1. Mr. Anthony Gates Chemistry Dubuque Senior High School
Gas Laws
Mr. Anthony Gates
Chemistry
Dubuque Senior High School

2. Standard temperature and pressure:
Review STP
Standard temperature and pressure:
P=1 atmosphere (atm)
T=0◦C (273K)
The volume of one mole of an ideal gas is 22.4L
Oh so that’s where that number came from!

3. Tires When you add more air to your tires, what happens?
Increasing the amount of air in the tires, increases the pressure.
As you release air, the pressure decreases.

4. Adding or removing gas
The relationship between the number of particles and pressure is a Direct Relationship.
If the number of particles is doubled, the pressure doubles.
If the pressure is decreased to 1/3 of the original amount, then there is 1/3 the original number of particles in the container.

5. Changing the size of the container
By increasing the volume, the particles are free to roam around more space which in turn causes less collisions and thus less pressure.
Volume and Pressure are Inversely Proportional
V goes up, P goes down and vice-versa

6. Temperature and Pressure are Directly Proportional
Heating and Cooling
Adding heat to a gas speeds up the particles creating higher impact collisions resulting in more pressure.
Temperature and Pressure are Directly Proportional
As temp goes up, pressure goes up

7. System vs. Surroundings
Two types of systems:
Closed (contained) Systems: easy to control variables
Open (uncontained) Systems: difficult to control variables
In all of the cases we study, we are assuming the systems are closed unless otherwise mentioned.

8. Gas Laws: Boyle’s Law P1V1=P2V2
Used to explain the inverse relationship between pressure and volume
In order for this law to hold true, temperature must be held constant
UNITS ON BOTH SIDES MUST BE THE SAME

9. Boyle’s Law
Ex: A sample of neon has a volume of 239 cm3 at 2.00 atm of pressure. What would the pressure be when the gas has a volume of 500 cm3?
P1=2.00 atm V1= 239 cm3 V2= 500 cm3 P2= ?
P1V1=P2V2
(2.00 atm)(239 cm3)=P2(500 cm3 )
(500 cm3 ) (500 cm3 )
.956 atm = P2

10. Gas Laws: Charles’s Law
𝑉 1 𝑇 1 = 𝑉 2 𝑇 2
Pressure must be constant for this law to hold true
TEMPERATURE MUST BE IN KELVINS
K= °C + 273

11. Absolute Zero and Charles’s Law
Absolute Zero can be derived using Charles’ Law
Absolute zero is the point where a substance has no kinetic energy, thus no heat.

12. Charles’s LAw
Ex: If a gas has a volume of 1.5 L at -25 °C, what will its volume be at -14 °C?
V1= 1.5 L T1= -25 °C V2= ? T2= -14 °C
V1 = V2
T T2
1.5 L = V2
248 K K
1.6 L = V2

13. Gas Laws: Gay-Lussac’s Law
P1 = P2
T T2
Explains the direct relationship between temperature and pressure.
Volume must be constant for this law to hold true.
Temperature must be in kelvins.
K= °C + 273

14. Gay-Lussac’s Law
Ex: If a gas has a pressure of 720. mmHg at 200. K, what will its pressure be at 300. K?
P1= 720. mmHg T1= 200. K P2= ? T2= 300. K
P1 = P2
T T2
720 mmHg = P2
200 K K
1080 mm Hg = P2

15. Gas Laws: The Combined Gas Law
P1V1 = P2 V2
T T2
Used to explain a situation where volume, temperature, and pressure of a gas are variables
Combination of the three previous laws
If T is constant, then Boyle’s Law
If P is constant, then Charles’ Law
If V is constant, then Temp-Pressure Rel.

16. The Combined Gas Law
If a gas that occupies 3.7 L of space at 37˚C at a pressure of 3.7 atm is compressed to 2.7 L and cooled to 10˚C, what will the new pressure of the gas be?
P1V1 = P2V2
T T2
3.7 L x 3.7 atm = L x P2
310 K K
4.6 atm = P2

17. Identify the appropriate gas law to use and solve the problem:
Practice
Identify the appropriate gas law to use and solve the problem:
A gas sample contained in a cylinder equipped with a moveable piston occupied mL at a pressure of atm. What would be the final pressure if the volume were increased to mL at constant temperature?
Boyle’s Law : 1.20atm

