1. Kinetic Molecular Theory Matter is composed of tiny particles (atoms, molecules or ions) with definite and characteristic sizes that never change. The particles are in constant random motion, that is they possess kinetic energy. E k = 1 / 2 mv 2 The particles interact with each other through attractive and repulsive forces (electrostatic interactions), that is the possess potential energy. U = mgh The velocity of the particles increases as the temperature is increased therefore the average kinetic energy of all the particles in a system depends on the temperature. The particles in a system transfer energy form one to another during collisions yet no net energy is lost from the system. The energy of the system is conserved but the energy of the individual particles is continually changing.

2. PRESSURE A physical property of matter that describes the force particles have on a surface. Pressure is the force per unit area, P = F/A Pressure can be measured in: atmosphere (atm)atmosphere (atm) millimeters of mercury (mmHg)millimeters of mercury (mmHg) (torr) after Torricelli, the inventor of the mercury barometer (1643)(torr) after Torricelli, the inventor of the mercury barometer (1643) 1 atm = 760 mmHg = 760 torr

3. TEMPERATURE A physical property of matter that determines the direction of heat flow. Measured on three scales. Fahrenheit o F Celsius o CFahrenheit o F Celsius o C Kelvin KKelvin K o F = (1.8 o C) + 32 o C = ( o F - 32)/1.8 o F = (1.8 o C) + 32 o C = ( o F - 32)/1.8 K = o C + 273.15K = o C + 273.15

4. GAS LAWS Boyle’s Law P 1 V 1 = P 2 V 2 Charles’ LawV 1 / T 1 = V 2 / T 2 Guy-Lussac’s LawP 1 / T 1 = P 2 / T 2 Avogadro’s LawV 1 / n 1 = V 2 / n 2 Combined Gas Law P 1 V 1 / T 1 = P 2 V 2 / T 2 Ideal Gas Law PV = nRT P = pressure (atm)V = volume (L) n = chemical amount (mol)T = Temperature (K) R = ideal gas constant = 0.08206 L-atm / mol-K

5. Empirical Gas Laws 1. At 25 o C, a sample of N 2 gas under a pressure of 689 mmHg occupies 124 mL in a piston-cylinder arrangement before compression. If the gas is compressed to 75% of its original volume, what must be the new pressure (in atm) at 25 o C? First make a list of the measurements made: P 1 =689 mmHgV 1 = 124 mL P 2 = ?V 2 = 75% V1 From the variables, choose the appropriate equation, in this case Boyle’s Law: P 1 V 1 =P 2 V 2 (689 mmHg) (124 mL) = P 2 (0.75 x 124 mL) Solve for P 2 : P 2 = (689mmHg) (124 mL) / (93 mL) = 919 mmHg Now convert to atm: 1.21 atm 919 mmHg (1 atm / 760 mmHg) = 1.21 atm

6. Empirical Gas Laws 2. The gases in a rigid Helium filled ball at 25 o C exerts a pressure of 4.2 atm. If the ball is placed in a freezer and the pressure decreases to 1/8 of its original value, what is the temperature inside the ball? First make a list of the measurements made: P 1 =4.2 atmT 1 = 25 o Cc + 273.15 = 298.15 P 2 = 1/8 P 1 T 2 = ? From the variables, choose the appropriate equation, in this case Guy Lussac’s Law: P 1 /T 1 =P 2 /T 2 (P 1 ) / (298 K) = (1/8 P 1 ) / T 2 Solve for T 2 : T 2 = [(298 K) (1/8 P 1 )] / (P 1 ) = 298 / 8 = 37.3 K or -235 o C 3. A balloon containing 6.50 moles of NH 3 has a volume of 550L at a certain temperature and pressure. How many grams of NH 3 would have to be removed from the balloon in order for the volume to decrease to 250 L under the same conditions? Mass of NH 3 removed = 60.3 g of NH 3.

