1. How can we calculate Pressure, Volume and Temperature of our airbag?
Section 3.7—Gas Laws
Objectives:
Compare different pressure units
Relate the Kelvin and Celsius scales for temperature
Define standard temperature and pressure
Define and perform calculations for 5 gas laws
How can we calculate Pressure, Volume and Temperature of our airbag?

2. Pressure Units Pressure can be measured using several different units.
Symbol
atmospheres
atm
Pascals, kiloPascals
Pa, kPa
millimeters of mercury or torr
mm Hg, torr
pounds per square inch
psi

3. Pressure Units
It is fairly easy to convert from one unit to another. Use these as conversion factors.
1 atm =
Pa =
101.3 kPa* =
760 mmHg =
760 torr =
14.7 psi
* This is the SI unit for pressure.

4. Practice Convert the following pressure units. 750 mm Hg to atm
145 kPa to mm Hg
1.5 atm to kPa

5. Temperature The SI scale for temperature is the Kelvin scale.
Kelvin (K)– temperature scale whose lowest temperature is “0”, called absolute zero.
Temperatures cannot fall below an absolute zero!!
A temperature scale with absolute zero is needed in Gas Law calculations because you can’t have negative pressures or volumes

6. Temperature
It is very easy to convert temperatures in oC to K through this expression:
Practice:
25 oC = ___ K
350 K = ___ OC
0 OC = ___ K

7. Standard Temperature and Pressure
To ensure that scientists worldwide discuss gas behavior using the same temperature and pressure units, the international scientific community uses something called STP.
Standard Temperature and Pressure (STP) = 1 atm (or the equivalent in another unit) and 0°C (or 273 K)

8. Gas Laws
The gas laws summarize observations regarding how gases behave under different conditions.
Recall that the KMT explains why gases behave as they do. The laws summarize how they behave.
What are the gas laws?

9. “Before” and “After” in Gas Laws
4 of the gas laws we will learn have “before” and “after” conditions.
In the one of the laws we will learn, the expression is:
P1V1 = P2V2
P1 and V1 represent the starting conditions (or conditions “before” they are changed) of pressure and volume for a sample of gas.
P2 and V2 represent the resulting conditions (or conditions “after” they are changed) of pressure and volume for the same gas.

10. Avogadro’s Law
Avogadro’s Law relates # of moles and volume when temperature and pressure are held constant.
V = Volume
n = # of moles of gas
Hint: The two volume units must be the same
on both sides of the equation!

11. Avogadro’s Law Problem:
n1 = 0.15 mol L = V2
V1 = 2.5 L mol mol
n2 = 0.55 mol V2 = (0.55 mol)(2.5L)
V2 = ? (0.15 mol)
V2 = 9.2 L
A sample with 0.15 moles of gas has a volume of 2.5 L. What is the volume if the sample is increased to 0.55 moles?

12. Practice Problems
If a container holds 3.6 moles of helium in 4.7 L, how many moles could it hold if the container is increased to 5.8 L? (Hint: Use cross-multiplication to solve!)
A sample of 9.5 mol of oxygen occupies 8.2 L. What volume of the gas would be occupied by 13.0 mol?
2.8 mol of a gas are put in a container that has a volume of 15.0 L. If the size of the container is increased to 25 L, how many moles of gas could it then hold?

13. Boyles’ Law
Boyles’ Law relates pressure and volume when the temperature and number of moles are held constant.
P = pressure
V = volume
The two pressure units must match and
the two volume units must match!

14. Boyle’s Law Problem: A 2.5 L gas sample is held at
1.05 atm. What volume will it occupy if
the pressure is changed to atm.
V1 = 2.5 L (1.05 atm)(2.5 L) = (0.980 atm)V2
P1 = 1.05 atm V2 = (1.05 atm)(2.5 L)
V2 = ? (0.980 atm)
P2 = atm V2 = 2.7 L

15. Practice Problems
If 98 mL of a gas at 50.0 kPa has its volume reduced to 65 mL, what will the new pressure be?
A gas cylinder contains 25.0 L of gas under 5.0 atm of pressure. If the gas is transferred to a 30.0 L cylinder, what will the new pressure of the gas be?
A sample of gas has a volume of 12 L at 0.78 atm. The sample is put into a new tank under 1.4 atm of pressure. What is the volume of the tank?

