationships are to be used.  TK=  tc  +  273.15  or      tc  =  TK  -  273.15

23. Questions • Liquid nitrogen (sometimes abbreviated LOX) is used in liquid-fuel rockets. Its boiling point is -183oC. What is this temperature in Kelvin’s?  • A substance is heated from 300 K to 315 K. What is the change in temperature expressed in °C.

24. Questions • Perform the following conversions

25. Questions • A clinical thermometer registers a patient's temperature to be 37.13oC. What is this in Kelvin’s? • The coldest permanently inhabited place on earth is the Siberian village of Oymyakon in Russia. In 1964 the temperature reached a shivering -71.11oC. What is this temperature in Kelvin’s?

26. Helium has the lowest boiling point of any liquid. It boils at 4 K. What is this in oC?

27. Charles Law

28. Charles Law • The direct relationship between the volume of a gas and the temperature of the gas (on the Kelvin temperature scale) is known as Charles Law. According to this law, • as the temperature of a gas increases, the volume increases proportionally, provided that the pressure and the amount of gas remains the same.

29. Charles's Law • However, as the graph above shows, the volume extrapolates to zero at a temperature of -273.15oC. If this temperature were taken as the zero of a temperature scale then all negative temperatures could be eliminated. 

30. Charles's Law • Such a temperature scale is now the fundamental scale of temperature in the SI. It is called the absolute scale, the thermodynamic scale, and the Kelvin scale. Temperature on the Kelvin scale, and only on the Kelvin scale, is symbolized by T. 

31. Charles’s Law Charles’s Law can be written as V1T2= V2T1

32. Example: 1 • The volume of a sample of gas is 23.2 cm3 at 20oC. If the gas is ideal and the pressure remains unchanged what is its volume at 80oC?

33. Example 1

34. Example: 2 • Compressed oxygen is widely used in hospitals and retirement homes. To make it easier to transport, the oxygen is cooled. How many degrees Celsius would the gas be if 200 L’s at 23 degrees Celsius is compressed to 40 L?

35. Example: 2

36. Questions: page 338 # 6-9

37. Dalton’s Law of Partial Pressures

38. Dalton’s Law of Partial Pressures • When Dalton was conducting his studies, which led him to the atomic-molecular theory of matter, he also included studies of the behaviour of gases. These led him to propose, in 1803, what is now called Dalton's law of partial pressures:  • Partial Pressures - The pressure, p, that a gas in a mixture would exert if it were the only gas in the same volume, at the same temperature.

39. Dalton’s Law of Partial Pressures Dalton law states that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.

40. Dalton’s Law of Partial Pressures The laws equation is expressed as: Ptotal = P1 + P2 + P3 + ... Where Ptotal is the total pressure of the mixture and P1, P2, and P3 are the partial pressures of each has in the mixture.

41. Dalton’s Law of Partial Pressures

42. This law can be explained by the molecular kinetic theory, the type of gas particle doesn’t matter because they are all behaving in the same manner. They are all consistently moving, and colliding with each other and with the walls of the container.

43. Example • The air that we are breathing right now is primarily composed of nitrogen, oxygen and carbon dioxide. What is the air pressure in this room if the following pressures occur? N2 = 79.03 kPa, O2 = 21.28 kPa and CO2 = 1.01 kPa.

45. Questions page 339 # 10, 11, 12.