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1. Engineering Chemistry Level Zero Prof. Dr. Moustapha Ibrahim Salem [email protected] 01005857099

2. Ground Rules for Lectures Arrive on time. Listen actively and attentively. Bring something to write with and in. Turn your cell phone off. Do not leave class early without okaying it with the instructor in advance. Ask questions if you are confused. Try not to distract or annoy your classmates

3. Gases

4. Outlines The gas laws The ideal gas equation Applications of the ideal gas equation Gas mixtures and partial pressures The kinetic molecular theory of gases Real gases: deviation from ideal gas behavior

5. Gases Substances exist in any of the following distinct states: ( i ) solids, (ii) liquids, and (iii) gases.

6. Substances that are liquids or solids under ordinary conditions can also exist in the gaseous state, where they are often referred to as vapors. For example, water substance (H 2 O) can exist as liquid water, solid ice, or water vapor

7. Gases differ significantly from solids and liquids in several respects: A gas expands spontaneously to fill its container. Consequently, the volume of a gas equals the volume of its container. Gases also are highly compressible: When pressure is applied to a gas, its volume readily decreases. Solids and liquids, on the other hand, do not expand to fill their containers and are not readily compressible.

8. The gas laws The gas laws are equations developed to express the relationships between the four variables that are needed to define the physical condition, or state, of a gas.

9. These four variables are as follows: Temperature. Pressure. Volume. Amount of gas (usually expressed as number of moles)

10. Because volume is easily measured, the gas laws to be studied expressed the effect of one of the variables on volume, while the remaining two variables held constant

11. Pressure Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa. If you’ve ever inflated a tire, you’ve probably made a pressure measurement in pounds (force) per square inch (area).

12. Pressure Units KEY UNITS AT SEA LEVEL 101.325 kPa (kilopascal) 1 atm 760 mm Hg 760 torr 14.7 psi

13. Volume Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m 3 . A more common and convenient unit is the liter, L. Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…)

14. Amount (moles) Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas. By definition, one mole of a substance contains approximately 6.022 x 10 23 particles of the substance. You can understand why we use mass and moles!

15. Temperature Temperature is the measurement of heat…or how fast the particles are moving. Gases, at room temperature, have a lower boiling point than things that are liquid or solid at the same temperature. Remember : Not all substance freeze, melt or evaporate at the same temperature. Water will freeze at zero degrees Celsius. However alcohol will not freeze at this temperature.

16. Temperature (cont.) Always use absolute temperature (Kelvin) when working with gases. ºF ºC K -459 32 212 -273 100 273 373

17. STP: you need to memorize this Standard Temperature & Pressure 0°C 273 K 1 atm or 101.325 kPa

18. How do they all relate? Some relationships of gases may be easy to predict. Some are more subtle. Now that we understand the factors that affect the behavior of gases, we will study how those factors interact.

19. Boyle’s Law This lesson introduces Boyle’s Law, which describes the relationship between pressure and volume of gases. P V P 1 V 1 = P 2 V 2

20. Boyle’s Law This law is named for Charles Boyle, who studied the relationship between pressure , p, and volume , V, in the mid-1600s. Boyle determined that for the same amount of a gas at constant temperature, results in an inverse relationship : when one goes up, the other comes down. pressure volume

21. Boyle’s law states that the volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure

22. The value of the constant depends on temperature and on the amount of gas in  

23. Charles’ Law This lesson introduces Charles’ Law, which describes the relationship between volume and temperature of gases. V T V 1 T 1 = V 2 T 2

24. Notice that the extrapolated (dashed) line passes through . Note also that the gas is predicted to have zero volume at this temperature. However, this condition is never realized because all gases liquefy or solidify before reaching this temperature  

25. Absolute zero In 1848 William Thomson (1824–1907), a British physicist whose title was Lord Kelvin, proposed an absolute temperature scale, now known as the Kelvin scale. On this scale 0 K, called absolute zero, equals .  

