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Ch. 5: GasesCh. 5: Gases
Dr. Namphol Sinkaset
Chem 200: General Chemistry I
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I. Chapter OutlineI. Chapter Outline
I. Introduction
II. Gas Pressure
III. Gas Laws
IV. Gas Law Problems
V. Dalton’s Law of Partial Pressures
VI. Kinetic-Molecular Theory of Gases
VII. Real Gases
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I. The Unique Gas PhaseI. The Unique Gas Phase
• Physical properties of a gas are nearly independent of its chemical identity!
• Gas behavior is markedly different than solid or liquid behavior.
• We look at the origins of equations used to describe gases and then theorize the reasons why gas behavior is so universal.
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II. PressureII. Pressure
• Pressure is simply a force exerted over a surface area.
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II. Atmospheric PressureII. Atmospheric Pressure
• Patm is simply the weight of the earth’s atmosphere pulled down by gravity.
• Barometers are used to monitor daily changes in Patm.
• Torricelli barometer was invented in 1643.
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II. ManometersII. Manometers
• In the lab, we use manometers to measure pressures of gas samples.
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II. Units of PressureII. Units of Pressure
• For historic reasons, we have units such as torr and mm Hg. (Why?)
• The derived SI unit for pressure is N/m2, known as the pascal (Pa).
• Standard conditions for gases (STP) occurs at 1 atm and 0 °C. Under these conditions, 1 mole of gas occupies 22.4 L.
• Note that 1 atm = 760 mm Hg = 760 torr = 101.325 kPa.
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III. Gas LawsIII. Gas Laws
• A sample of gas can be physically described by its pressure (P), temperature (T), volume (V), and amount of moles (n).
• If you know any 3 of these variables, you know the 4th.
• We look at the history of how the ideal gas law was formulated.
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III. Volume and Pressure – III. Volume and Pressure – Boyle’s LawBoyle’s Law
• The volume of a gas is inversely related to pressure, i.e. if P increases, V decreases.
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III. Volume and Temperature – III. Volume and Temperature – Charles’s LawCharles’s Law
• The volume of a gas is directly related to its temperature, i.e. if T is increased, V will increase.
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III. The Combined Gas LawIII. The Combined Gas Law
• Boyle’s and Charles’s Laws can be combined into a convenient form.
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III. Volume and Moles – III. Volume and Moles – Avogadro’s LawAvogadro’s Law
• The pressure of a gas is directly related to the number of moles of gas, i.e. if n increases, V will increase.
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III. The Ideal Gas LawIII. The Ideal Gas Law
• The ideal gas law is a combination of the combined gas law and Avogadro’s Law.
R = 0.082058 L atm/K mole
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IV. Gas Law ProblemsIV. Gas Law Problems
• There are many variations on gas law problems.
• A few things to keep in mind:1) Temperature must be in Kelvin
2) If problem involves a set of initial and final conditions, use combined gas law.
3) If problem only gives information for one set of conditions, use ideal gas law.
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IV. Sample ProblemIV. Sample Problem
• What’s the final pressure of a sample of N2 with a volume of 952 m3 at 745 torr and 25 °C if it’s heated to 62 °C with a final volume of 1150 m3?
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IV. Sample ProblemIV. Sample Problem
• What volume, in mL, does a 0.245 g sample of N2 occupy at 21 °C and 750 torr?
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IV. Sample ProblemIV. Sample Problem
• A sample of N2 has a volume of 880 mL and a pressure of 740 torr. What pressure will change the volume to 870 mL at the same temperature?
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IV. Other Uses of Ideal Gas LawIV. Other Uses of Ideal Gas Law
• The ideal gas law can be used to find other physical values of a gas that are not as obvious. gas density, d = mass/volume gas molar mass, MW = mass/mole stoichiometry, via moles and a balanced
equation
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IV. Sample ProblemIV. Sample Problem
• Find the density of CO2(g) at 0 °C and 380 torr.
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IV. Sample ProblemIV. Sample Problem
• An unknown noble gas was allowed to flow into a 300.0 mL glass bulb until the P = 685 torr. Initially, the glass bulb weighed 32.50 g, but now it weighs 33.94 g. If the temperature is 27.0 °C, what’s the identity of the gas?
