1. Gas Laws

2. Gases No definite shape or volume Easily compressible
Kinetic Theory of Matter - All particles are moving all the time.

3. What do we know about gas particles?
Can be either molecules or atoms; e.g. He, O2, C3H8
Very far apart from one another.
Between particles is empty space.
No attractive or repulsive forces between particles.
Move randomly.
Move at high speeds (O2 at 20oC moves at 1700 km/h).
Travel in straight paths.
Only change direction when collide with another particle/object.
Collide elastically (no kinetic energy lost).  Ideal Gas

4. Gas Pressure The force exerted by a gas per unit of surface area.
 Created by the collision of gas particles with a surface.

5. Atmospheric Pressure
Atmospheric Pressure: created by the gases that make up Earth’s atmosphere.
 Atmospheric pressure decreases as elevation increases (lower density of gases).
 Measured using a Barometer.

6. Units of Pressure SI Unit = pascal (Pa) Other units: atmospheres (atm)
millimeters of mercury (mmHg)
torr
pounds per square inch (psi)
Standard Pressure: kPa = 1 atm = 760 mmHg = 760 torr = 14.7 lb/in2 (psi)
Rmv psi

7. Pressure Conversion Practice
7.31 psi = _______ mmHg psi x 760 mm Hg = mm Hg
14.7 psi
1140 torr = _______ kPa
1140 torr x kPa = 152 kPa
760 torr
19.0 psi = ________ kPa
19.0 psi x kPa = 131 kPa
202 kPa = ________ atm
202 kPa x atm = 1.99 atm
101.3 kPa
Rmv psi

8. Temperature
Temperature: average kinetic energy of particles
The faster the particles are moving, the higher the temperature.
Kelvin temperature is directly proportional to the average kinetic energy of the particles of the substance.
Particles at 200K have twice the average KE of particles at 100K.
Absolute Zero: KE = 0; all motion of particles stops
 TK = TC + 273

9. Vacuum empty space  no particles no pressure
A vacuum pump is a device that removes gas molecules from a sealed volume in order to leave behind a partial vacuum

10. Gas Laws P1V1 P2V2 T1 T2 = (FOR A FIXED AMOUNT OF GAS)
(COMBINED GAS LAW)

11. Boyle’s Law
Boyle’s Law: At constant temperature, the pressure and volume of a gas are inversely proportional.
P1V1 = P2V2
Graph:

12. Boyle’s Law

13. Boyle’s Law Conceptual Problems
If the volume of a gas is decreased by half, what happens to its pressure?
Pressure is doubled
2) If the pressure tripled, what must have happened to the volume of the gas?
Volume decreases by a third
If the volume doubles, what happens to pressure?
Pressure decreases by half

14. Boyle’s Law -. Both Pressures must be in the same unit
Boyle’s Law - *Both Pressures must be in the same unit *Both Volumes must be in the same unit.
Math Problems
The volume of a gas at 99 kPa is 300 mL. If the pressure is increased to 188 kPa, what will be the new volume?
99 ( 300) = 188 V mL = V2
2) The pressure of a sample of helium in a 1.0-L container is atm. What is the new pressure if the sample is placed in a 2.0-L container?
0.988 (1) = P2 (2)
0.494 atm = P2

15. Cartesian Diver
How does it work???

16. Charles’s Law
Charles’s Law: At constant pressure, the volume of a gas is directly proportional to its Kelvin temperature.
V1 = V2
T1 T2
Graph:

17. Charles’s Law

18. Liquid Nitrogen

19. Charles’s Law Conceptual Problems
If the temperature of a gas is doubled, what must happen to volume in order for pressure to remain constant?
Pressure is doubled
2) If the volume of a gas decreases to one-third its original volume, what happens to the temperature in order for pressure to remain constant?
Temperature decreases one-third

20. Charles’s Law The Math…
The Kelvin temperature of a 3.0-L sample of gas is lowered from 353 K to 303 K. What will be the resulting volume of this gas?
= V2
(303) = 353V2
2.58 L = V2
2) A gas at 89oC occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L?
Change temp to K: = 362 K
= 1.12 T2
0.67T2 = 1.12 (362)
T2 = 605 K
Change temp back to Celsius: 605 = C + 273
332 oC = T2

21. Gay-Lussac’s Law
Gay-Lussac’s Law: At constant volume, the pressure of a gas is directly proportional to its Kelvin temperature P1 = P2
T T2

22. Gay-Lussac’s Law
What happens to pressure if temperature increases and volume is held constant?
Pressure increases
The pressure in an automobile tire is 1.88 atm at 25oC. What will be the pressure if the temperature warms up to 37oC?

23. Combined Gas Law Combined Gas Law: for a fixed amount of gas.
P1V1 = P2V2
T T2
STP = 273 K (0 oC), 1 atm

24. Use gas laws to solve the following problems
A gas occupies 12.3 liters at a pressure of mmHg. What is the volume when the pressure is increased to 60.0 mmHg?
The temperature of a 4.00 L sample of gas is changed from 10.0 °C to 20.0 °C. What will the volume of this gas be at the new temperature if the pressure is held constant?
If a gas is cooled from K to K and the volume is kept constant what final pressure would result if the original pressure was mmHg?

