Unit IX: Gases… Part II

Unit IX: Gases… Part II Chapter 11… think we can cover gases in one day? Obviously not… since this is day 2… but let’s plug away at it!

Density of Gases • You are trying to determine, by experiment, the formula of a gaseous compound to replace chlorofluorocarbons in air conditioners. You have determined the empirical formula is CHF2, but now you want to know the molecular formula. To do this, you need the molar mass of the compound. You therefore do another experiment and find that a 0.100g sample exerts a pressure of 70.5 mm Hg in a 256mL container at 22.3°C. What is the molar mass of the compound? What is its molecular formula?

Density of Gases • d = 0.100g/0.256L = 0.391 g/mL • M = dRT/P • M = (0.391)(0.082057)(295.5)/(0.0928) • Molar mass = 102 g/mol • Formula of the compound = C2H2F4

Gas Laws and Chemical Reactions • This means stoichiometry… oh joy! • You are asked to design an air bag for a car. You know that the bag should be filled with gas with a pressure higher than atmospheric pressure, say 829 mm Hg, at a temperature of 22.0°C. The bag has a volume of 45.5 L. What quantity of sodium azide, NaN3, should be used to generate the required quantity of gas? The gas producing reaction is: 2NaN3 (s)  2Na(s) + 3N2(g)

Gas Laws and Chemical Reactions • P = 829 mm Hg = 1.09 atm • V = 45.5 L • T = 22.0°C = 295.15 K • PV = nRT • (1.09)(45.5) = n(0.082057)(295.15) • n = 2.05 mol N2 • 2.05mol N2 (2mol NaN3 /3mol N2)(65.01g/1mol NaN3) = 88.8g NaN3

Gas Mixtures and Partial Pressure • Breathe in • That air contained a mixture of nitrogen, oxygen, argon, carbon dioxide, water vapor, and small amounts of other gasses. • Each of these gases exerts its own pressure and the sum of the pressures exerted by each gas equals the total pressure

Gas Mixtures and Partial Pressures • Daltons Law of Partial Pressure: • the pressure of a mixture of ideal gases is the sum of the partial pressures of the different gases in the mixture • Ptotal = PA + PB + PC + … • Ptotal = nA(RT/V) + nB(RT/V) + nC(RT/V) + …

Gas Mixtures and Partial Pressures • Mole Fraction (X) • the number of moles of a particular substance in a mixture divided by the total number of moles of all substances present. • XA = nA/(nA + nB + nC) = nA/ntotal • PA = XAPtotal • The pressure of a gas in a mixture of gases is the product of its mole fraction and the total pressure of the mixture.

Gas Mixtures and Partial Pressures • Halothane, C2HBrClF3, is a nonflammable, nonexplosive, and nonirritating gas that is commonly used as an inhalation asnesthetic. The total pressure of a mixture of 15.0 g of halothane vapor and 23.5 g of oxygen gas is 855 mm Hg. What is the partial pressure of each gas? • Phalothane = 80.2 mm Hg • Poxygen = 775 mm Hg (pg 532)

Kinetic Molecular Theory • Description of the behavior of matter on the molecular or atomic level.

Kinetic Molecular Theory • Gases consist of particles (molecules or atoms) whose separation is much greater than the size of the particles themselves. • 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.

Kinetic Molecular Theory • The particles of a gas are in continual, random, and rapid motion. As they move, they collide with one another and with the walls of their container, but they do so without loss of energy.

Kinetic Molecular Theory • The average kinetic energy of gas particles is proportional to the gas temperature. All gases, regardless of their molecular mass, have the same average kinetic energy at the same temp.

Molecular Speed and Kinetic Energy • Speed of an individual molecule: • KE = ½mu2(u = speed of molecule) ____ __ • Average Speed of molecules: KE = ½mu2 • Experiments show the KE of a sample of gas molecules is directly proportional to temperature with a proportionality constant of 3/2R…. Using this and the knowledge that KE is proportional to ½mu2 and T

Molecular Speed and Kinetic Energy • Maxwell’s Equation : • Shows that the speed of gas molecules are related directly to the temperature. • root-mean-square (rms speed) • √(u2) = √(3RT/M) • R = 8.3145 J/K·mol • M = molar mass

Molecular Speed and Kinetic Energy • Calculate the rms speed of oxygen molecules at 25°C. • √(u2) = √(3RT/M) • √(u2) = √(3(8.3145)(298)/(32.0 kg/mol)) • U = 482 m/s

Diffusion and Effusion • Diffusion • the spread of one substance throughout a space or throughout a second substance. • The mixing of molecules of two or more gases due to their random molecular molecules is due to this

Diffusion and Effusion • Effusion • the escape of gas molecules through a tiny hole into an evacuated space.

Diffusion and Effustion • The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.

Diffusion and Effusion • Graham’s Law: • The rate of effusion of a gas (the amount of gas moving from one place to another in a given amount of time) is inversely proportional to the square root of it’s molar mass (rate of effusion of gas 1) = √molar mass of gas 2 (rate of effusion of gas 2) molar mass of gas 1

Diffusion and Effusion • Tetrafluoroethylene, C2F4, effuses through a barrier at a rate of 4.6 x 10-6 mol/h. An unknown gas, consisting only of boron and hydrogen, effuses at a rate of 5.8 x 10-6 mol/h under the same conditions. What is the molar mass of the unknown gas? • 63 g/mol

Nonideal Behavior: Real Gases • In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure

Nonideal Behavior: Real Gases • Even the same gas will show wildly different behavior under high pressure at different temperatures.

Nonideal Behavior: Real Gases • The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

(P + ) (V − nb) = nRT n2a V2 Nonideal Behavior: Real Gases • Johannes van der Waals studied the breakdown of the ideal gas law and developed an equation to correct for the errors arising from nonideality • van der Waals equation:

Unit IX: Gases… Part II