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Chapter 9 Gases: Their Properties and Behaviors. General Properties of Gases. There is a lot of “free” space in a gas. Gases can be expanded infinitely. Gases fill containers uniformly and completely. Gases diffuse and mix rapidly. Breaking the speed limit everywhere.

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## Chapter 9 Gases: Their Properties and Behaviors

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**Chapter 9**Gases: Their Properties and Behaviors**General Properties of Gases**• There is a lot of “free” space in a gas. • Gases can be expanded infinitely. • Gases fill containers uniformly and completely. • Gases diffuse and mix rapidly.**Atomic World: Fast and Furious**Helium 3,000 miles per hour Air (oxygen + nitrogen) 1,000 miles per hour 7,000,000,000 collisions per second**So you see there is no such thing as still air. The air**molecules are constantly moving at an average of 1,000 miles per hour.**Properties of Gases**Gas properties can be modeled using math. Model depends on— • V = volume of the gas (L) • T = temperature (K) • ALL temperatures in MUST be in Kelvin!!! No Exceptions! • n = amount (moles) • P = pressure (atmospheres)**1 hitsec**2 hitssec 9 hits9 sec 18 hits9 sec = = 0 Seconds 00010203040506070809 9 Hits 18 ½ volume Pressure comes from the gas molecules hitting the side of the container. Let’s count them out loud.**VOLUME DECREASES**PRESSURE INCREASES So we saw that as volume decreases the pressure increases.**V = 1**P V = 30 P V=0.5 , P=2 V=0.1, P=10 V=6 , P=5 V=3, P=10 1 x P V = P x P We can also show this by having them multiply by each other. They are inversely proportional. BOYLES LAW**1 hitsec**9 hits9 sec = 27 ºC = 300 K 0 Seconds 00010203040506070809 9 18 27 ºC = 300 K We saw that we can increase pressure by reducing the volume, but we can also do it by increasing the temperature and therefore the speed of the gas molecules. At room temperature the hits are 1 hit/sec 0 K**9 hits4.5 sec**2 hitssec = 327 ºC = 600 K 327 ºC = 600 K 0 Seconds 9 00010203040506070809 18 27 ºC = 300 K We are going from room temperature 27 ºC = 300 K to double that temperature, which is 600 Kelvin. Let’s count the number of collisions at this higher speed. We get twice the number of collisions and therefore twice the pressure. 0 K**15 psi, 300 K**P T 30 psi 3 psi 600 K 60 K So we just saw that when temperature goes up, so does the pressure. This makes sense because higher temperature means the gas molecules are going faster, colliding more often, and hitting harder. Gay-Lussac’s Law**P**n n=# moles Pressure is proportional to the number of gas molecules, which we count in moles. Another way to increase pressure is to increase the number of gas molecules. This is the approach the steam engine used by heating water.**This is also a safety problem. Any closed container that has**liquid in and gets heated will likely increase pressure dramatically until the container bursts.**P**T V V V n Let’s review what we learned. If the volume decreases the pressure will increase. Then the reverse happens if the volume increases. The pressure drops as gas molecules are farther apart.**P**T V V n As we also learned, we can increase pressure by introducing more molecules of the gas into the volume.**P**T V n doubles We also learned that if temperature doubles, the pressure doubles if volume is fixed. Or if the container is flexible, the volume will double with pressure staying constant. Or both can increase such that the product of the two doubles.**R**P T V n = • P is pressure measured in atmospheres. • V is volume measured in Liters • n is moles of gas present. • R is a constant that converts the units. It's value is 0.0821 atm•L/mol•K • T is temperature measured in Kelvin. • Simple algebra can be used to solve for any of these values. • P = nRTV = nRTn = PVT = PVR = nT • V P RT nR PV To make these quantities equal, we need a conversion constant. We call it R (the Universal Gas Constant)**12.2 K**R x1 P 1 T V n = • Pressure=1 atmosphere • Volume=1 Liter • n = 1 mole • R=0.0821 L atm mol-1 K-1 • What is the temperature? 1 x 0.0821 Let’s find what temperature the gas must be if we have the following readings for these other properties. Normally 1 mole of a gas at 1 atmosphere pressure takes up 22.4 liters. So it must be very cold to only have a volume of 1 liter.**Pressure**Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink) P of Hg pushing down related to • Hg density • column height**Evangelista Torricelli**1608 –1647**Pressure**Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink) P of Hg pushing down related to • Hg density • column height**Manometers**from Greek manos meaning sparse**CONVERSIONS**• 760 mm of Hg • 760 torr • 29.9 in. of Hg • 1 Atmosphere • 101.325 KPa (Kilopascals) • 14.7 lbs. per sq. in. • about 34 feet of water! All Equal**Standard Temperature and Pressure (STP)**P = 1 atmosphere T = 0 °C The molar volume of an ideal gas is 22.42 liters at STP. 1 mol occupies 22.42 L at STP**sphygmomanometer**• sphygmometer • Greek sphygmos meaning pulse (from sphyzeinto throb) Measures to 300mm Hg**When a pressure cooker is used, what**causes the increased pressure? PV=nRT P=nRT V Temperature goes from 25oC to 100oC Turn to Kelvin by adding 273 to Celsius 297K to 373K 75K/297K=25% increase in pressure**P1V1=n1RT1 P2V2=n2RT2**n1T1 n1T1 n2T2 n2T2 P1V1= R P2V2= R n1T1 n2T2 P1V1= P2V2 n1T1 n2T2 We can take advantage of the fact that the R constant is the same even if the conditions of the gas changes. Change in Conditions Problem**1. What volume will 52.5 g of CH4 occupy at STP?2. You heat**1.437 g NH3 in a stoppered 250 mLflask until it explodes (425 °C). What was thepressure inside the flask immediately prior to theexplosion?