25. Combined Gas Law Conceptual Problems
What happens to temperature if volume and pressure are both doubled?
Temperature is multiplied by 4
What happens to pressure if volume and temperature are both tripled?
Temp increases by multiple of 9
What must happen to volume if pressure is halved and temperature is doubled?
Volume is multiplied by 4

26. Combined Gas Law Math Problems
A helium-filled balloon at sea level has a volume of 2.1 L at atm and 36oC. If it is released and rises to an elevation at which the pressure is 0.9 atm and the temperature is 28oC, what will be the new volume of the balloon?
V1 = 2.1 L V2 = ?
P1 = atm P2 = 0.9 atm
T1 = = 309 K T2 = = 301 K V2 = 2.27L
At STP, a sample of gas occupies 30 mL. If the temperature is increased to 30 oC and the entire gas sample is transferred to a mL container what will be the gas pressure inside the container?
P1 = 1 atm P2 = ?
T1 = 273 K T2 = = 303 K
V1 = 30 mL V2 = 20 mL
P2 = 1.67 atm

27. Ideal Gas Law n = number of moles
Ideal Gas Law – Amount of Gas Varies
PV = nRT
n = number of moles
R = Gas constant (see reference tables for different values)

28. Ideal Gas Law
What pressure is exerted by mol of a gas at 25oC if the gas is in a L container?
PV = nRT P = ? P (.650) = .450(0.0821)(298)
V = L P = 11
n = mol P = 16.9 atm
T = = 298 K
R = L-atm/(mol K)
2) Determine the volume occupied by mol of a gas at 15oC if the pressure is 81.8 kPa.

29. Ideal Gases vs Real Gases
What we know about Ideal Gases:
No attractive/repulsive forces
Collide elastically (no loss of KE)
Ideal gas behavior occurs at HIGH temps and LOW pressure.
This keeps gases moving and far apart, causing no intermolecular forces
Real Gases:
Attractive/repulsive forces are present
Collide in-elastically
More collisions will occur at HIGH pressures
Attractive/repulsive forces increase as temperatures DECREASE

30. Ideal Gas Law Problems
How many moles of gas are contained in mL at 21.0 °C and mmHg pressure?

31. At what pressure would 0.150 mole of nitrogen gas at 23.0 °C occupy 8.90 L?

32. Calculate the volume 3. 00 moles of a gas will occupy at 24
Calculate the volume 3.00 moles of a gas will occupy at 24.0 °C and mmHg.

33. What volume will 1.27 moles of helium gas occupy at STP?

34. Avogadro’s Law
Avogadro’s Law – the amount of gas (# of moles) is directly proportional to the volume of the gas.
n1 = n2
V1 V2

35. Avogadro’s Law
Assuming that pressure and temperature remain constant, what happens to the volume of a gas if the number of moles doubles? Volume doubles
If you have two moles of a gas in a 4-liter container, how many moles of the gas would occupy a 3-liter container and retain the same pressure and temperature.

36. Mixtures of Gases
Dalton’s Law of Partial Pressures: the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture.
Ptotal = P1 + P2 + P3 + …
Partial Pressure of a Gas: the portion of the total pressure contributed by a single gas.

37. Dalton’s Law of Partial Pressures
What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total pressure is 600 mmHg and the partial pressure of helium is 439 mmHg?
PT = P1 + P2
600 = P2
161 mmHg = P2

38. Dalton’s Law Problem
Ex. A mixture of neon and argon gases exerts a total pressure of 2.39 atm.   The partial pressure of the neon alone is 1.84 atm, what is the partial pressure of the argon?

39. Dalton’s Partial Pressure Example
A synthetic atmosphere is created by blending 2 mol percent CO2, 0.2 mol O2 and 1.5 mol N2. If the total pressure is 750 torr, calculate the partial pressure of each component. (Hint: What percent of the mixture is each gas?)

40. Dalton’s Partial Pressure Example
Consider the flask diagramed below with the following pressures: 492 torr for H2 and 286 torr for N2. What are the final partial pressures of H2 and N2 after the stopcock between the 2 flask is opened? (Assume the final volume is 3.00L) What is the total pressure in torr?

41. Gas Laws Question 1996 FRQ
Represented above are five identical balloons, each filled to the same volume at 25°C and 1.0 atmosphere pressure with the pure gases indicated.
Which balloon contains the greatest mass of gas? Explain.
(b) Compare the average kinetic energies of the gas molecules in the balloons. Explain.
(c) Which balloon contains the gas that would be expected to deviate most from the behavior of an ideal gas? Explain.
(d) Twelve hours after being filled, all the balloons have decreased in size. Predict which balloon will be the smallest. Explain your reasoning.
CO2
All the same He

42. Bellwork Complete the following problems:
1. If 4 moles of a gas are at a pressure of 5.4 atm and have a volume of 120 L, what is the temperature?
2. My car has an internal volume of 2600 L. If the sun heats my car from 20oC to 55oC, what will the pressure inside my car be? (Assume the initial pressure was 760 mmHg).
How many moles of gas are in my car?