7. Avogadro’s Hypothesis Avogadro pictured the moving molecule as occupying a small portion of the larger space apparently occupied by the gas. Thus the “volume” of the gas is related to the spacing between particles and not to the particle size itself. Imagine 3 balloons each filled with a different gas (He, Ar, & Xe). These gases are listed in increasing particle size, with Xe being the largest atom. According to Avogadro’s Hypothesis, the balloon filled with one mole of He will occupy that same volume as a balloon filled with one mole of Xe. V  nSo for a gas, the “volume” and the moles are directly related. V  n

8. Avogadro’s Hypothesis A sample of N 2 gas at 3.0 atm and 20.0 o C is known to occupy a volume of 1.43 L. What volume would a 0.179 mole sample of NH 3 gas occupy at the same pressure and temperature? First calculate the number of moles of nitrogen gas: PV = nRT where P = 3.0 atm, V = 1.43 L, R = 0.082 L-atm/mol-K, and T = 20.0 o C + 273 = 293K n = PV / RT = (3.0 atm x 1.43L) / (0.082 L-atm/mol-K x 293K) = 0.179 moles of N2N2 So since the moles of N2 N2 is 0.179 mol and the moles of ammonia is 0.179 mol according to Avogadro’s hypothesis the volume of NH 3 at that pressure and that temperature is 1.43 L, the same!!!

9. At STP, gas molecules are so far apart that for 1 mole of gas, the overall volume does not change. STP : P = 1 atm & T = 273 K

10. COMBINED GAS LAW A gas occupies a volume of 720 mL at 37 o C and 640 mmHg pressure. Calculate the volume the gas would occupy at STP. P 1 V 1 / T 1 = P 2 V 2 / T 2 rearranged to solve for V 2 is: V 2 = P 1 V 1 T 2 / P 2 T 1 V 2 = (640 mmHg)(720 mL) (273 K) / (760 mmHg) (310 K) V 2 = 534 mL

11. COMBINED GAS LAW A gas occupies a volume of 720 mL at 37 o C and 640 mmHg pressure. –Calculate the pressure if the temperature is increased to 1000 o C & the volume expands to 900 mL. –Calculate the temperature if the pressure is decreased to 10 torr & the volume is reduced to 500 mL. P 2 = 2.1 x 10 3 mmHg T 2 = 3.4 K or -270 o C

12. IDEAL GAS LAW Q. What is the pressure inside a gas balloon if it filled with 852 g of Xe gas at 25.0 o C and occupies a volume of 7.00 L? P = ? 852 g Xe ( 1 mol / 131 g) = 6.50 mol V = 7.00 L T = 25 o C + 273 = 298 K P = nRT V P = (6.50 mol) (0.082 L-atm / mol-K) (298 K) 7.00 L P = 22.7 atm

13. IDEAL GAS LAW ¶What would be the temperature of 100 g of Ar gas contained in a 500 L sealed container at 0.8976 atm. ·How much would a balloon weigh if it contained 40.0 L of O 2 gas at 987 mmHg and 45.3 o C? T 2 = 1914 o C mass O 2 = 63.7 g mass O 2 = 63.7 g

14. DENSITY OF A GAS The density of a gas at STP can be calculated by d STP = molar mass/molar volume ¶Calculate the density of hydrogen sulfite gas at STP. ·Identify an unknown homonuclear diatomic gas that was found to have a density of 3.165 g/L at STP. d (STP) = (82 g/mol) / 22.4 L/mol) = 3.66 g/L Cl 2

15. Properties of Gases  DIFFUSION Diffusion is the ability of two or more gases to mix spontaneously until a uniform mixture is formed. Example: A person wearing a lot of perfume walks into an enclosed room, eventually in time, the entire room will smell like the perfume.   EFFUSION Effusion is the ability of gas particles to pass through a small opening or membrane from a container of higher pressure to a container of lower pressure. The lighter the gas, the faster it moves. The General Rule is: The lighter the gas, the faster it moves. Graham’s Law of Effusion: Rate of effusion of gas A = √ (molar mass B / molar mass A) Rate of effusion of gas B The rate of effusion of a gas is inversely proportional to the square root of the molar mass of that gas.

16. DALTON’S LAW OF PARTIAL PRESSURES If there is more than one gas present in a container, each gas contributes to the total pressure of the mixture. P total = P gas A + P gas B + P gas C … If the total pressure of a system was 2.5 atm, what is the partial pressure of carbon monoxide if the gas mixture also contained 0.4 atm O 2 and 1.48 atm of N 2 ? P T - P O2 - P N2 = P CO 2.5 atm - 0.4 atm - 1.48 atm = 0.62 atm

17. STOICHIOMETRY & THE GAS LAWS. Write a balanced chemical equation 1. Write a balanced chemical equation 2. Convert to moles (if gas, use PV=nRT or Molar Volume) 3. Use the mole ratio to convert from moles of “A” to moles of “B”. 4. Convert moles of “B” to desired measurement, if a gas use PV=nRT. 1. What volume of O 2 is needed to combust 348.0 L of C 3 H 8 ? C 3 H 8 + 5 O 2  3 CO 2 + 4 H 2 O Due to Avogadro’s Hypothesis, the moles of a gas are directly related to the volume of a gas therefore it is possible to use the mole ratio on volumes of gas. 348.0 L C 3 H 8 (5 mol O 2 / 1 mol C 3 H 8 ) = 1740 L O 2