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IV. Sample ProblemIV. Sample Problem
• How many mL of HCl(g) forms at STP when 0.117 kg of NaCl reacts with excess H2SO4?
H2SO4(aq) + 2NaCl(s) Na2SO4(aq) + 2HCl(g)
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V. Partial PressuresV. Partial Pressures
• Each gas in a mixture behaves like it’s the only gas there.
• Dalton’s Law of Partial Pressures states that the total pressure of a mixture of unreacting gases is the sum of all individual pressures.
• Each individual pressure is a partial pressure. Ptotal = P1 + P2 + P3 + P4 + …
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V. Partial PressuresV. Partial Pressures
• You already have experience with partial pressures.
• Ptotal = PH2 + PH2O
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V. An OV. An O22/N/N22 Gas Mixture Gas Mixture
• Let’s say we have O2 and N2 as a gas mixture. Then Ptotal = PO2 + PN2. Applying the ideal gas law…
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V. An OV. An O22/N/N22 Gas Mixture Gas Mixture
• Now we add the individual pressures to find the total pressure.
• Note that the total pressure is related to the total moles.
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V. An OV. An O22/N/N22 Gas Mixture Gas Mixture
• What happens if we divide PO2 by Ptotal?
• A new quantity which we call the mole fraction appears.
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V. Mole FractionV. Mole Fraction
• We define a new unit of concentration, the mole fraction (X).
• Partial pressures are directly related to the mole fraction.
• For the O2/N2 mixture, for N2 specifically, we have…
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V. Sample ProblemV. Sample Problem
• Calculate the partial pressures of 5.50 g He, 15.0 g Ne, and 35.0 g Kr at STP.
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VI. Kinetic-Molecular TheoryVI. Kinetic-Molecular Theory
• Why do gas laws work well for all gases?• The Kinetic-Molecular Theory of gases was
proposed which consists of 3 postulates.1) Gas particles are negligibly small, and any sample
has a huge # of particles. The volume of each particle is so small that we assume they have mass but no volume.
2) The average kinetic energy of a particle is proportional to the kelvin temperature
3) Gas particles collide in perfectly elastic collisions w/ themselves and container walls and they move in straight lines between collisions, neither attracting nor repelling one another.
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VI. Imagining a Sample of GasVI. Imagining a Sample of Gas
• We imagine a sample of gas – chaos, molecules bumping into each other constantly.
• After a collision, 2 molecules may stop completely until another collision makes them move again.
• Some molecules moving really fast, others really slow.
• But, there is an average speed.
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VI. Gas Molecular SpeedsVI. Gas Molecular Speeds
• As temp increases, avg. speed increases.
• i.e. avg. KE is related to temp!!
• Any 2 gases at same temp will have same avg. KE!
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VI. Why Do Gas Laws Work VI. Why Do Gas Laws Work So Well?So Well?
• Recall that the gas laws apply to any gas – the chemical identity is not important.
• Gas particles only interact when they collide. Since this interaction is so short, chemical properties don’t have time to take effect!!
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VI. Explaining Boyle’s LawVI. Explaining Boyle’s Law
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VI. Explaining Charles’s LawVI. Explaining Charles’s Law
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VI. Explaining Avogadro’s LawVI. Explaining Avogadro’s Law
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VI. Explaining Dalton’s LawVI. Explaining Dalton’s Law
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VII. Deviations from PV=nRTVII. Deviations from PV=nRT
• Under extreme conditions (high P or low T), gases deviate from ideal gas law predictions.
• Why? What’s so different about these conditions?
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VII. Gas Particle VolumeVII. Gas Particle Volume
• Gas molecules do take up space! When very close to one another, entire volume of container is not available for travel, so actual volume of gas is larger.
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VII. Intermolecular ForcesVII. Intermolecular Forces
• Gas molecules interact if they are very close to one another…
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VII. van der Waals EquationVII. van der Waals Equation
• Under extreme conditions, ideal gas law cannot be used.
correction terms for P and V