16. Charles’ Law
Charles’ Law relates temperature and Volume when pressure and number of moles are held constant.
V = Volume
T = Temperature
The two volume units must match and
temperature must be in Kelvin!

17. Charles’ Law
Problem: V2 = ? 10.5 L = V2 V1 = 10.5 L 298 K 323 K T1 = 25 oC = 298 K V2 = (323K)(10.5 L) T2 = 50 oC = 323 K 298 K V2 = 11.4 L
What is the final volume if a 10.5 L sample of gas is heated from 25C to 50C?

18. Practice Problems
A gas sample at 40 0C occupies a volume of 2.32 L. If the temperature is raised to 75 0C, what will the volume be, assuming the pressure remains constant?
A gas at 89 0C occupies a volume of 0.67 L. At what temperature will the volume be increased to 1.12 L?
What is the volume of air in a balloon that occupies L at 25 0C if the temperature is lowered to 0 0C?

19. Combined Gas Law P = Pressure Each “pair” of units must match and
V = Volume
n = # of moles
T = Temperature
Each “pair” of units must match and
temperature must be in Kelvin!

20. Problem
What is the final volume if a mole sample of gas at 1.7 atm, 1.5 L and 298 K is changed to STP when enough gas is added to increase the number of moles to mole?
V1 = 1.5 L V2 = ?
n1 = mol n2 = mol
P1 = 1.7 atm P2 = 1.0 atm
T1 = 298 K T2 = 273 K
(1.7 atm)(1.5 L) = (1.0 atm)V2_
(0.125 mol)(298 K) (0.225 mol)(273 K)
V2 = (0.225 mol)(273 K)(1.7 atm)(1.5 L) = 4.2 L
(0.125 mol)(298 K)(1.0 atm)

21. Practice Problems
mol of gas at 110 kPa and 30 0C fills a flexible container with an initial volume of 2.0 L. If the temperature is raised to 80 0C, the pressure is increased to 440 kPa, and the number of moles increases to 4.5 mol, what is the new volume?
2. At STP, a 6.5 mol gas sample occupies 30 mL. If the temperature is increased to 30 0C, the entire sample is transferred to a 20 mL container, and 3.5 additional moles of gas are added, what will be the gas pressure inside the container?

22. The Combined Gas Law Is All You Need
The combined gas law can be used for all of the gas law problems we have learned so far!
For example, if the temperature and number of moles are
held constant, then T1 = T2 and n1 = n2. When variables
are the same, you can cancel them on both sides.
The combined gas law becomes Boyle’s Law!

23. Transforming the Combined Law
Watch as variables are held constant and the combined gas law “becomes” the other 3 laws
Hold pressure and temperature constant
Avogadro’s Law
Hold moles and temperature constant
Boyles’ Law
Hold pressure and moles constant
Charles’ Law

24. The Ideal Gas Law
The Ideal Gas Law does not compare situations—it describes a gas in one situation.
P = Pressure
V = Volume
n = moles
R = Gas Law Constant
T = Temperature
The value for “R” depends on the unit that is used for pressure. There are two possibilities:
Choose the one with units that match your pressure units!

25. The Ideal Gas Law Example
Problem: A sample with 0.55 mol of gas is at
105.7 kPa and 27 oC. What volume does it
occupy?
n = 0.55 mol (105.7 kPa)V =
(0.55 mol)( )(300 K)
P = kPa
T = 27 oC = 300 K V = (0.55)(8.31 L-kPa)(300)
V = ? (105.7 kPa)
R = V = 13 L

26. Practice Problems
1. Calculate the number of moles of gas contained in a 3.0 L
vessel at 3000 K with a pressure of 1.50 atm.
2. Determine the temperature of 2.49 moles of gas
contained in a 1.00 L vessel at a pressure of 143 kPa.
3. Calculate the pressure that a mol sample of a gas
have at 265 K and a volume of 7.8 L.
R = or

27. What did you learn about airbags?

28. Kinetic Molecular Theory
Airbags
Use different
Work because of changes
Changes
States of Matter
To produce
Which is a
Gas
With different
Properties
Properties explained by
One of which is
Kinetic Molecular Theory
Density
Gas Laws
Explanation for