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Gases 13.1 Gases and Pressure Gases – constituent atoms and molecules that have little attraction for one another Free to move in available volume Some properties of gases Mixtures are always homogenous Very weak attraction between gas molecules Identity of neighbor is irrelevant Compressible – volume contracts when pressure is applied 0.10% of volume of gas is occupied by molecules Exert a measurable pressure on the walls of their container 13.1 Units of Pressure Pressure – force exerted per unit area SI unit equals Pascal (Pa) Alternative units 1 Pa = 1 N/m2 (1 N = 1 (kg•m)/s2) Millimeters of mercury (mmHg) Atmosphere (atm) 1.0 atm = 760 mmHg = 101, 325 Pa 1.0 atm = 14.69 psi Pressure Atmospheric pressure – pressure created from the mass of the atmosphere pressing down on the earth’s surface Standard atmospheric pressure at sea level – 760 mmHg Measuring pressure Barometer – long thin mercury filled tube sealed at once end and inverted into a dish of mercury Downward pressure of Hg in column equals outside atmospheric pressure Manometer – U-tube filled with mercury, with one end connected to the gas – filled container and the other end open to the atmosphere. Examples The pressure of the air in a tire is measured to be 28 psi. Represent this pressure in atm, torr and pascals On a summer day in Breknridge, Colorado, the atmospheric pressure is 325 mmHg. What is the pressure in atmostphere? 13.2 Pressure and Volume; Boyle’s Law Showing the relationship between pressure and volume P x V = k (constant value @ specific temp and constant moles of gas) k = 1.40 x 103 P = 1/ V (inverse relationship) Can predict a new volume of pressure is changed P1V1 = k = P2V2 P1V1 = P2V2 Calculate V2 = Figures 13.6 Examples A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. This sample is transferred to a new container and the pressure is measured to be 1.87 atm. What is the volume of the new container? Assume constant temperature. A sample of neon gas has a pressure of 7.43 atm in a container with volume of 45.1 L. This sample is transferred to a container with a volume of 18.4 L. What is the new pressure of the neon gas? Assume constant temperature 13.3 Volume and Temperature: Charles’s Law Relationship between Volume and Temperature V = bT (b is a constant) V/T=b Can predict the new volume or temperature (V1/T1)= (V2/T2) V vs. T Examples A 2.0 L sample of air is collected at 298K and then cooled to 278 K. The pressure is held constant at 1.0 atm. Does the volume increase of decrease? Calculate the volume of the air at 278 K? Examples Consider a gas with a volume of 5.65 L at 27oC and 1 atm pressure. At what temperature will this gas have a volume of 6.69 L and 1 atm pressure? 13.4 Volume and Moles: Avogadro’s Law Relationship between volume of gas and number moles of gas V is directly proportional to n V = an or V / n = a (a = constant) Can predict the new volume or new moles of gas at constant pressure and temperature (V1/n1) = (V2/n2) V vs. n Examples Suppose we have a 12.2 L sample containing 0.50 mol of oxygen gas, O2 at a constant pressure of 1atm and a temperature of 25oC. If all of this O2 is converted to ozone, O3, at the same temperature and pressure, what will be the volume of ozone formed? Examples Consider two samples of nitrogen gas (composed N2 molecules). Sample 1 contains 1.5 mol of N2 and has a volume of 36.7 L at 25oC and 1 atm. Sample 2 has a volume of 16. L at 25oC and 1 atm. Calculate the number moles of N2 in sample 2 13.5 The Ideal Gas law Different gasses show similar physical behavior (unlike solid or liquid) Defined by four variables – pressure, temperature, volume, and number of moles Relationship of variable – gas laws Ideal gas – behavior follows the gas laws exactly Describes how the volume of a gas is affected by changes in pressure, temperature and amount. PV = nRT; R = gas constant = 0.08206 L•atm K•mol Examples A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0oC and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. (Assume that the gas behaves ideally.) Examples What volume is occupied by 0.250 mol of carbon dioxide gas at 25oC and 371 torr? A 0.250 mol sample of argon gas has a volume of 9.00L at a pressure of 875 mmHg. What is the temperature (in oC) of the gas? Combine Gas Law is an expression obtained by mathematically combining Boyle’s and Charles’ law P1V1 = P2V2 @ constant n T1 T2 can predict P, V or T when condition is changed Examples Suppose we have a 0.240 mol sample of ammonia gas at 25oC with a volume of 3.5 L at a pressure of 1.68 atm. The gas compressed to a volume of 1.35 L at 25oC. Use the combined gas law to calculate the final pressure. Examples Consider a sample of hydrogen gas of 63oC with a volume of 3.65L at a pressure of 4.55 atm. The pressure is changed to 2.75 atm and the gas is cooled to -35oC. Calculate the new volume of the gas 13.6 Dalton’s Law of Partial Pressure A. Gas laws apply to mixtures of gases B. Dalton's law of partial pressure – Ptotal = P1 + P2 + P3 + ….. at constant V, T where P1, P2, ….refer to the pressure of the individual gases in the mixture C. Partial pressures refer to the pressure each individual gas would exert if it were alone in the container (P1, P2, …) 1. Total pressure depends on the total molar amount of gas present 3. Ptotal = ntotal (RT/V) Examples Mixture of helium and oxygen are use in the “air” tanks of underwater divers for deep dives. For a particular dive, 12 of O2 at 25oC and 1.0 atm and 46 L of He at 25oC and 1.0 atm were both pumped into a 5.0 L tank. Calculate the partial pressure of each gas and the total pressure in the tank at 25oC Examples A 2.0 L flask contains a mixture of nitrogen gas and oxgyen gas at 25oC. The total pressure of the gas mixture is 0.91 atm, and the mixture is known to contain 0.050 mol of N2. Calculate the partial pressure of oxygen and the moles of oxygen present 13.8 The Kinetic Molecular Theory of Gas A. Model that can explain the behavior of gases .Assumptions 1. A gas consists of particles in constant random motion 2. Most of the volume of a gas is empty spaces 3. The attractive and repulsive forces between molecules of gases are negligible 4. The total kinetic energy of the gas particles is constant at constant T 5. Average Ek α T 13.10 Gas Stoichiometry Stoichiometric calculations involves the application of the ideal gas law One of the variables in the ideal gas law equation is unknown. Example E.g Pure oxygen gas was first prepared by heating mercury(II) oxide, HgO 2 HgO(s) 2 Hg(l) + O2(g) What volume (in liters) of oxygen at STP is released by heating 10.57 g of HgO? Step1: Calculate moles of HgO Step 2: Calculate mole O2 Step 3: Calculate volume using Ideal gas law Examples Consider the reaction represented by the equation P4(s) + 6 H2(g) 4H3(g) What is the amount of P4 is required to react with 5.39 L of hydrogen gas at 27oC and 1.25 atm? Molar volume and STP The molar volume of an ideal gas is 22.4L/mole STP = Standard Temperature (273K) Pressure ( 1.0 atm) examples A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present? examples Quicklime, CaO, is produced by heating calcium carbonate, CaCO3. Calculate the volume of CO2 produced at STP from the decomposition of 152 g of CaCO3 according to the reaction CaCO3(s) CaO(s) + CO2(g)