26. Charles’s law states The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature.

27. Mathematically, Charles’s law takes the form: with the value of the constant depending on the pressure and on the amount of gas  

28. Charles’ Law This law is named for Jacques Charles, who studied the relationship volume , V, and temperature , T, around the turn of the 19 th century. This defines a direct relationship: With the same amount of gas he found that as the volume increases the temperature also increases . If the temperature decreases than the volume also decreases . volume temperature

29. Gay-Lussac’s Law The pressure and absolute temperature (K) of a gas are directly related at constant mass & volume. P T P 1 T 1 = P 2 T 2

30. What does it mean? For a gas at constant mass and volume, the pressure and temperature are directly related. pressure temperature

31. Avogadro’s Principle Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any ideal gas V n V 1 n 1 = V 2 n 2

32. Avogadro’s law states that the volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas. In other words, the gas volume is not only a function of its temperature and its pressure but also depends on its amount (number of moles)

33. where (n) is number of moles. Thus, for instance, doubling the number of moles of gas causes the volume to double if (T) and (P) remain constant.  

34. Avogadro’s hypothesis Equal volumes of gases at the same temperature and pressure contain equal number of molecules. For example, of any gas at and contain gas molecules (that is, 1 mol)  

35. What does it mean? For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas. volume pressure

36. The ideal gas equation The gas laws, discussed in previous section, can be represented as follows: Boyle’s law: constant Charles’s law: constant Avogadro’ law: constant  

37. and if we call the proportionality constant R, we obtain an equality:  

38. Numerical values of R

39. Combined Gas Law It is a law that combines the previous laws into one . P 1 V 1 T 1 = P 2 V 2 T 2 P 1 V 1 T 2 = P 2 V 2 T 1

40. Applications of the ideal gas equation Since the density has units of mass per unit volume , we can arrange the ideal gas equation to obtain the similar units of moles per unit volume.  

42. Gas mixtures and partial pressures While studying the properties of air, John Dalton (1766–1844) made an important observation that is the total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone

43. Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P 2 + ...

44. Dalton’s law The pressure exerted by a particular component of a mixture of gases is called the partial pressure of that component.  

45. Suppose a gas mixture consists of 3 components For 1 st component For 2 nd component For 3 rd component  

47. Partial pressures and mole fractions The ratio is called the mole fraction of component in the gas mixture, which is denoted . The mole fraction is a dimensionless number that expresses the ratio of the number of moles of one component in a mixture to the total number of moles in the mixture.  

48. The kinetic molecular theory of gases We need a model that helps us explain what happens to gas particles when conditions such as pressure or temperature change.

49. Such a model, known as the kinetic-molecular theory of gases, was developed over a period of about 100 years, culminating in 1857 when Rudolf Clausius (1822–1888) published a complete and satisfactory form of the theory

50. Graham’s law According to the kinetic-molecular theory of gases, the average kinetic energy of any collection of gas molecules, , has a specific value at a given temperature. Thus, for two gases at the same temperature a gas composed of low-mass particles, such as He, has the same average kinetic energy as one composed of more massive particles, such as Xe .  

51. The mass of the particles in the He sample is smaller than that in the Xe sample. Consequently, the He particles must have a higher ( ) speed than the Xe particles. The equation that expresses this fact quantitatively is:  

52. In 1846 Thomas Graham (1805–1869) discovered that the speed of gas molecules is inversely proportional to the square root of its molar mass according to the following equation:  

53. The kinetic-molecular theory (the theory of moving molecules ) is summarized by the following statements Gases consist of large numbers of molecules that are in continuous, random motion. The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained. Attractive and repulsive forces between gas molecules are negligible.

54. Energy can be transferred between molecules during collisions but, as long as temperature remains constant, the average kinetic energy of the molecules does not change with time. The average kinetic energy of the molecules is proportional to the absolute temperature. At any given temperature the molecules of all gases have the same average kinetic energy.

55. Real gases: deviation from ideal behavior

56. At high pressures (generally above 10 atm) the deviation from ideal behavior is large and different for each gas. Real gases, in other words, do not behave ideally at high pressure At lower pressures (usually below 10 atm), however, the deviation from ideal behavior is small, and we can use the ideal-gas equation without generating serious error

57. As temperature increases, the behavior of a real gas more nearly approaches that of the ideal gas In general, the deviation from ideal behavior increases as temperature decreases, becoming significant near the temperature at which the gas liquefies

58. The van der Waals equation The term accounts for the attractive forces. The equation adjusts the pressure upward by adding because attractive forces between molecules tend to reduce the pressure  

59. The added term has the form because the attractive force between pairs of molecules increases as the square of the number of molecules per unit volume, .