Chapter 5. Gases Chem. 1A van Koppen Consider the three physical states of substances: solid, liquid and gas. Gases occupy the full volume of their containers. Gases are generally highly compressible. When a gas is subjected to pressure, its volume decreases. Gases form homogeneous mixtures with other gases. Chemical properties vary significantly for gases. Physical properties are simpler to understand. The most useful physical properties for describing gases are: volume, V, pressure, P, and temperature, T. By studying these properties, we can understand the behavior of gases. Pressure is the force acting on an object per unit area: P = F/A Gravity exerts a force on the earth's atmosphere. Atmospheric pressure is measured using a barometer. If a tube, completely filled with mercury (Hg), is inverted into a dish of mercury, mercury will flow out of the tube until the pressure of the column of mercury equals the pressure of the atmosphere on the surface of the mercury in the dish. The height of the mercury in the tube is 760 mm for 1 atm of pressure. Units: 1 atm = 760 mm Hg = 760 torr = 14.69 psi = 1.013251 x 105 Pa atm = standard atmosphere, psi = pounds per square inch, Pa = pascal = 1 kg m-1 sec-2 Gas Laws: Boyle's Law: V α (1/P) (fixed temperature and fixed amount of gas) The volume of a fixed quantity of gas at a fixed temperature is inversely proportional to pressure, that is, an decrease in pressure causes the volume to increase. Charles' Law: V α T (fixed pressure and fixed amount of gas) The volume of a fixed quantity of gas at constant pressure increases as the temperature increases. A plot of V versus T is a straight line and the intercept of this plot, when T is measured in oC, is – 273.15 oC. The absolute zero of temperature is defined as 0 K = – 273.15 oC. T(in Kelvin) = T(in oC) + 273.15 Avogadro's Law: V α n (fixed pressure and fixed temperature) For a gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas, n. Ideal Gas Law: PV = nRT where T is the absolute temperature in Kelvin, K The ideal gas law holds for gases at P ≤ 1 atm and is more accurate as pressure decreases, the gas must be far from its liquification point. Real gases behave "ideally" at low pressure. R = Universal Gas Constant R = 0.08206 L atmmol K R = 1.987 calmol K R = 8.314 Jmol K = 8.314 kg m2sec2 mol K STP = standard temperature and pressure T = 0oC and P = 1 atm The state of a gas is defined by P, V, T, n. For a change in state: P1, V1, T1, n1 —> P2, V2, T2, n2 P1V1n1T1 = P2V2n2T2 P1V1T1 = P2V2T2 at constant n P1V1 = P2V2 at constant n and T V1T1 = V2T2 at constant n and P How about when T and P are constant? The variables that remain constant cancel out. Gas Mixtures, Partial Pressures and Mole Fraction Suppose a mixture of gases occupies a container at a certain temperature. Each gas in the mixture exerts a pressure, called the partial pressure of that gas. At low pressures each gas independently obeys the ideal gas law, so that P1V = n1RT P2V = n2RT P3V = n3RT etc. Dalton's law states that the total pressure Ptot is the sum of the partial pressures of the individual gases. Ptot = P1 + P2 + P3 + ... = (n1 + n2 + n3 + ...)RTV = ntotRTV where ntot = total number of moles in the gas mixture The mole fraction of a given component in a gas mixture is the number of moles of that component, divided by the total number of moles in the gas mixture. χ1 = n1ntot = n1n1 + n2 + n3 + ... P1 = χ1 PtotKinetic Theory of Gases One of the goals of physics and chemistry is to quantitatively interpret observed properties of a system in terms of the kinds of atoms or molecules present in the system and in terms of the forces of interaction between the atoms and molecules. In kinetic theory of gases, the laws of mechanics and statistics are applied to develop a model to predict properties of a system of atoms or molecules of an ideal gas. A good model will predict properties in agreement with the observed properties. The physical properties of gases are relatively simple and are relatively easy to describe theoretically, so we can use a simple model. Kinetic Theory of Gases (basic assumptions): 1) A pure gas consists of a large number of identical particles (atoms or molecules) separated by a distance that is large compared with their size (assume particles have negligible volume). 2) The molecules are constantly moving in random directions with a distribution of speeds. 3) The molecules exert no forces on one another between collisions, so between collisions they move in straight lines with constant velocity. 4) The collisions of molecules with the walls of the container are elastic, no energy is lost in a collision. Using this model, the relationship between speeds of molecules and temperature was shown: (KE)av = 12mu2 = 32RT u2 = average of the square of the speed (KE)av = Total average kinetic energy associated with random motion of molecules in one mole of gas (molar translational energy of an ideal gas). (KE)av = (3/2) RT provides an interpretation of temperature. A major triumph of kinetic theory! Temperature is associated with the average kinetic energy of a large number of molecules, not just a single molecule. It is a statistical concept. Random motion is often called thermal motion. Speed Distributions Particles have a distribution of speeds due to collisions with other particles and the walls of the container. For a given temperature, given sufficient time, particles will attain an equilibrium distribution of velocities. This distribution is used to compute the average velocity, uav, the most probable velocity, ump, and the root mean square velocity, urms. uav = u = 8RTπM ump = 2RTM urms = u2 = 3RTM Units: R = 8.314 kg m2sec2 mol K , T is in Kelvin, K , M is in kgmol, speed, u , is in msec For two gases at the same temperature, T, the lower the molar mass, M, the greater the velocity. u1u2 = M2M1 Intermolecular Collisions The number of collisions between molecules in a gas is directly proportional to the average speed, u, and the