Lecture 9. Properties of gases. Professor Hicks Inorganic Chemistry (CHE151) Three factors affect the properties of gases

Transcription

1 Lecture 9 Professor Hicks Inorganic Chemistry (CHE151) Properties of gases Three factors affect the properties of gases 1) P = pressure 2) T = Kelvin temperature 3) V = volume 4) n = number of moles of gas 1

2 Pressure force area Force divided by area Force visualized as all matter piled up on top of a surface Calculate the pressure due to a 150 pound man if his feet have a total area of 40 square inches pressure = 150 pounds 40 square inches = 3.75 lbs/in 2 Pressure on earth Space pressure 1.0 atm Column of air above every square inch weighs 14.7 pounds 1.0 atm = 14.7 psi Earth s atmosphere Earth 2

3 Scuba diving space pressure 1.0 atm Column of air above every square inch weighs 14.7 pounds Earth s atmosphere 10 meters + pressure 1.0 atm the 10 m column of water above every square inch weighs 14.6 pounds Water = 2 atm! Units of pressure pressure on earth 1) Pounds per square inch (psi) 2) Atmospheres (atm) average P on earth = 1 atm 3) Millimeters of mercury (mm Hg) aka torr pressure 1.0 atm Column of air from earth to space column of air space Earth s atmosphere Mercury metal (Hg) is very dense (13.6 g/ml) Earth 1.0 atm = 760 mm Hg Column of mercury metal 760 mm A 760 mm column Hg creates same force as an air column of same area that goes from earth up to space 3

4 Barometer Used to measure the atmospheric pressure P atm + P Hg1 = P Hg2 atmospheric = P atm pressure Average day on earth h = 760 mm mercury 1.0 atm = 760 mm Hg P = 0 vacuum P atm = P Hg2 P Hg1 P atm = h P atm h = height difference between columns measured with a ruler h=p Hg2 P Hg1 liquid mercury (Hg) or water + P Hg1 P Hg2 P mercury column 1 = P Hg1 P mercury column 2 = P Hg2 Water has a density 1/13th that of mercury barometer using water will have h = 13 x 760 mm Manometer Used to measure unknown pressures P gas + P Hg1 = P atm + P Hg2 Unknown P of sample = P sam Atmospheric = P atm pressure P gas = P atm + P Hg2 - P Hg1 P gas = P atm + h P s P atm is found with a barometer P atm h Liquid mercury (Hg) or water + P Hg1 + P Hg2 P mercury 1 = P Hg1 P mercury 2 = P Hg2 4

5 Empirical gas laws (discovered by experimentation) Boyles Law Applies to a sample of gas kept at constant temperature PV = constant Charles Law Applies to a sample of gas kept at constant pressure (T must be in Kelvins) V T = constant Boyles Law PV = constant Applies to a sample of gas kept at constant temperature The deepest part of the ocean is known as the Mariana s Trench. The depth is 11,000 meters! This produces a pressure of 1101 atm! Estimate the volume of a 2.0 liter soda bottle filled with air on the earth s surface if it was brought to the bottom of the Mariana s Trench without changing its temperature. PV = constant (Boyles Law) 1101 atm x V = 2.0 lit*atm On earths surface, for this sample of air the Boyles law constant is PV = 2.0 liters x 1.0 = 2.0 lit*atm V= 2/1100 lit = liter 5

6 Empirical gas laws V T = constant Charles Law applies to a sample of gas kept at constant pressure (T must be in Kelvins) Liquid nitrogen boils at -196 C. It is commonly used to achieve low temperatures in the laboratory. If a balloon is filled with 1.55 liters of air at 25 C, what volume will the balloon shrink to if it is placed in a liquid nitrogen bath? V/T = constant (Charles law) K= C K= = 298 V/T = 5.20 x 10-3 at 77 K V/77 = 5.20 x 10-3 V = 77 x 5.20 x 10-3 V = liters K= = 77 K the Charles law constant under the lab conditions is V/T = 1.55 liters / 298 K Always express temperature in = 5.20 x 10-3 lit / K Kelvin's when using gas laws equation for a line V = constant*t Charles Law and Kelvin Temperature scale y = mx + b m = Charles law constant b = 0 Volume cannot become negative T = -273 C Absolute zero! 0 samples of gas taken and cooled. Volume measured at each temperature extrapolate to V=0 Find T = -273 C Basis of the Kelvin temperature scale gas sample 1 gas sample 2 gas sample 3 6

7 e cm water 7

8 5.19 A gas occupying a volume of 725 ml at a pressure of atm is allowed to expand at constant temperature until its pressure reaches atm. What is its final volume? 5.23 A 36.4-L volume of methane gas is heated from 25 C to 88 C at constant pressure. What is the final volume of the gas? 8

9 5.30 Why is the density of a gas much lower than that of a liquid or solid under atmospheric conditions? What units are normally used to express the density of gases? Ideal Gas Law PV = nrt R is called the universal gas constant R replaces all constants in the named laws R = Joules mole K = liter*atm mole K SI Units most used SI unit is not used as much when actually working with gases since SI unit V is the m 3 which is too big to use in the lab 9

10 volume mass compound V= nrt P multiply molar mass divide molar mass moles of formula units, molecules, atoms, or ions divide stoichiometric number n= PV RT divide Avogadro's number multiply Avogadro's number number formula units, molecules, atoms, or ions equivalents A sample of nitrogen gas kept in a container of volume 1.6 L and at a temperature of 36 C exerts a pressure of 4.8 atm. Calculate the number of moles of gas present. 10

11 . Given that 5.5 moles of carbon monoxide gas are present in a container of volume 23.4 L, what is the pressure of the gas (in atm) if the temperature is 166 C? A certain amount of gas at 37 C and at a pressure of 0.60 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of 3.00 atm. How high can you raise the temperature of the gas without bursting the vessel? 11

