Understanding Pressure and Gas Laws in Physics

1. Chapter 11:Gases

2. Section 1: Gases and Pressure

3. Units of Pressure • Millimeters of Mercury (mm Hg) is the most common because mercury barometers are most often used. Average atmospheric pressure at sea level at 0°C is 760 mm Hg. • Torr is another name for pressure when a mercury barometer is used in honor of Torricelli for his invention of the barometer. 1 torr = 1 mm Hg

4. One atmosphere of pressure (1 atm) is defined as being exactly equivalent to 760 mm Hg. • One pascal (Pa) is defined as the pressure exerted by the force of one Newton (1 N) acting on an area of one square meter. Can also be expressed in kilopascals (kPa). 1 atm = 1.01325 x 105 Pa = 101.325 kPa 1 atm = 760 mm Hg = 760 torr

5. Standard Temperature and Pressure • Because volumes of gases change so much when the temperature or pressure changes, scientists have agreed on standard conditions of exactly 1 atm pressure and 0˚C. • These are called standard temperature and pressure or STP.

6. 738 mm Hg • 0.971 atm x 760 mm Hg = 1 1 atm • 0.971 atm x 101.325 kPa = 1 1 atm 98.4 kPa

7. Dalton’s Law of Partial Pressures • Partial Pressure is the pressure of each gas in a mixture of a gas. • Dalton’s Law of Partial Pressure states that the total pressure of a gas mixture is the sum of the partial pressures of the component gases. PT = P1 + P2 + P3 + …

8. PTis the total pressure of the mixture. • P1, P2, P3, and so on, are the partial pressures of the component gases. Examples: • PT = 2.00 atm + 3.00 atm + 4.00 atm • PT = 9.00 atm • 4.00 atm = 2.30 atm + PAr • Par = 4.00-2.30 = 1.70 atm

9. Gases Collected by Water Displacement • The pressure of the water vapor must be taken into account when determining the pressure of the gas. Patm = Pgas + PH20 • The vapor pressure of water is dependent on temperature (Table A-8 on page 859).

10. Example: • Oxygen gas from the decomposition of potassium chlorate, KClO3, was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0 torr and 20.0°C. What was the partial pressure of the oxygen collected? • Patm = 731.0 torr and PH2O = 17.5 torr at 20.0°C • Patm = PO2 + PH2O  PO2 = Patm – PH2O • PO2 = 731.0 torr – 17.5 torr = 713.5 torr

11. Example: • Some Hydrogen gas is collected over water at 20.0°C. The partial pressure of hydrogen is 742.5 torr. What was the barometric pressure at the time the gas was collected? • PH2 = 742.5 torr and PH2O = 17.5 torr at 20.0°C • Patm = PH2 + PH2O • Patm = 742.5 torr + 17.5 torr = 760.0 torr

12. Section 2:The Gas Laws

13. Boyle’s Law: Pressure-Volume Relationship P1x V1 = P2 x V2 • What must stay constant for Boyle’s Law to work? Temperature • Pressure can be in any unit, but both must be the same. • Volume can be in any unit, but both must be the same.

14. Example: • A sample of oxygen gas has a volume of 150.0 mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant? • Trying to find the new volume V2 • So we rearrange the equation V2 = P1 x V1 / P2 • Plug in the 3 known values and solve. V2 = 144 mL

15. Example: • A balloon filled with helium gas has a volume of 500 mL at a pressure of 1 atm. If the pressure decreases to 0.5 atm and the temperature remained the same, what volume does the gas now occupy? • Trying to find the new volume V2 • So we rearrange the equation V2 = P1 x V1 / P2 • Plug in the 3 known values and solve. V2 = 1000 mL

16. Charles’s Law: Volume-Temperature Relationship V1 = V2 T1 = T2 • What must stay constant for Charles’s Law to work? pressure • Volume can be in any unit, but both must be the same. • Temperature must in Kelvins. K = 273 + °C

17. Example: • A sample of Neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant? • Trying to find the new volume V2 Convert °C to Kelvins • Rearrange the equation  V2 = V1 x T2 / T1 • Plug in the 3 known values and solve. V2= 815 mL Ne

18. Example: • A sample of Nitrogen gas in a container has a volume of 375 mL at 0.0°C. To what temperature must the gas be heated to occupy a volume of 500.0 mL? • Trying to find the new temperature T2 Convert °C to Kelvins • Rearrange the equation T2= V2x T1/ V1 • Plug in the 3 known values and solve. T2= 364 K or 91°C

19. Gay-Lussac’s Law: Pressure-Temperature Relationship P1= P2 T1 = T2 • What must stay constant for Gay-Lussac’s Law to work? volume • Pressure can be in any unit, but both must be the same. • Temperature must in Kelvins. K = 273 + °C

20. Example: • The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C? • Trying to find new pressure P2. Convert °C to Kelvins • Rearrange equation  P2 = P1 x T2 / T1 • Plug in the three known values and solve. P2= 3.27 atm

21. Example: • A sample of helium gas has a pressure of 1.20 atm at 22°C. At what Celsius temperature will the helium reach a pressure of 2.00 atm, assuming constant volume? • Trying to find new temperature T2. Convert °C to Kelvins • Rearrange equation T2= P2x T1/ P1 • Plug in the three known values and solve. T2= 219°C

22. The Combined Gas Law P1 V1 = P2 V2 T1 T2 • This law works when nothing is staying constant. • Pressure can be in any unit, but both must be the same. • Volume can be in any unit, but both must be the same. • Temperature must in Kelvins. K = 273 + °C

23. Example: • A helium-filled balloon has a volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10°C? • Trying to find the new volume V2 • Rearrange equation V2= P1 x V1 x T2 / T1 x P2 • Convert °C to Kelvins • Plug in the known values and solve. V2= 60.0 L

24. Example: • The volume of a gas is 27.5 mL at 22.0°C and 0.974 atm. If the volume decreased to 26.3 ml at 0.993 atm, what is the new temperature of the gas? • Trying to find the new temperature T2 • Rearrange equation T2= P2x V2x T1/ P1x V1 • Convert °C to Kelvins • Plug in the known values and solve. T2= 288 K or 14.6°C

25. Section 3:Gas Volumes and Ideal Gas Law

26. Standard Molar Volume of A Gas: the volume occupied by one mole of a gas at STP is 22.4 L. 22.4 L or 1 mol 1 mol 22.4 L • Using this conversion, you can get from grams  moles  Liters or vice versa. • Remember: this only works at STP

27. Examples • What volume does 0.8980 mol of gas occupy at STP? • What quantity of gas, in moles, is contained in 2.21 L at STP?

28. Ideal Gas Law • The Ideal Gas Law is the mathematical relationship among pressure, volume, temperature, and the number of moles of gas. PV = nRT P = Pressure V = Volume n = number of moles R = ideal gas constant T = Temperature

29. Ideal Gas Constant • The value you will use is R = 0.0821 L·atm/(mol·K) • It may be necessary to convert units. Example • What is the pressure in atmospheres exerted by a 0.750 mol sample of nitrogen gas in a 10.0 L container at 298 K?

30. Section 4:Diffusion and Effusion

31. Graham’s Law of Effusion • Diffusion: the gradual mixing of two or more gases due to their spontaneous, random motion. • Effusion: the process whereby the molecules of a gas confined in a container randomly pass through a tiny opening in the container.

32. Examples • Compare the rates of effusion of hydrogen and oxygen at the same temperature and pressure. • Compare the rates of effusion of helium and argon at the same temperature and pressure.