Chapter 5 Gases and Their Properties Why Study Gases? some very common elements exist in a gaseous state our gaseous atmosphere provides one means of transferring energy and material throughout the globe gases are the most understood states of matter Gas Pressure The Properties of Gases Units of pressure: - millimeters of mercury (mmhg) [also known as torr] - pascal (Pa) [SI unit of pressure] - atmospheres (atm) - bar 1 atm = 760 torr/mmhg = 101.325 kpa = 1.013 bar
How do we measure pressure? With a barometer The kinetic Molecular Theory of Gases What is the kinetic molecular theory? But first, what is kinetic energy? Kinetic energy is the movement of molecules. It is dependent on temperature as shown below KE T Principle features of the kinetic molecular theory Gases consist of molecules whose separation is much greater than the size of the molecules themselves. The molecules of a gas are in continual, random, and rapid motion. The average kinetic energy of gas molecules is proportional to the gas temperature. All gases, regardless of their molecular mass, have the same kinetic energy at the same temperature. Gas molecules collide with one another and with the walls of their container, but they do so without loss of energy.
Also, kinetic energy is proportional to the average mass and speed of a molecule. This relationship is shown below. KE = ½ (mass) (speed) 2 or KE = ½ mu 2 ½mu 2 = CT where C is a proportionality constant The Effect of Molecular Mass on the Distribution of Speeds Average Kinetic Energy E = 3RT 2N A Try Example 5-2 on page 195
Distribution of Molecular Speeds Rates of Gas Movement u avg = 3RT MW This is called the root-mean-square Diffusion and Effusion Diffusion mixing of molecules of two or more gases due to their molecular motions Effusion the movement of gas through a tint opening in a Container into another container where the pressure is very low
Graham s Law of Effusion Rate of Effusion of gas 1 = molar mass of gas 2 Rate of effusion of gas 2 molar mass of gas 1 Gas Laws: The Experimental Basis Boyle s Law Robert Boyle observed that the volume of a fixed amount of gas at any given temperature is inversely proportional to the pressure exerted by the gas P 1 V At constant temperature
Think about this in a different way such as circles in two different size squares The smaller the square, the more the ten circles press on the sides of the squares. How can you use Boyle s law in regard to inflating a bike tire? Boyle also found that the pressure multiplied volume is a constant (C B ) at a given temperature where C B is determined by the number of moles of gas and the Temperature. PV = C B Therefore, this means that if the pressure-volume product is known for one set of conditions, then it is also known for a new set of conditions. P 1 V 1 = P 2 V 2 The Effect of Temperature on Gas Volume: Charles s Law Charles s law states that the volume of a fixed quantity of gas at constant pressure increases as you increase the temperature V T At constant pressure
Using a proportionality constant, C C, we can write the equation: Or V = C C T V =C C T V 1 = V 2 T 1 T 2 Avogadro s Law The volume of a gas at a given temperature and pressure is directly proportional to the quantity of the gas V n At constant temperature and pressure V = C A n Where C A is the proportionality constant The Gay-Lussac s Law This law states that pressure is proportional to temperature at a constant volume P T At constant volume P 1 = P 2 T 1 T 2
The Gay-Lussac s Law of Combining Volumes The ratio of the volumes of gases in reaction is always a small whole number, as long as the volumes were measured at the sample temperature and pressure. If all the laws were combined, the result would be: V nt P Then add in a proportionality constant, R which gives the Ideal Gas Law Equation. PV = nrt Two Sets of Conditions P 1 V 1 = P 2 V 2 T 1 T 2
Gas Stoichiometry using the Ideal Gas Law Equation Let s try some problems on page 217-221. Determination of Molar Mass by The Ideal Gas Law Equation n = PV RT Set equal to one another. Rearrange: m MW MW n = = PV RT = mrt PV m MW Try Example 5-9 on page 211 Gas Mixtures and Partial Pressures The air that you breathe is a mixture of oxygen, nitrogen, carbon dioxide etc Each one of these exerts there own pressure known as their partial pressure. According to Dalton s Law of Partial Pressure, the total pressure Of the mixture of gas is the sum of all the partial pressures. P total = P 1 + P 2 + P 3..
P total = n total (V/RT) How would you determine the partial pressure of each gas in a mixture? by multiplying the mole fraction of the gas by the total pressure P A = X A P total Try Example 5-10 on page 215 The Van Der Waals Equation
Non-Ideal Gases Fig 10-4 Pg 431 Even though bromine is a liquid at room temperature and pressure, enough molecules escape into the gas phase to give the gas above a liquid sample a distinct red color. Courtesy John Olmsted Fig 10-5 Pg 432 Variations in PV/nRT with pressure for chlorine gas at room temperature. The inset shows the low-pressure region on an expanded scale. Fig 10-6 Pg 432 Variation in PV/nRT For He, F 2, CH 4, and N 2 at 300K.