18. STOICHIOMETRY & THE GAS LAWS 2. How many grams of CO 2 is produced from 348.0 L of C 3 H 8 if the temperature is 40.0 o C and the pressure is 654 torr? C 3 H 8 + 5 O 2  3 CO 2 + 4 H 2 O P = 654 torr (1 atm / 760 torr) = 0.861 atm T = 40 o C + 273 = 313 K PV / RT = n = (0.861 atm) (348.0 L) /(0.082 L-atm/mol-K) (313 K) = 11.67 mol of C 3 H 8 11.67 mol C 3 H 8 (3 mol CO 2 / 1 mol C 3 H 8 ) = 35.02 mol CO 2 1541 g of CO 2 35.02 mol CO 2 (44 g / 1 mol) = 1541 g of CO 2

19. STOICHIOMETRY & THE GAS LAWS 3. In lab, you decomposed potassium chlorate into oxygen and potassium chloride. What volume of O 2 at STP can be formed from 3.65 g of potassium chlorate? 2 KClO 3  3 O 2 + 2 KCl 3.65 g (1 mol / 122.6g) = 0.02977 mol KClO 3 3.65 g (1 mol / 122.6g) = 0.02977 mol KClO 3 0.02977 mol KClO 3 (3 mol O 2 / 2 mol KClO 3 ) = 0.04466 mol O 2 0.02977 mol KClO 3 (3 mol O 2 / 2 mol KClO 3 ) = 0.04466 mol O 2 0.04466 mol O 2 ( 22.4 L / 1 mol) = 1.00 L 0.04466 mol O 2 ( 22.4 L / 1 mol) = 1.00 L

20. PRACTICE PROBLEMS # 20 1. Both hydrogen and helium have been used as buoyant gas in blimps. If a small leak were to occur, which gas would effuse more rapidly and by what factor? 2. At STP, 560 mL of a gas has a mass of 1.08 g. What is the molecular weight of the gas? 3. You prepared carbon dioxide by adding aqueous HCl to marble chips, calcium carbonate. According to your calculations, you should obtain 79.4 mL of carbon dioxide at 0 o C and 760 mmHg. How many milliliters of gas would you obtain at 27 o C? 4. A 50.0 L cylinder of nitrogen has a pressure of 17.1 atm at 23 o C. What is the mass of nitrogen in the cylinder? 5. When a 2.0 L bottle of concentrated HCl was spilled, 3.0 kg of CaCO 3 was required to neutralize the spill. CaCO 3 (s) + 2HCl (aq)  CaCl 2 (aq) + H 2 O (l) + CO 2 (g) What volume of CO 2 gas was released by the neutralization at 735 mmHg and 20 o C? Hydrogen effuses first by a factor of 1.41 43.2 g/mol 87.3 mL 986 g 745 L

21. Group Study Problem # 20 1. Measured at 65 o C and 500.0 torr, the mass of 3.21 L of a gas is 3.5 g. What is the molar mass of this gas 2. A 100.0 mL sample of air is analyzed and found to contain 0.835 g N 2, 0.0640 g CO 2 and 0.197 g O 2 at 35 o C. What is the total pressure of the sample and the partial pressure of each component? 3. What volume would 5.30 L of H 2 gas at STP occupy if the temperature was increased to 70 o F and the pressure to 830 torr? 4. Divers working from a North Sea drilling platform experiences pressures of 50 atm at a depth of 5.0 x 10 2 m. If a balloon is inflated to a volume of 5.0 L (the volume of a lung) at that depth at a water temperature of 4.0 o C, what would the volume of the balloon be on the surface (1.0 atm) at a temperature of 11 o C? 5. Hydrogen gas is produced by the complete reaction of 8.34 g of aluminum metal with an excess of gaseous hydrogen sulfate. How many liters of hydrogen will be produced if the temperature is 50.0 oC and the pressure is 0.950 atm?

22. Group Study Problem Answers: 1. 45.9 g/mol 2. P N 2 =7.53 atm, P O 2 =1.55 atm, P CO 2 =0.380 atm; P T = 9.46 atm 3. 5.23 L 4. 256 L 5. 12.9 L