1. Unit 10 part 1: Kinetic Molecular Theory: GASES and Gas Laws

2. 10.1.1: A Model to Explain Gas Behavior The Nature of Gas –All gases have mass –They are easy to compress –They fill their containers completely –They can diffuse (different gases can move through each other). You can smell dinner cooking. –They exert pressure –The pressure exerted depends on the TEMPERATURE of the gas.

3. The Kinetic-Molecular Theory Describes the behavior of Gases –1. Consists of very small particles with mass –2. Distance between molecules large compared to size. –3. Particles in constant, rapid, random motion.

4. –4. Collision of gas particles with each other or their container are perfectly elastic. –5. The kinetic energy of gas particles depends on the temperature. Higher temp = more KE Lower temp = less KE –http://www.chm.davidson.edu/chemistryapplets/kineticmoleculartheory/PT.htmlhttp://www.chm.davidson.edu/chemistryapplets/kineticmoleculartheory/PT.html –6. Gas particles exert no force on one another. Their attractive forces are very weak.

5. 10.1.2 Measuring Gases “In order to describe a gas sample and then make predictions about its behavior under changed conditions, it is important to deal with the values of FOUR VARIABLES – amount of gas, volume, temperature and pressure” Translation: we will describe and study gases with respect to those 4 variables.

6. Amount of Gas (n)- this is how many moles of gas you have. Volume (V)- Measured in liters, the volume of a gas is always the same volume as it’s container. –1 L = 1000cm 3 Temperature (T)- Measured in °C from a thermometer. However, Kelvin temp is needed for running your calculations. YOU MUST CONVERT! –T(K) = T (°C) + 273 Pressure (P)- This is the outward force applied to the container of the gas.

7. Atmospheric Pressure & the Barometer Atmospheric pressure- pressure exerted by the column of air in the atmosphere. Units of pressure: 1 PaPascal = 1 N/m 2 (The SI unit) 1 psi= 1 lb/in 2 (English unit) = 6,891 Pa 1 Bar= 10 5 N/m 2 = 100 kPa ≈ 1 atm 1 Torr= 1 mm Hg = 133.3 Pa 1 atm= 101.3 kPa = 760 mm Hg = 29.92 in Hg = 14.70 psi = 760 torr

8. Practice converting pressure units The air pressure in the cabin of a plane is 8.3lb/in 2. What is this pressure in atm? –0.56 atm The pressure in a tire in 109 kPa. What is this pressure in Pa and atm? –109,000 Pa –1.08 atm The pressure in a submarine is.625 atm. What is this pressure equivalent to in torr?

9. Barometer- instrument used to measure atmospheric pressure. You want to measure the height of the mercury in the tube. Usually as mmHg.

10. Enclosed Gases When the gas is in an open container, it’s pressure is equal to the atmospheric pressure. If the container is closed, then the pressure can be different than the atmospheric pressure. To measure this pressure we use a Manometer.

11. To use the manometer, you want to measure the DIFFERENCE in the heights of the mercury on each side of the U-shaped tube.

12. Practice problems A soccer ball is attached to an open-ended manometer. The Hg level in the manometer is 10mm higher on the side attached to the ball than the side open to the atmosphere. Atmospheric pressure has already been determined to be 770 mm Hg. What is the pressure in the ball? –760 mmHg A gas container is fitted with a manometer. The level of the Hg is 15mm higher on the open side. The atmospheric pressure has been determined to be 750 mmHg. What is the pressure IN ATMOSPHERES of the gas in the container? –1.007 atm

13. STP To make it easier to study and describe gas behavior we assume the gas is at Standard Temperature and Pressure. –273 K or 0°C –1atm or 760 mmHg or 101,325 Pa

14. 10.1.3 The Gas Laws There are 4 scientists that made great strides in understanding gas behavior. 1. Robert Boyle 2. Jacques Charles 3. Avogadro 4. John Dalton

15. Boyle’s Law: The Pressure-Volume Relationship English Chemist/Physicist Used a J – shaped tube to investigate the relationship between pressure and volume. “The pressure and volume of a sample of gas at constant temperature are inversely proportional to each other.” P 1 V 1 = P 2 V 2

16. Example Problem A gas at a pressure of 608 mmHg is in a 545 cm 3 volume container. The volume is increased to 1065 cm 3 with no change in temperature. What is the new pressure? P 1 V 1 = P 2 V 2 (608 mmHg) × (545 cm 3 ) = (P 2 ) × (1065 cm 3 ) P 2 = (608 mmHg) × (545 cm 3 ) (1065 cm 3 )

17. Charles’s Law: The Temperature- Volume Relationship A French physicist who used a cylinder with a moveable piston to test the relationship between Temperature and Volume. “At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature.” V 1 T 2 = V 2 T 1

18. Practice Problems What will the volume of a gas be at 355K if its volume at 273K is 8.57L? Assume pressure remains unchanged. V 1 T 2 = V 2 T 1 (8.57L) × (355K) = V 2 × (273K) V 2 = (8.57L) × (355K) (273K)

19. Avogadro’s Law: the Amount- Volume Relationship Equal volumes of gases at the same temperature and pressure contain an equal # of particles/moles.

20. Dalton’s Law of Partial Pressure The sum of the partial pressures of all the components in a gas mixture is equal to the total pressure of the gas mixture. P T = P a + P b + P c + …

21. Practice Problem What is the atmospheric pressure if the partial pressures of N 2, O 2 and Ar are 604.5 mmHg, 162.8 mmHg and 0.5 mmHg respectively? P T = P a + P b + P c + … P T = 604.5 + 162.8 + 0.5 http://www.youtube.com/watch?v=xtrEN-YKLBM

22. 10.1.4: The Ideal Gas Law Describes the behavior of an IDEAL gas. A gas described by the Kinetic-Molecular theory. PV= n RT P- pressure V- volume N- moleR- universal gas constant T- temperature

23. Universal gas constant (R) It’s value depends on the Pressure units. Numerical ValueUnits 0.0821atm - L/ mol - K 8.314 Pa – m 3 / mol – K kPa – L/ mol- K J/ mol – K Bar- L/ mol - K 62.4mmHg- L/ mol- K torr- L/ mol- K

24. Practice problems How many moles of gas at 100 °C does it take to fill a 2.5L flask at 1.50 atm? Convert 100 °C to K … 100 + 273 = 373K PV= n RT – (1.50 atm) (2.5L) = n (0.0821 atm-L/mol-K) (373K) = 0.122455777 moles

25. Deviations from Ideal Behavior At high pressures and low temperatures… real gases do not behave the Ideal gas law. –At high pressures, the distance between the molecules becomes much smaller thus, the volume of the gas molecules becomes important. –At low temperatures, the gas molecules slow down and now become attracted to each other. We no longer have perfectly elastic collisions.

26. 10.1.5 How Gases Work Lifting Power: –When the gas is less dense than air, it can be used to inflate balloons and blimps http://www.youtube.com/watch?v=F54rqDh2mWA

27. Effusion: The movement of gas molecules through a hole so tiny they pass through ONE molecule at a time. →

28. Graham’s Law @ constant T & P