18. Identify the appropriate gas law to use and solve the problem:
Practice
Identify the appropriate gas law to use and solve the problem:
A sample of gas occupies 10.0 L at torr and 27.0C. Calculate the pressure if the temperature is changed to 127C while the volume remains constant.
Gay-Lussac’s Law : 133torr

19. Identify the appropriate gas law to use and solve the problem:
Practice
Identify the appropriate gas law to use and solve the problem:
A given sample of gas has a volume of 4.20 L at 60.0C and 1.00 atm pressure. Calculate its pressure if the volume is changed to 5.00 L and the temperature to 27C.
Combined Gas Law : 0.757atm

20. Identify the appropriate gas law to use and solve the problem:
Practice
Identify the appropriate gas law to use and solve the problem:
A fixed quantity of gas at 23.0C exhibits a pressure of 748 torr and occupies a volume of 10.3 L. Calculate the volume the gas will occupy if the temperature is increased to 145C while the pressure is held constant.
Charles’s Law : 14.5L

21. Extra Practice
A hot air balloon begins with 50,000.0 cubic meters of air at STP (1.00atm and 0.00°C), but after heating up the balloon, it reaches a pressure of atm the air in the balloon takes up 74, cubic meters. What is the temperature of the air in the balloon after heating?
Combined Gas Law: 392K or 119°C

22. Additional Practice
If a sealed rigid container at 52.0°C and 760torr is cooled down so that the new pressure is 657torr, what is the new temperature in degrees Celsius?
Gay-Lussac/Temp-pressure relationship: 7.95°C

23. More Practice
In a temperature controlled room, a 2.50L piston is expanded to 4.20L. If the final pressure of the gas in the piston is 12.6 psi, what was the initial pressure?
Boyle’s Law: 21.2 psi

24. Extra Practice
In a constant pressure system a gas is allowed to expand to 738.0ml of space. If the temperature rose from 25.0°C to 68.4°C, what was the initial volume?
Charles’s Law: 644ml

25. Gas Laws: The Ideal Gas Law
PV=nRT
Takes into account the number of particles (n) of gas involved
“n” is equal to the number of moles of gas involved

26. Deriving the Ideal Gas Law
**P and V are inversely proportional, so they are put together on the top half of the equation, and T and n are directly proportional so they are put on the bottom.
**If you put the values at STP in for P, V, n, and T, you can find the value for a constant “R”

27. Deriving the Ideal Gas Law cont.
“R” is the Ideal Gas Constant
PV = R nT
“R” will always be the same (one of 3 values)
if using kPa, L, mol, and K………… R= 8.31 kPa L/mol K
if using atm, L, mol, and K………………. R= atm L/mol K
if using mmHg, L, mol, and K………….. R= mmHg L/mol K

28. Ideal Gas Law
What is the volume of 29 g of O2 gas at 25°C and kPa?
29 g O mol O = .91 mol O2
32.0 g O2
P V = n R T
125.1 kPa x V =.91 mol x 8.31 kPa L/mol K x 298 K
V = 18 L

29. Practice… it makes perfect… or so I hear
A balloon of gas takes up 3.2L at a pressure of 1.02atm and 24.6◦C. How many moles are in the balloon?
0.1336mol of gas.

30. Dalton’s Law of Partial Pressures
Ptotal = P1 + P2 + P3 …
Dalton’s Law of Partial Pressures: At constant volume and temperature, the pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases
Partial Pressure: the contribution each gas makes to the total pressure

31. Dalton’s Law of Partial Pressures
Ex: A container containing O2, N2, and CO2 has a total pressure of 2.00 atm. What is the pressure of O2 if N2 has a pressure of .76 atm and CO2 has a partial pressure of .96 atm?
Ptotal = PO2 + PCO2 + PN2
2.00 atm = PO atm atm
PO2 = .28 atm

32. 𝑃 1 𝑃 𝑇 = 𝑛 1 𝑛 𝑇 Partial Pressures
The partial pressures are related to the number of moles of the gases.
PT = P1 + P2 + P3 + …..
Nt = n1 + n2 + n3 + ….. So…
𝑃 1 𝑃 𝑇 = 𝑛 1 𝑛 𝑇

33. Measuring pressure
Barometer measures pressure as the external pressure applies force to the mercury in the dish causing the mercury in the tube to rise. (left)
Manometers measure the pressure through the height changes the mercury undergoes. (right)

34. Ideal gas laws and other stuff… #ChemFun