Section 3.7—Gas Laws

1. 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. Unit 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 = 101300 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.

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 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? Problem: n1 = 0.15 mol 2.5 L = V2 V1 = 2.5 L 0. 15 mol 0.55 mol n2 = 0.55 mol V2 = (0.55 mol)(2.5L) V2 = ? (0.15 mol) V2 = 9.2 L

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 0.980 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 = 0.980 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 0.620 L at 25 0C if the temperature is lowered to 0 0C?

19. Combined Gas Law P = Pressure 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 0.125 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 0.225 mole? V1 = 1.5 L V2 = ? n1 = 0.125 mol n2 = 0.225 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 1. 3.0 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 = 105.7 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 0.323 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. Work because of changes Use different To produce Which is a With different Properties explained by One of which is Explanation for Airbags Changes States of Matter Gas Properties Kinetic Molecular Theory Density Gas Laws