12 Molar Mass from Ideal Gas Law Molar Mass units grams/mole If you can measure a mass and a # moles their ratio is the substance s molar mass! Molar Mass = mass sample / # moles evaporate a liquid gas If you can measure P, V, T you can calculate n! Condense the vapor and measure the mass of the liquid A quantity of gas weighing g at 1482 torr and 44 C occupies a volume of 5.40 L. What is its molar mass? 12

13 Partial Pressure Pressure each gas would have by itself (same T and V) written as P subscript gas example partial pressure of is P N2 N2 Air = + + N2 N2 N2 P N2 P O2 P H2O Daltons Law of Partial Pressures For a mixture of gases P gas (total) = P gas1 + P gas2 + P gas3 For example air P air = P N2 + P O2 + P H2O etc N2 = N O 2 13

14 Partial pressure C and breathing rate C levels are detected in the lower brain C is an unwanted byproduct of metabolism but C is the gas the brain monitors to determine breathing rate not When a cell uses more energy it releases more C Higher C stimulates faster breathing cells put C into blood cells add C breathing removes C lungs release C cell [C ] blood lungs Note this slide was out of order Mole Fraction ( ) Ratio of moles of gases N2 N 2 O 2 If expressed as % aka molar percentage N 2 N 2 O 2 mole fraction of nitrogen N2 = moles total moles gas sample moles molar percentage = x 100% total moles gas sample = N 2 N 2 N2 N 2 O 2 14

15 Partial pressure & scuba diving Space pressure 1.0 atm is 21% of air so 21% of 1.0 atm is P O2 = 0.21 atm Earth s atmosphere scuba divers breath trimix to decrease P O =10 atm! meters! pressure 9 atm breathing high P O2 can be toxic if you breath air down partial pressure of is 10x higher! P O2 = 2.1 atm! trimix 10/70 is a mixture of gases used for extremely deep dives. It has 10% to reduce P 02 Water if you breath trimix 10/70 P O2 = 1.0 atm! (10% of 10 atm) Partial pressure and mountain climbing P atm = 0.33 atm K2 is the second highest mountain in world 28,251 ft If you breathe air on top of K2 P O2 is reduced b/c all pressure is lower P 02 = 0.07 atm is reduced to about 1/3 of what we have at sea level (mountain climbers are being almost suffocated!) but if you breathe pure instead of air on top of K2 100% means P total = P O2 P 02 = 0.33 atm Mountain climbers breathe pure to increase P O2 Life requires a certain range of P O2 not % 15

16 D= m / V Density is intensive Density of a gas Imagine 1 mole as the sample size Mass of 1 mole of a gas is its Molar Mass Volume of 1 mole of gas depends on T and P V= RT/P Density = Molar Mass / RT /P A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.60 atm and 0.10 atm, respectively. Calculate the total pressure and the mole fractions of the gases. 16

17 A mixture of gases contains CH 4, C 2 H 6, and C 3 H 8. If the total pressure is 2.50 atm and the numbers of moles of the gases present are 0.21 mole for CH 4, 0.36mole for C 2 H 6, and 0.16 mole for C 3 H 8, calculate the partial pressures of the gases. A 2.5-L flask at 25 C contains a mixture of three gases,, He, and Ne, at partial pressures of 0.12 atm for, 0.18 atm for He, and 0.46 atm for Ne. (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the is removed selectively. 17

18 Calculate the density of argon gas at 300 K and a pressure 1.1 atm. Kinetic Molecular Theory Model to explain properties of gases 3 postulates of KMT Ludwig Boltzmann 1) Gas particles small compared to distance between them 2) Average kinetic energy proportional to the Kelvin temperature 3) Collisions are all elastic (no KE turned into heat in collisions) 18

19 KMT and pressure P = Force Area In Kinetic Molecular Theory the force part of pressure is due to collisions of gas molecules. Force created by constant collisions of gas particles Area Boyles Law (PV=constant) revisited increase pressure when a gas is compressed into smaller volume collisions with wall become more frequent increasing the pressure smaller volume higher pressure (same temp) 19

20 KMT and Temperature Kinetic energy of a gas is proportional to Kelvin temperature At higher temperatures gas molecules move more quickly As temperature increases two effects More frequent collisions with walls More energetic collisions with walls Charles Law revisited (V/T = constant) decrease temperature When cooled the gas molecules slow down collide less often and not as hard. This causes the volume to shrink under the applied pressure. smaller volume lower temperature (same pressure) 20

21 % students with a score % molecules with a speed Boltzmann Speed/Energy Distribution Increasing temperature increases average speed Higher speeds = higher energy - kinetic energy = ½mv 2 Ludwig Boltzmann lower temperature average speed 50% 50% higher temperature speed (m/s) Boltzmann Energy Distribution like the Hicks Grade Distribution Superior teaching increases students understanding Better understanding higher MCAT scores Charles Hicks class averages on MCAT other classes medical school MCAT requirement class % students with required grade 20% 4% Hicks class MCAT Score Hicks lesser instructors 20% 4% 21

22 % molecules with a speed % molecules with a speed % molecules with a speed Boltzmann Speed/Energy Distribution Higher speeds = higher energy Reactions have energy requirements lower temperature Ludwig Boltzmann At the higher temperature larger % of molecules have enough kinetic energy to react Reaction requires this speed (energy) 80% don t or greater have enough lower energy temperature higher temperature 80% 20% 20% have enough energy speed (m/s) Every speed has a kinetic energy KE = ½mv speed (m/s) 45% don t have enough energy 45% higher temperature 55% 55% have enough energy speed (m/s) 22

23 Which molecule is heavier? two different molecules at the same temperature. molecule 1 molecule 2 23

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