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Final Grade for CHE 103 Calculated as stated in syllabus: EXAM1 + EXAM2 + EXAM 3 + QUIZZES 350 Outline I. Gases & Gas Laws - Kinetic Molecular Theory - Simple variable relationships - Ideal/Combined Gas Law States of Matter - solid, liquid, gas Gaseous State Characterized by dominance of kinetic energy over potential energy Gas particles have enough kinetic energy to move far apart from each other. There is very little attraction between particles Four Important Gas Variables 1. n = number of moles 2. T = temperature; must be in Kelvin! K = oC + 273.15 3. V = Volume 4. P = Pressure = force/area 1 atm = 760 mm Hg Relationship Between Pressure and Volume (Boyle’s Law) When the pressure is increased on a gas, its volume goes down. PV = constant (T fixed) useful form: P1V1 = P2V2 Volume/Pressure Calculation A balloon is inflated to a volume of 12.6L on a day when the atmospheric pressure is 675 mm Hg. The next day, a storm drops the pressure to 651 mm Hg. Assuming constant temperature, what is the new volume of the balloon? Relationship Between Temperature and Volume (Charles’ Law) When the temperature (K) is increased on a gas, its volume goes up by a constant: V/T = constant (P fixed) useful form: V1/T1 = V2/T2 Volume/Temperature Calculation The volume of a sample of air at 30. oC is 3.50 L. Assume that the pressure is held constant. What would be the volume of air at 300. oC? Relationship between Temperature and Pressure (Gay-Lussac’s Law) When the temperature (K) is increased on a gas, its pressure goes up as a constant: P/T = constant (V fixed) Useful form: P1/T1 = P2/T2 When the Temperature increases, gas molecules are moving faster and hitting the sides of their container more….creating more pressure….according to KMT! Pressure/Temperature Calculations Consider a container with a volume of 22.4 L filled with a gas at 1.00 atm at 273 K. What will be the new pressure if the temperature increases to 298 K? P1/T1 = P2/T2 P1 = 1.00atm, P2 = ? T1 = 273K T2 = 298K P2 = (1.00atm)(298K) (273K) = 1.09atm Avogadro’s Law: Volume and Moles In Avogadro’s Law: The volume of a gas is directly related to the number of moles of gas T and P are constant V1 = V2 n1 n2 Learning Check If 0.75 mol of helium gas occupies a volume of 1.5 L, what volume will 1.2 mol of helium occupy at the same temperature and pressure? 1) 0.94 L 2) 1.8 L 3) 2.4 L V2 = (1.5L)(1.2mol) (0.75mol) STP The volumes of gases can be compared when they have the same conditions of temperature and pressure (STP, Standard Temperature and Pressure). Standard temperature (T) 0°C or 273 K Standard pressure (P) 1 atm (760 mm Hg) Molar Volume At standard temperature and pressure (STP), 1 mol of a gas occupies a volume of 22.4 L, which is called its molar volume. Molar Volume as a Conversion Factor The molar volume at STP can be used to form conversion factors. 22.4 L 1 mol and 1 mol 22.4 L Learning Check A. What is the volume at STP of 4.00 g of CH4? B. How many grams of He are present in 8.00 L of gas at STP? Important Simple Gas Relationships Boyles Law Charles Law Gay-Lussacs Avogadros Law P1V1 = P2V2 (T fixed) V1/T1 = V2/T2 (P fixed) P1/T1 = P2/T2 (V fixed) V1/n1 = V2/n2 (T&P fixed) STP - Standard Temperature and Pressure (Gases) T = 273 K (0 oC) and P = 1 atm (760 mmHg) 1 mole of a gas at STP = 22.4L Combined Gas Laws Relates the changes in pressure, volume and temperature, and quantity change of a gas PV = nT constant Useful form of the expression: P1V1 n1T1 = P2V2 n2T2 Combined Gas Law Practice A fixed quantity of nitrogen gas in a 275 mL container at a pressure of 625 mm Hg is transferred to a container with a volume of 750. mL. What is the new pressure if the temperature changes from 25 oC to 17 oC? Ideal Gas Law Let’s now solve for the constant: PV/nT = constant = R One set of conditions we know - 1 mole of a gas at STP. (atm L/mol K) The Ideal Gas Law Describes the relationships among the four variables for gaseous substances: P, T, V, n PV = nRT R is called the ideal gas constant 0.0821 atm·L/mol·K Always make sure you have all your units correct! Gas Law Calculations What is the temperature (in oC) of a sample of 3.00 moles of He at 27.5 atm of pressure and in a 6.00 L container? A. 670. B. 397 C. 273 Gas Law Calculations Methane, CH4, can be used as fuel for an automobile; however, it is a gas at normal temperatures and pressures, which causes some problems with storage. One gallon of gasoline could be replaced by 655 g of CH4. What is the volume of this much methane at 25 oC and 745 mm Hg. A. 30.9 B. 510. C. 1020