1. Gas Laws Chapter 14 Mrs. Hayen, Fall ‘03

2. Kinetic Molecular Theory Gas particles do not attract or repel each other. Gas particles are much smaller than the spaces between them. Gas particles are in constant, random motion. No kinetic energy is lost when gas particles collide with each other or with the walls of their container. All gases have the same kinetic energy at the same temperature.

3. Three factors that affect gases: Temperature: A measure of the kinetic energy of a gas Measured in ºC or in K Volume: A measure of the amount of space the gas occupies (equal to vol. of container) Measured in L or mL Pressure: A measure of the number of times the molecules collide (with each other and/or with the walls of the container) Measured in mm Hg, kPa, or atm. (SI unit for pressure)

4. Important Info STP = Standard Temperature & Pressure 0 °C 1 atm 273 K 101.3 kPa 760 mmHg Pressure unit conversions: 1 atm = 760 mmHg = 101.3 kPa Temperature unit conversions: Kelvin = °C + 273 Temperature should always be in Kelvin units for gas law problems The “Big Three…”

5. Boyle’s Law Pressure is inversely related to volume. [In other words: as pressure increases, volume decreases.] P 1 V 1 = P 2 V 2 Example: A sample of compressed methane has a volume of 648 mL at a pressure of 503 kPa. To what pressure would the methane have to be compressed in order to have a volume of 216 mL? Answer: 1510 kPa

6. Charles’ Law Volume is directly proportional to temperature. [In other words: as temperature increases, volume increases.] V 1 /T 1 = V 2 /T 2 Example: A weather balloon contains 5.30 kL of He gas when the temperature is 12 ºC. At what temperature will the balloon’s volume have increased to 6.00 kL? Answer: 50 ºC

7. Gay-Lussac’s Law Pressure is directly proportional to temperature. [In other words: as temperature increases, pressure increases.] P 1 /T 1 = P 2 /T 2 Example: Pressure inside a jelly jar before it is sealed is 1.75 atm at 25 ºC. Volume is constant. After the jar is heated to 100. ºC, what is the new pressure? Answer: 2.19 atm

8. Combined Gas Law The combined laws of Boyle, Charles, and Gay-Lussac: P 1 V 1 /T 1 = P 2 V 2 /T 2 Example: A student collects 285 mL of O 2 gas at 15 ºC and a pressure of 99.3 kPa. The next day, the same sample occupies 292 mL at a temperature of 11 ºC. What’s the new pressure? Answer: P 2 = 95.6 kPa

9. Avogadro’s principle The principle that equal volumes of all gases at the same conditions of temperature and pressure have the same number of molecules. I mol = 22.4 L @ STP Now you can interrelate the following for any gas: Mass, moles, pressure, volume, and temperature Example: What is the volume of 7.17 g of Ne (g) at 24 º C and 1.05 atm? Answer: 8.24 L Ne

10. Gases can be ideal or real: Ideal gases follow the principles of the kinetic molecular theory and obey the previous laws exactly. Real gases show slight deviations from the laws. However, at normal (not extreme) temperatures and pressures, these deviations can be ignored and therefore the gases we discuss can be treated as ideal gases.

11. Ideal Gas Law The equation that relates moles, pressure, volume, and temperature and adjusts for conditions other than STP PV = nRT where n = number of moles & R= ideal gas constant R= 8.314 LkPa = 0.0821 Latm molK molK

12. Ideal Gas Law (cont’d) Example: What pressure (in atm) will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temperature of 45 ºC? R= 8.314 LkPa = 0.0821 Latm molK molK Answer: 40.5 atm

13. Dalton’s Law Each gas in a mixture exerts pressure independently of the other gases. The total pressure of a mixture is equal to the sum of the pressures of the individual gases. P Total = P 1 + P 2 + P 3 +… P n Example: Air is made up of four main gases: N 2, O 2, Ar, and CO 2. Air presusre at sea level is approximately 760 mm Hg. Calculate the partial pressure of O 2 given the following: N 2 = 594 mm Hg; Ar = 7.10 mm Hg; CO 2 = 0.27 mm Hg. Answer: 158.63 mm Hg

14. Graham’s Law Gases move from areas of high concentration to areas of low concentration based on their molecular mass. [In other words, the bigger the molecule, the slower it will diffuse.] Identify formula & understand concept only. Rate A = molar mass B Rate B molar mass A

15. Know these laws: Boyle’s Law Charles’ Law Gay-Lussac’s Law Combined Gas Law Ideal Gas Law Dalton’s Law Graham’s Law

16. Gas Stoichiometry Ammonium Sulfate can be prepared by a reaction between ammonia gas and sulfuric acid. The skeleton equation is: NH 3 (g) + H 2 SO 4  (NH 4 ) 2 SO 4 (aq) What volume of ammonia gas, measured at 78ºC and a pressure of 1.66 atm, will be needed to produce 5.00 X 10 3 g of ammonium sulfate? [You have to balance the equation first!] 2 Answer: 1310 L