Kinetic Theory of Gases PDF

Kinetic Theory of Gases Table 1. shows the locations in the periodic table of those elements that are commonly found in the gaseous, liquid, and solid states.  Gas is a substance that is characterized by widely separated molecules in rapid motion. Gases assume the volume and sh...

Kinetic Theory of Gases Table 1. shows the locations in the periodic table of those elements that are commonly found in the gaseous, liquid, and solid states.  Gas is a substance that is characterized by widely separated molecules in rapid motion. Gases assume the volume and shape of their containers Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids.  Gases are normally in the gaseous state at 25°C and 1 atm pressure Vapor is the gaseous form of any substance that is liquid or solid at normal temps. or pressure.  Pressure is the forces exerted by gas on the walls of the container Force Pressure = Area SI unit is the Pascal = N/m2 = (kg m s-2)/m2 = 1 kg / ms2 The pressure of a gas is considered as the measurements of a gas pressure relative to the atmospheric pressure  The atmospheric pressure is the change in gas pressure with distance from earth's surface The gas pressure is measured by Barometer that is invented by Torricelli. The unit of the barometer measurement is 1 Torr = 1mm Hg 1 atm pressure = 760mm Hg = 760 Torr 1 atm is equivalent to 101325 Pa =101.325 KPa  The Volume occupied by the gas is inversely proportional to the pressure at constant temperature and number of moles P a 1/V P *V = constant P1 * V1 = P2 * V2 A weather balloon has a volume of 400L at atmospheric pressure (1.0atm). The balloon is released to a height of 6.5 km where the pressure is 0.4 atm. What is the new volume of the balloon? Answer: Using Boyle's Law P1 V1 = P2 V2 V2 = V1 * P1/P2 V2 = 400L * 1.0atm/0.40atm = 1000 L  At constant pressure, the volume of a fixed quantity of the gas is directly dependent on its absolute temperature. VaT V = constant *T V1/T1 = V2 /T2 Temperature must be in Kelvin T (K) = t (0C) + 273.15 As T increases V increases A sample of CO2 occupies 7.50 L at 150°C. If the pressure remains constant, calculate the temperature at which the CO2 will occupy 3.76 L. Answer: V1 = 7.60L V2 = 3.76L T1 = (273.15 + 150) K = 423.2 K T2 = ? T2 = V2 / V1 x 423.2 K = 3.76 L / 7.50 L x 423.2 K = 212 K.  The pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. P P1 P2 PaT T = a con stant or T1 = T2 A car tire in the summer has a pressure of 220 kPa at a temperature of 25°C.In the winter, the tire pressure is measured at 176 kPa. Calculate the temperature of the air inside the tire. Answer: P1 = 220 kPa P2 = 176 kPa T1 = (25 + 273) K = 298K T2 = ? The volume of a gas at constant T and P is directly proportional to the number of moles of gas. V a number of moles (n) V = constant x n V1 / n1 = V2 / n2 Example 1 mole CO2 occupies 22.414 L at 273.15K, and P = 1.000 atm; 2 moles of CO2 gas would occupy 44.86 L. V a 1/P (at constant n and T) Boyle’s Law V a T (at constant n and P ) Charles’ and Gay Lussac's Law Van (at constant P and T ) Avogadro’s Law PaT ( at constant V ) Amonton’s Law  Va nT P V = constant x nT = R nT P P PV = nRT  Calculate the volume occupied by 32.06 g of Ne gas at 5.0°C and 630 mm Hg. Answer: P = 630 mm Hg x 1 atm/760 mm Hg P = 0.8289 atm T = (5 °C + 273 °C) 1 ºC / 1 K = 278 K n Ne = 32.06 g Ne x 1 mol Ne / 20.18 g = 1.589 moles P V = n RT V = n RT / P V= 1.589 moles x 0.08206 L atm / (K mol) x 278. K / 0.829 atm = 43.7L  PV = nRT m is the mass of the gas in g m M is the molar mass of the gas PV=M RT m d = V = PM RT Molar Mass (M ) of a Gaseous Substance dRT M= P d is the density of the gas in g/L A 2.10 L vessel contains 4.65 g of a gas at 1.00 atm and 27.0 0C. What is the molar mass of the gas? M = dRT P m 4.65 g g d=V = = 2.21 2.10 L L g 2.21 L x 0.0821 L atmx300.15 K mol K M= 1 atm M = 54.5 g/mol The total pressure, Ptotal, of a mixture of gases is the sum of their individual gas partial pressures V and T are constant P11 P2 Ptotal = P1+ P2 Consider a case in which two gases, 1 and 2, are in a container of volume V. P1 / Pt = [n1 RT/V] / [(n1 + n2)RT/V] = n1 / (n1 + n2) = X1 where X1 is defined as the mole fraction of gas 1 The mole fraction is a dimensionless quantity; it gives the ratio of the number of moles of gas 1 to the total number of moles of gases present in the mixture  Partial pressure of gas 1 (P1) = X1 * PT  Partial pressure of gas 2 (P2) = X2 * PT In general, in gaseous mixtures, the partial pressure of the ith component is related to the total pressure by Pi = Xi PT where Xi is the mole fraction of gas i. A sample of natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)? Pi = Xi PT PT = 1.37 atm 0.116 = 0.0132 Xpropane = 8.24 + 0.421 + 0.116 Ppropane = 0.0132 x 1.37 atm = 0.0181 atm (A) If 4 moles of gas are added to a container that already holds 1 mole of gas, how will the pressure change inside the container? a. The pressure will be five times higher. b. The pressure will double. c. The pressure will be four times higher. d. The pressure will not change (B)At a certain temperature and pressure, 0.20 mol of carbon dioxide has a volume of 3.1 L. A 3.1-L sample of hydrogen at the same temperature and pressure ____. a. has the same mass b. contains the same number of atoms c. has a higher density d. contains the same number of molecules