Chapter 12 Gases and the Kinetic-Molecular TheoryComparison of Solids, Liquids, and Gases.Matter is arbitrarily classified into three physical states: solids,liquids, and gases. Most substances can exist in the gas phase, and mostcan be liquefied and then solidified at appropriate temperatures andpressures. The volumes of gases change greatly as temperature andpressure change. Volumes of solids and liquids change very little withchanges in temperature and pressure. Gases are less dense than solids andliquids.The Atmosphere and Some Properties of Gases.The atmosphere is a mixture of gases. Some observations on gases are:• Gases exert pressure on their surroundings.• Gases can be compressed.• Gases can expand without limit.• Gases diffuse into each other, i.e., they are miscible (mix with eachother) in all proportions unless they react chemically.• Gases can be described in terms of their volume, temperature, pressure,and the number of molecules (moles) of gas present.Pressure. Pressure is defined as force per unit area It may be expressedin many units. Average atmospheric pressure at sea level is 14.7 poundsper square inch. The mercury barometer is a convenient device formeasuring pressure. The average pressure at sea level is referred to asstandard pressure Standard pressure is 76 cm of mercury, 760 mm ofmercury or 760 torr, and is referred to as one atmosphere of pressure. Inthe SI system of units, one atmosphere is 1.013 x 105 Pascals (Pa) or 101.3kilopascals (kPa).Boyle’s Law: The Pressure-Volume RelationshipBoyle’s Law is usually state: At constant temperature the volumeoccupied by a definite mass of a gas is inversely proportional to thepressure applied to the gas. This statement is a summary of manyobservations of the behavior of gases.V a 1/P or k = PVor when comparing a fixed mass at constant temperature:P1V1 = P2V2Example 1: At 25o C a sample of helium occupies 400 ml under apressure of 760 torr. What volume would it occupy under a pressure of2.00 atmospheres at the same temperature?V1 = 400 mL P1V1 = P2V2P1 = 760 torr = 1 atm rearranging P2 = 2 atm V2 = P1V1/P2V2 = ? V2 = (1 atm)(400 mL) = 200 mL 2 atmCharles’ Law: The Temperature/Volume Relationship.The fact that gases expand when heated and contract when cooled hasbeen common knowledge for many year. However, evolution of a simplerelationship between the volume and temperature of a sample of gas had toawait the evolution of an absolute temperature scale. Charles and Gay-Lussac studied the relationship between the volume and temperature of asample of gas at constant pressure. Charles observed that a plot of volumeversus temperature gives a straight line. Charles’ Law is usually stated: atconstant pressure the volume occupied by a definite mass of a gas isdirectly proportional to the absolute temperature.A Famous Temperature/Volume EquationThe volume-temperature line intercepts the temperature axis at-273.15oC. This temperature is taken as absolute zero or 0 K. Therelationship between the Celsius (centigrade) and the absolute (Kelvin)temperature scales isCharles’ and Gay-Lussac’s observations may be represented symbolicallyasV a T or V = k TWhen comparing a system at constant mass and pressure:V1 V2____ = ____T1 T2Example 2: A sample of hydrogen, H2, occupies 100 ml at 25oC and 1.00atmosphere. What volume would it occupy at 50o C under the samepressure?V1 = 100 mLT1 = 25o + 273o = 298 K T2 = 50o + 273o = 323 K V1 = V2 T1 T2V2 = ? V2 = V1T2 = (100 mL)(323) T1 298 V2 = 108.4 mLStandard Temperature and PressureBecause the volume of a gas varies with both temperature and pressure,we establish reference points for temperature and pressure. These arecalled standard conditions (SC or STP) and refer to 0oC (273.15 K) andone atmosphere of pressure (760 torr or 101.3 kPa).The Combined Gas Law EquationBoyle’s Law tells us that at constant temperature the volumeoccupied by a definite mass of a gas is inversely proportional to thepressure under which it is confined. Charles’ Law tells us that at constantpressure the volume occupied by a definite mass of the gas is directlyproportional to the absolute temperature. Putting them all together wehave the combined gas law equation: P1V1 P2V2 ____ = ____ T1 T2This equation contains six variables. If five are known, we can find thesixth.Example 3: A sample of nitrogen, N2, occupies 750 ml at 75oC under apressure of 810 torr. What volume would it occupy at standardconditions.?V1 = 750 mL P1V1 = P2V2 T1 = 75o + 273o = 348 K T1 T2P1 = 810 torrV2 = ? V2 = P1V1T2T2 = 273 K T1P2P2 = 760 torr V2 = (810)(750)(273) (348)(760) V2 = 627 mLAvogadro’s Law and the Standard Molar Volume of Gases.Avogadro’s Law states that at the same temperature and pressure equalvolumes of all gases contain the same number of molecules (moles).V a n or V = k nWhen comparing a system at constant temperature and pressure:V1 V2 ____ = ____ n1 n2Standard Molar Volumes (that 22.4 liters number)The volume occupied by one mole of a gas at standard conditions is thestandard molar volume. One mole of an ideal gas occupies 22.4 liters at0oC and one atmosphere of pressure. Real gases do not behave exactly asideal gases. However, at reasonable temperatures and pressures thebehavior of many gases is nearly ideal. We may assume ideal behaviorwithout introducing serious errors into our calculations. The idealstandard molar volume, 22.4 liters, is good approximation of the standardmolar volume of many real gases.Example 4: One (1.00) mole of a gas occupies 36.5 liters, and its densityis 1.36 g/L at a given temperature and pressure.(a) What is its molecular weight?n = 1 mole mole = g/MW ==> MW = g/moleV = 36.5 L r = g/L ===> g = r Ldensity = r = 1.36 g/LMW = r /mole = (1.36 g/L)(36.5 L) / (1 mole) = 49.6 g/mole(b) What is the density of the gas at the standard conditions?r = g/L = ? L = 22.4 at STPr = 49.6 g/22.4 L = 2.2 g/LSummary of the Gas Laws - The Ideal Gas Equation.The relationship among the pressure,
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