1. Chapters 10 and 11: Gases Chemistry Mrs. Herrmann

2. Kinetic Molecular Theory Kinetic-Molecular Theory: based on idea that particles of matter are always in motion Kinetic-Molecular Theory: based on idea that particles of matter are always in motion IDEAL GAS = an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory. IDEAL GAS = an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory.

3. 5 Assumptions of K-M Theory 1. Gases consist of large numbers of tiny particles that are far apart relative to their size. 2. Collisions between gas particles and between particles and container walls are elastic collisions (no net loss of kinetic energy K.E. = ½ mv 2 and temperature constant). 3. Gas particles are in continuous, rapid, and random motion. So they possess K.E. 4. There are no attractive or repulsive forces between gas particles. 5. The average kinetic energy of gas particles is dependent on the temperature of the gas. (All gases at same temperature have the same average kinetic energy!

4. Ideal Gases Kinetic Molecular theory applies only to ideal gases Kinetic Molecular theory applies only to ideal gases Most gases behave as ideal if Most gases behave as ideal if 1. pressure is NOT very high 2. temperature is NOT very low. 3. particles are far enough apart 4. particles have enough kinetic energy 5. particles of gases are nonpolar (more polar the more the deviation from ideal behavior)

5. Definitions Diffusion: spontaneous mixing of the particles of two or more substances caused by their random motion --depends on speed, diameter, and attractive forces between particles Effusion: process by which gas particles pass through a tiny opening. --directly proportional to the velocities of particles

6. More Definitions Pressure: force per unit area on a surface --pressure exerted by gas depends on 1. volume 2. temperature 3. number of molecules present Atmospheric pressure at sea level = 10.1 N/cm 2 (78% nitrogen, 21% oxygen, and 1% other gases (Ar and CO 2 ) Barometer: device used to measure atmospheric pressure

7. Common Units of Pressure 1mm Hg = 1 torr 1mm Hg = 1 torr Average atmospheric pressure at sea level at 0ºC = 760 mm Hg so Average atmospheric pressure at sea level at 0ºC = 760 mm Hg so 1 atms = 760 mm Hg = 101.325 kPa 1 atms = 760 mm Hg = 101.325 kPa SI unit for pressure is the pascal where SI unit for pressure is the pascal where 1 Pa = pressure exerted by a force of one newton on an area of one square meter.

8. STP STP = standard temperature and pressure 1 atms pressure 0ºC temperature

9. GAS LAWS Boyle’s Law: the volume of a fixed mass of gas varies inversely with the pressure at constant temperature Boyle’s Law: the volume of a fixed mass of gas varies inversely with the pressure at constant temperature P 1 V 1 = P 2 V 2 --where 1 indicates intitial conditions and 2 indicates the new conditions --inverse relationship between volume and pressure V P

10. GAS LAWS Charles’s Law: the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature. Charles’s Law: the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature. V 1 = V 2 V 1 = V 2 T 1 T 2 T 1 T 2 --volume of a gas is directly proportional to the temperature of the gas --volume of a gas is directly proportional to the temperature of the gas V T

11. GAS LAWS Charles’s Law: the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature. Charles’s Law: the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature. V 1 = V 2 V 1 = V 2 T 1 T 2 T 1 T 2 --volume of a gas is directly proportional to the temperature of the gas --volume of a gas is directly proportional to the temperature of the gas ** K = ºC + 273 V T

12. GAS LAWS Gay-Lussac’s Law: the pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature Gay-Lussac’s Law: the pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature Gas pressure varies directly with Kelvin temperature at constant volume Gas pressure varies directly with Kelvin temperature at constant volume P 1 = P 2 P 1 = P 2 T 1 T 2 T 1 T 2

13. GAS LAWS Combined Gas Law: expresses the relationship between pressure, volume and temperature of a fixed amount of gas. Combined Gas Law: expresses the relationship between pressure, volume and temperature of a fixed amount of gas. P 1 V 1 = P 2 V 2 P 1 V 1 = P 2 V 2 T 1 T 2 T 1 T 2

14. GAS LAWS Dalton’s Law of Partial Pressures: the total pressure of a mixture of a gases is equal to the sum of the partial pressures of the component gases. Dalton’s Law of Partial Pressures: the total pressure of a mixture of a gases is equal to the sum of the partial pressures of the component gases. P tot = P 1 + P 2 + P 3 + P 4 + …. P tot = P 1 + P 2 + P 3 + P 4 + …. Why is this useful? Gas collected by water displacement is not pure but is always mixed with water vapor, so that P atm = P gas + P water P atm = P gas + P water where the pressure atmosphere read from a barometer in the room, the pressure of water is taken from a standard reference table for water at a specific temperature, and the pressure for the dry gas is then calculated.

15. GAS LAWS Ideal Gas Law: mathematical relationship among pressure, volume, temperature, and the number of moles of a gas. PV = nRT R is known as the ideal gas constant and its value depends on the units chosen for pressure, volume and temperature.

16. IDEAL GAS CONSTANT Numerical values of the Gas constant depending on units of pressure used: Numerical Numerical Unit of Pressure value of R Unit of R mm Hg 62.4 LmmHg mm Hg 62.4 LmmHg mol K mol K atm 0.0821 Latm_ atm 0.0821 Latm_ mol K mol K kPa 8.314 _LkPa_ kPa 8.314 _LkPa_ mol K mol K

17. AVOGADRO’S LAW Avogadro’s Law: states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. The volume occupied by one mole of a gas at STP is known as the standard molar volume of a gas. 1 mole of gas = 22.41410 Liters

18. Stoichiometry of Gases Use Gay-Lussac and Avogadro’s Law to calculate the stoichiometry of reactions involving gases. Use Gay-Lussac and Avogadro’s Law to calculate the stoichiometry of reactions involving gases. For gaseous reactions the coefficients in chemical equations not only indicate molar amounts and mole ratios, but also the volume ratios. For gaseous reactions the coefficients in chemical equations not only indicate molar amounts and mole ratios, but also the volume ratios. Volumes can be compared in this way only if all are measured at the same temperature and pressure. Volumes can be compared in this way only if all are measured at the same temperature and pressure. When in doubt, go to moles! When in doubt, go to moles!