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Unit 8 Characteristics of Gas Pressure Partial Pressures Mole Fractions Boyles Law Charles Law Avogadro’s Law Guy-Lussac’s Law Ideal Gas Law Ideal Gases Real Gases Density of Gases Volumes of Gases Standard molar volume Gas stoichiometry Gas Laws Effusion/Diffusion Graham’s Law Expansion – gases expand to fill their containers Compression – gases can be compressed Fluids – gas particles flow past each other Density – gases have low density 1/1000 the density of the equivalent liquid or solid Gases effuse and diffuse 1. Gases consist of large numbers of tiny particles that are far apart relative to their size. 2. Collisions between gas particles and between particles and container walls are elastic. Elastic collision – collision in which there is no net loss of kinetic energy 3. Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy. 4. There are no forces of attraction between gas particles. 5. The temperature of a gas depends on the average kinetic energy of the particles of the gas. At the same conditions of temperature, all gases have the same average kinetic energy KE 1 2 mv 2 m = mass v = velocity At the same temperature, small molecules move FASTER than large molecules V = velocity of molecules M = molar mass R = gas constant T = temperature A force that acts on a given area Force Pressure = Area The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century Called a barometer The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high 1 atmosphere (atm) 760 mm Hg (millimeters of mercury) 760 torr 1.013 bar 101300 Pa (pascals) 101.3 kPa (kilopascals) 14.7 psi (pounds per square inch) Standard Temperature and Pressure (STP) 1 atmosphere 273 K Partial pressure – pressure exerted by particular component in a mixture of gases Dalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of the component gases Pt = P1 + P2 + P3+… Mole fraction – expresses the ratio of the number of moles of one component to the total number of moles in the mixture P1 = Pt or P1 = X1Pt X1 = mole fraction of gas 1 Example: The mole fraction of N2 in air is 0.78 (78% of air is nitrogen). What is the partial pressure of nitrogen in mmHg? PN2 = (0.78)(760 mmHg) = 590 mmHg Gas collected by water displacement is always mixed with a small amount of water vapor Must account for the vapor pressure of the water molecules Ptotal = Pgas + PH2O Note: The vapor pressure of water varies with temperature Robert Boyle Jacques Charles Amadeo Avogadro Joseph Louis Gay-Lussac Pressure is inversely proportional to volume when temperature is held constant. P1V1 P2V 2 The volume of a gas is directly proportional to temperature. (P = constant) V1 T1 V2 T2 Temperature MUST be in KELVINS! The pressure and temperature of a gas are directly related, provided that the volume remains constant. P1 T1 P2 T2 Temperature MUST be in KELVINS! Expresses the relationship between pressure, volume and temperature of a fixed amount of gas P1V1 T1 P2V 2 T2 For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = constant × n V = volume of the gas n = number of moles of gas For example, doubling the moles will double the volume of a gas Imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory PV = nRT P = pressure V = volume n = moles R = ideal gas constant T = temperature (Kelvin) Numerical Value of R Units 0.0821 (atm∙L)/(mol∙K) 8.314 J/(mol∙K) 62.4 (mmHg∙L)/(mol∙K) Note: 1 J = 1 Pa∙m3 STP of 1 mole of gas = 1 atm and 273K PV = nRT (1atm)(V) = (1mol)(.0821)(273) V = 22.4 L Volume of 1 mole of gas at STP = 22.4 liters Real Gas – does not behave completely according to the assumptions of the kinetic molecular theory At high pressure (smaller volume) and low temperature gases deviate from ideal behavior Particles will be closer together so there is insufficient kinetic energy to overcome attractive forces The Van der Waals Equation adjusts for nonideal behavior of gases (p. 423 of book) 2 n Pobs a x (V nb ) nR T V corrected pressure Pideal corrected volume Videal … so at STP… Combine density with the ideal gas law (V = p/RT) M = Molar Mass P = Pressure R = Gas Constant T = Temperature in Kelvins If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios. 3 H2(g) 3 moles H2 3 liters H2 + N2(g) 2NH3(g) + 1 mole N2 2 moles NH3 + 1 liter N2 2 liters NH3 How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen? 3 H2(g) + N2(g) 2NH3(g) 12 L H2 2 L NH3 3 L H2 = 8.0 L NH3 How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2 KClO3(s) 2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 122.55 g KClO3 3 mol O2 22.4 L O2 2 mol KClO3 1 mol O2 = 13.7 L O2 How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2 KClO3(s) 2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 122.55 g KClO3 V nRT P 2 mol KClO3 (0.612 mol)(0.082 1 L atm mol K 0.930 atm = 0.612 mol O 2 )(310 K) = 16.7 L Spontaneous mixing of two substances caused by the random motion of particles The rate of diffusion is the rate of gas mixing The rate of diffusion increases with temperature Small molecules diffuse faster than large molecules Process by which gas particles pass through a tiny opening Rate of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. M1 = Molar Mass of gas 1 M2 = Molar Mass of gas 2