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Kinetic Molecular Theory of Gases 1.A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume. 2.Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic. 3.Gas molecules exert neither attractive nor repulsive forces on one another. 4.The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy

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Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa Barometer Pressure = Force Area

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Sea level1 atm 4 miles0.5 atm 10 miles0.2 atm

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P 1/V P x V = constant P 1 x V 1 = P 2 x V 2 Boyles Law Constant temperature Constant amount of gas Boyle's Law ( scuba style! ) ACSBR physics mini project – YouTube SIAbw

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A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ? V 2 = 154 mL P 2 = P 1 x V 1 V2V2 726 mmHg x 946 mL 154 mL = = 4460 mmHg

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As T increasesV increases

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Variation of gas volume with temperature at constant pressure. V T V = constant x T V 1 /T 1 = V 2 /T 2 T (K) = t ( 0 C) Charles & Gay-Lussacs Law Temperature must be in Kelvin

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A sample of carbon monoxide gas occupies 3.20 L at C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V L x K 3.20 L = = 192 K V 1 /T 1 = V 2 /T 2 charles law demonstration - Google Videos Giant Koosh Ball in Liquid Nitrogen! - YouTube

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Avogadros Law V number of moles (n) V = constant x n V 1 /n 1 = V 2 /n 2 Constant temperature Constant pressure

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Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure? 4NH 3 + 5O 2 4NO + 6H 2 O 1 mole NH 3 1 mole NO At constant T and P 1 volume NH 3 1 volume NO

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Ideal Gas Law Charles law: V T (at constant n and P) Avogadros law: V n (at constant P and T) Boyles law: V (at constant n and T) 1 P V nT P V = constant x = R nT P P R is the gas constant PV = nRT

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The conditions 0 0 C and 1 atm are called standard temperature and pressure (STP). PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)( K) R = L atm / (mol K) Experiments show that at STP, 1 mole of an ideal gas occupies L.

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What is the volume (in liters) occupied by 49.8 g of HCl at STP? PV = nRT V = nRT P T = 0 0 C = K P = 1 atm n = 49.8 g x 1 mol HCl g HCl = 1.37 mol V = 1 atm 1.37 mol x x K Latm molK V = 30.6 L

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Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the lightbulb (in atm)? PV = nRT n, V and R are constant nR V = P T = constant P1P1 T1T1 P2P2 T2T2 = P 1 = 1.20 atm T 1 = 291 K P 2 = ? T 2 = 358 K P 2 = P 1 x T2T2 T1T1 = 1.20 atm x 358 K 291 K = 1.48 atm Egg in a Bottle.wmv - YouTube

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Density (d) Calculations d = m V = PMPM RT m is the mass of the gas in g M is the molar mass of the gas Molar Mass ( M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L

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Deviations from Ideal Behavior of Gases Deviation from ideal behavior is large at high pressure and low temperature At lower pressures and high temperatures, the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error.

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Deviation from ideal behavior as a function of temperature As temperature is decreased below a critical value, the deviation from ideal gas behavior becomes severe, because the gas CONDENSES to become a LIQUID.

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J. D. van der Waals corrected the ideal gas equation in a simple, but useful, way (a) In an ideal gas, molecules would travel in straight lines. (b) In a real gas, the paths would curve due to the attractions between molecules.

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Mixtures of Gases Dalton's law of partial pressure states: –the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

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Dalton's Law of Partial Pressure P T = P 1 + P 2 + P 3 + …….

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Partial Pressure in terms of mole fraction OR X A P total = P A (X A = mole fraction of A and P A = partial pressure of gas A)

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Mole fraction What is the mole Fraction of Gas A in mixture I? What is the mole fraction of Gas B in mixture II?

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Example: If there are 3 moles of gas A, 4 moles of gas B and 5 moles of gas C in a mixture of gases and the pressure of A is found to be 2.5 atm, what is the total pressure of the sample of gases? X A = 3= P A = 2.5 atm P T = P A / X A = 2.5/0.2 = 12.5 atm

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2KClO 3 (s) 2KCl (s) + 3O 2 (g) Bottle full of oxygen gas and water vapor P T = P O + P H O 22

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Grahams Law of Effusion Grahams law states that the rates of effusion of two gases are inversely proportional to the square roots of their molar masses at the same temperature and pressure: Grahams Law of Effusion diffusion of a gas - YouTube

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Grahams Law of Effusion The velocity of effusion is also inversely proportional to the molar masses:

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Grahams Law of Effusion But the time required for effusion to take is directly proportional to the molar masses: The density of the gas is also directly proportional to the molar masses:

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Grahams Law of Effusion Compare the rate of effusion for hydrogen and oxygen gases.

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