1. Combined Gas Laws

2. Measurement For measuring temperature and pressure: STP: Standard Temperature and Pressure T = 0 0 C or 273 K P = 101.3 kPa at sea level SATP: Standard Ambient Temperature and Pressure T = 25 0 C or 298 K P = 100 kPa at sea level (use 3 s.d.)

3. Combined Gas Law using Boyle’s Law and Charles’ Laws If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! (use T K )

4. Combined Gas Law Sample problems: 1.A balloon has a volume of 5.5 L at SATP. What volume will the same balloon occupy at –5.0 0 C and a pressure of 125 kPa? (ans: 4.0 L) 2. To what temperature (in 0 C) must 25.0 mL of argon gas at STP be heated such that the new volume is 30.0 mL and the pressure is 110 kPa? (ans: 83 0 C) 3. Rearrange the combined gas law equation to solve for a) P 2 b) T 1

5. 5 Combined Gas Law Problem A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? [331°C] A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

6. Recap So far we have manipulated 3 variables: ______, _______, and _______ The one variable that has remained constant is ________ What happens when we change the quantity (i.e. number of moles) of a gas?

7. Predict… 2 L of H 2(g) 1 L of O 2(g) ___ L of ____ (g)

8. The Law of Combining Volumes Gay-Lussac ’ s “ real ” law “ When temperature and pressure remain constant, the volumes of gaseous reactants and products are always in simple whole number ratios ” STOICH!

9. AVOGADRO’S LAW The volume of a gas is directly proportional to the amount of gas, when temperature and pressure remain constant. V He = 2 L V Ar = 2 L V  n V 1 = V 2 n 1 n 2 Ar He

10. AVOGADRO’S LAW Example: 1. A 224 L container of hydrogen gas at STP contains 10.0 moles of hydrogen. If 5.0 moles of hydrogen is added, and the temperature and pressure remain constant, determine the volume of the gas. (ans: 336 L)

11. AVOGADRO’S LAW Back to gases and chemical reactions … – In a balanced chemical equation, the coefficients for gaseous substances represent volume ratios as well as mole ratios. Ex:N 2(g) + 3H 2(g)  2NH 3(g) 1 mol 3 mol 2 mol 1 vol 3 voL 2 vol 1 L 3 L 2 L

12. AVOGADRO’S LAW Example: 2. The reaction below is known as the Haber Process. N 2(g) + 3H 2(g)  2NH 3(g) What volume of nitrogen is needed to react with 12.0 L of hydrogen? (ans: 4.00 L N 2 )

13. MOLAR VOLUME At STP (O˚C, 101.3 kPa) one mole of any gas occupies 22.4 L At SATP (25˚C, 100 kPa) one mole of any gas occupies 24.8 L Molar Volume: If equal volumes of any gas contain the same number of particles (at constant T & P)… Then one mole of any gas should occupy the same volume (under defined conditions)

14. Molar Volume Example: 3. Suppose you have 32.12 g of methane gas (CH 4(g) ) at STP. The volume occupied by this gas is 44.8 L. a)How many moles are present? (ans:2.00 mol) b) How many molecules are present? (1.20x10 24 molecules) c)What volume would 1.00 mol of this gas occupy at STP? (22.4 L)

15. Combined Gas Laws Recall (for constant T + P) or and (for constant T + P)(for a fixed amount of gas) Therefore (use T K )

16. Combined Gas Laws Example: 4. A 1.80 g sample of helium gas occupies 10.0 L at STP. If the gas container leaks, what will be the new volume if 0.50 g escapes when the temperature is raised to 15 0 C and the pressure changes to 95 kPa? (ans: 8.1 L)

17. Mixtures of Gases Partial pressure = the pressure, P, a gas in a mixture would exert if it were the only gas present in the same volume and at the same temperature

18. Dalton’s Law of Partial Pressure Consider a mixture of gases, the total pressure of the mixture is the sum of the pressures of each of the individual gases. P total = P 1 + P 2 + P 3 + …etc

20. Explaining Dalton’s Law of Partial Pressures with Kinetic Molecular Theory: – The pressure of a gas is caused by the collisions of molecules with the walls of the container – Gas molecules act independently of each other Therefore the total pressure (total of the collisions with the walls) is the sum of the individual pressures (collisions of only one kind of particle) of each gas present. Dalton’s Law of Partial Pressures

22. Dalton’s Law of Partial Pressure Sample problem: 1. A mixture of 3 gases has a total pressure of 138 kPa. This mixture is 35 % N 2(g), 54 % O 2(g) and the rest is CO 2(g). Calculate the partial pressure of each gas in this mixture. Ans: P N 2 = 48 kPa P O 2 = 75 kPa P CO 2 = 15 kPa

23. Percentage Composition of Air

24. Altitude vs Pressure

25. Partial Pressure Application At high altitude the percentage of oxygen in air may still be normal (21%) BUT the partial pressure of oxygen may be sufficiently low that the human system cannot function very well

26. Partial Pressure Application

27. Sea level: 101kPa – 21% of 101kPa = 21kPa Top of a mountain: 33kPa 21% of 33kPa = 7kPa – Most people require about 10kPa in order to survive

28. Airplanes & Altitude Humans organs have evolved to live at 1atm Airplanes function best at higher altitudes where the pressure is much lower This problem was originally discovered when the first pilots reached an altitude at which they lost consciousness

29. Airplanes & Altitude At first the problem was solved by filling tanks with pressurized oxygen and inhaling the gas through rubber tubes Later form-fitting face masks made oxygen delivery more reliable Then openings were sealed to prevent air from escaping, windows were reduced in size and strengthened, and the cabin inside became a pressure capsule - like a big aluminum can

30. Airplanes – Pressurized Cabins Airplanes fly at 35,000 feet, while the pressurization system maintains the cabin at the pressure you would experience at 7,000 feet, sea level

31. If an airplane is not pressurized? Passengers would suffocate at around 20,000 feet What would happen if you opened the emergency door of a commercial plane during a flight? The doors of an airplane cannot be opened in flight, because they are held closed by the air pressure inside the cabin. The doors are designed such that they must move inward before they can move outwards when they are being opened, and they cannot move inwards when the airplane is pressurized because the air pressure presses the doors against their frames with a pressure of several tons. Thus, there is no danger of anyone opening a door in flight.

32. Partial Pressures of Atmospheric Gases Air consists of a mixture of gases: N 2 = 78.08%O 2 = 20.95% Ar = 0.93 %CO 2 = 0.03% If Standard atmospheric pressure is 101.3 kPa, determine the partial pressure of each gas.

33. Gas Collection over Water Hydrogen gas from the reaction of Zinc with hydrochloric acid was collected by the displacement of water. Atmospheric conditions were 100.5 kPa and 20˚C. Determine the partial pressure of hydrogen gas. P tot = P atm = P H2 + P H2O P H2 = P atm - P H2O = 100.5 kPa - 2.3 kPa = 98.2 kPa

34. Deep Sea Diving Pressure increases the lower you go in water Divers need pressurized air tanks The tank containing compressed air is attached to a regulator that releases the air at the same pressure as the underwater surroundings

35. Deep Sea Diving If a diver ascends to normal pressure too quickly or while holding their breath… Boyle’s law… … the pressure decrease – the volume of air increases Lungs could rupture

36. Homework