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Honors Chemistry Chapter 5 Gases

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5.1 Gases Temperature vs. Intermolecular attraction Atomic Gases Noble Gases, H 2, N 2, O 2, F 2, Cl 2 Molecular Gases Usually light molecules with weak attraction forces Eg: HCl, CO 2, NH 3, H 2 S, NO 2 Ionic Compounds Strong forces; not normally gases

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5.2 Pressure Force per unit area P = F/A N/m 2 unit defined as Pascal (Pa) Standard air pressure = kPa Also called 1 atmosphere (atm) Measured by unequal mercury levels Manometers and barometers Common unit called mmHg (or Torr) Standard air pressure = 760 mmHg

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5.2 Dimensional Analysis Convert 75.0 kPa to mmHg 75.0 kPa 760 mmHg x = 563 mmHg kPa Try this one Convert 1.25 atm to kPa

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5.3 Boyle’s Law Pressure is inversely proportional to volume Hold temperature and amount of gas constant V 1/P V = k x (1/P) PV = k Best used with changing conditions P 1 V 1 = P 2 V 2

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5.3 Boyle’s Law Problems A 175 mL sample of methane is stored at 125 kPa. What pressure is needed to compress the gas to a volume of 50.0 mL? P 1 V 1 = P 2 V 2 (125 kPa) (175 mL) = P 2 (50.0 mL) P 2 = 438 kPa Try this one A sample of argon occupies 476 mL at 650 Torr. Find the volume at 975 Torr.

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5.3 Charles’ Law Also credited to Gay-Lussac Volume is directly proportional to temperature Hold pressure and amount of gas constant V T V = kT Linear relationship Must use Kelvins! V 1 V = --- T 1 T 2

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5.3 Charles’ Law Problems A 5.00 L helium balloon is heated from 20 o C to 75 o C. Find its new volume. V 1 /T 1 = V 2 /T L V = K 348 K V 2 = 5.94 L Try this one A 670 mL sample of chlorine is stored at 50 o C. At what temperature will its volume be 450 mL?

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5.3 More Gas Laws Another form of Charles’ Law Pressure is directly proportional to temperature P = kT P 1 /T 1 = P 2 /T 2 Avogadro’s Law Volume is directly proportional to the amount of gas present V n Volume relationships in chemical reactions

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5.3 Avogadro’s Law Problems How many liters of hydrogen are needed to completely react with 1 liter of oxygen? 2 H 2 + O 2 2 H 2 O 2 mol hydrogen react with 1 mol oxygen V n, so…. 2 L hydrogen react with 1 L oxygen Try this one How many liters of ammonia are formed when 1 L of hydrogen reacts with excess nitrogen?

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5.4 The Ideal Gas Equation Ideal Gas No intermolecular attraction forces Particles have no volume Combine Boyle’s, Charles, and Avogadro’s Laws PV = nRT STP = 1 atm, 273 K Molar volume of a gas = L at STP R = atm L / mol K

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5.4 Ideal Gas Equation Problems A sample of fluorine occupies 3.65 L at 45 o C and 2.50 atm. How many moles of fluorine are present? PV = nRT (2.50 atm)(3.65 L) = n (0.0821)(318 K) n = mol Try this one A mol sample of propane occupies 2.15 L. If the temperature is 28 o C, find the pressure.

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5.4 Gas Density Since n = m/M…. PV = (m/M) RT MPV = mRT Divide by V to get density (m/V) MP = RT Gas density expressed in g/L

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5.4 Gas Density Problems Find the density of nitrous oxide at STP. First, find molecular mass of N 2 O MP = RT (44.0 g/mol)(1.00 atm) = (0.0821)(273 K) = 1.96 g/L Try this one…. A gas is found to have a density of 2.54 g/L at 15 o C and 1.50 atm. Find its molecular mass.

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5.5 Gas Stoichiometry Mass-Mass problems (review) Volume-Volume problems Volume is proportional to moles, so…. Mol relationship from reaction can be used directly No conversions needed!

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5.5 Volume-Volume Problem 2 H 2 + O 2 2 H 2 O If 3.25 L of oxygen react, how many liters of water vapor are formed? 3.25 L O 2 2 L H 2 O x = 6.50 L H 2 O 1 1 L O 2 Volume-Volume is just Avogadro’s Law!

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5.5 Mass-Volume Problems Key step – get to moles! Mass conversion – use molecular mass Volume conversion – use gas equation Need to know temperature and pressure conditions

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5.5 Mass-Volume Problems 25.0 g of sodium react with excess water at STP. How many liters of hydrogen are produced? 2 Na + 2 H 2 O 2 NaOH + H g Na 1 mol Na 1 mol H x x = mol g Na 2 mol Na Now use ideal gas equation to get volume

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5.5 Mass-Volume Problems PV = nRT (1.00 atm) V = (0.543 mol)(0.0821)(273 K) V = 12.2 L Try this one Potassium chlorate decomposes into potassium chloride and oxygen gas. How many grams of KClO 3 are needed to produce 5.00 L of oxygen at atm and 18 o C? Hint: This one is backwards!

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5.6 Dalton’s Law Partial pressure – the pressure of an individual gas in a mixture of gases Total pressure of a mixture equals the sum of the partial pressures of each gas P t = P 1 + P 2 + P Partial pressure is proportional to the mol fraction (X 1 = n 1 / n t ) P 1 = X 1 P t

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5.6 Dalton’s Law 2.00 mol He is mixed with 1.00 mol Ar. Find the partial pressure of each at 1.75 atm pressure. X He = 2.00 mol / 3.00 mol = X Ar = 1.00 mol / 3.00 mol = P He = (0.667) (1.75 atm) = 1.17 atm P Ar = (0.333) (1.75 atm) = atm Try this... Find the partial pressure of oxygen in air if it makes up 21% of the Earth’s atmosphere by volume. (Note: The volume gives you the mole ratio because of Avogadro’s law.)

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5.7 Kinetic Molecular Theory Explains gas behavior in terms of molecular motion Energy Work done by a moving object Measured in SI unit Joule (J) Kinetic energy Energy due to motion K = ½ mv 2 KMT is a simplification of reality (ideal gas)

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5.7 Kinetic Molecular Theory Gas molecules are separated by great distances They can be treated as “point masses” Gas molecules are in constant random motion Frequent elastic collisions (no energy lost) No attractive or repulsive forces Average K is proportional to Temperature

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5.7 Distribution of Molecular Speeds Maxwell-Boltzmann Distribution Molecular speeds distributed around average Peak velocity depends on temperature and on molec. mass Root Mean Square Speed _____ v rms = √3RT/M Rate of diffusion

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5.8 Deviations from Ideal Behavior We made approximations! Point masses No intermolecular forces These approximations become bad at... High pressure Low temperature Liquefaction van der Waals Equation (P + an 2 /V 2 ) (V – nb) = nRT

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