**And so…. The gas laws**Boyle’s Law* Gay-Lussac’s Law At constant V : • Boyle’s Law- At constant temperature, volume is inversely proportional to pressure. Robert Boyle *Holds precisely only at very low pressures. Joseph-Louis Gay-Lussac**There’s more….**Charles’ Law Avogadro’s Law At constant V : For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). a = proportionality constant V = volume of the gas n = number of moles of gas 1 mol occupies 22.42 L at STP • At constant pressure the volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.**Charles’ Law**Charles’ Law Jacques Charles • At constant pressure the volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. Absolute Zero**There’s more….**Charles’ Law Avogadro’s Law At constant V : For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). a = proportionality constant V = volume of the gas n = number of moles of gas 1 mol occupies 22.42 L at STP • At constant pressure the volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.**Avogadro’s Law**At constant V : For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). a = proportionality constant V = volume of the gas n = number of moles of gas 1 mol occupies 22.42 L at STP Amedeo Avogadro Avogadro developed this law after Joseph Louis Gay-Lussac had published in 1808 his law on volumes (and combining gases). The greatest problem Avogadro had to resolve was the confusion at that time regarding atoms and molecules. The scientific community did not give great attention to his theory, so Avogadro's hypothesis was not immediately accepted. André-Marie Ampère achieved the same results three years later by another method**All of the laws can be summarized nicely…**Combined Gas Law**What temperature is required to cause the pressure of a**(steel) cylinder of gas to increase from 350 to 500 mm Hg? The initial temperature was 298 K.**A gas occupies a volume of 400. mL at 500. mm Hg pressure.**What will be its volume, at constant temperature, if the pressure is changed to 250 torr? Info. given: Question: what is V2? V1 = 400. mL P1 = 500. mm Temperature does not change P2 = 250 torr (760 mm=760 torr) = 250 mm We will use Boyle’s Law: P1V1 = P2V2 (500.mm)(400.mL)=(250.mm)(x) x= (500)(400) = 800. mL 250**A gas occupies a volume of 410 mL at 27°C and 740 mm Hg**pressure. Calculate the volume the gas would occupy at STP. Info. given: Question: what is V2? V1 = 410 mL T1 = 27°C T2 = 0 °C P1 = 740 mm P2 = 760 mm We will use the combined gas law: Oops…use Kelvin 27°C=300K; 0°C=273K**Suppose you have 856 mL of a gas. A weather front comes**through, and the barometric pressure changes from 780 mm Hg to 720 mmHg. Along with this, the temperature changesfrom 86 °F (30. °C) to 72 °F (22 °C). What isthe new volume of your gas?**Gas Stoichiometry**• When gases are involved in a reaction, das properties must be combined with stoichiometric relationships. • E.g. Determine the volume of gas evolved at 273.15 K and 1.00 atm if 1.00 kg of each reactant were used. Assume complete reaction (i.e. 100% yield) • CaO(s) + 3C(s) CaC2(s) + CO(g). • Strategy: • Determine the number of moles of each reactant to which this mass corresponds. • Use stoichiometry to tell us the corresponding number of moles of CO produced. • Determine the volume of the gas from the ideal gas law.**Kinetic Molecular Theory**• The first kinetic interpretation of gases was Robert Hooke in 1676. • At the time, Isaac Newton’s picture of a gas was the accepted view. Newton suggested that gas particles exert pressure on the walls of a container because of repulsive forces between the molecules. Isaac Newton**Enter Maxwell and Boltzmann**• James Clerk Maxwell in 1859 and Ludwig Boltzmann in the 1870s finally got people to listen to a kinetic theory of gasses.**Postulates of the Theory**• Gases are composed of molecules which are small compared to the average distance between them. • d(N2,g) = 0.00125 g/L (273°C) • d(N2,liq) = 0.808 g/mL (-195.8°C) • Molecules move randomly, but in straight lines until they collide with other molecules, or the walls of the container. • Forces of attraction and repulsion between gas molecules are negligible (except during collisions!) • All collisions between gas molecules are elastic. • The average kinetic energy of a molecule in a gas sample is proportional to the absolute temperature.**Kinetic Molecular Theory and the Ideal Gas Law**• Consider that pressure is due to the large number of collisions of gas molecules with the walls of the container. p (frequency of collisions)·(average force) u: average speed m: mass N: number of molecs.**Kinetic Molecular Theory and the Ideal Gas Law**½mu2 is the kinetic energy and T N is proportional to the number of moles. Insert a constant of proportionality.

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