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Derivation of the We have now identified the models of how we look at atoms and molecules, Ideal Gas Law studied reactions they undergo and have learned how energy is involved in these processes. Now we will turn our study to the different phases in which matter exists. You will find that these units on phases of matter and the kinetic-molecular theory will be quite extensively tested in the multiple-choice section of the national AP exam; especially the unit on gases. Be forewarned. Get out AP equation sheet Characteristics of Gases 1. Non metallic compounds Factors the Influence 2. Simple formulas w/ low M.W. Gas Behavior 3. A.k.a. Vapors for substances that are normally (s) or (l) at room temp. •Temperature (T) 4. Expand to fill their container = The indirect measure of the 5. Highly compressible average kinetic energy of a 6. Form homogeneous mixtures collection of particles (on the 7. Relatively far apart (behave Kelvin scale, K) independent of other molecules) •Volume (V) •Pressure (P) = The total space of a container that = The measure of the number of gases occupy due to the free random motion of the gas molecules collisions between gas particles (reported in liters, L) and a unit area of the walls of its container (reported in KPa or •Number of moles (n) atm) = The total number of gas P=F/A having the units (N/m2) molecules in a collection of particles. (reported in moles, mol) 1N/m2 = 1 Pascal (Pa) 1 8 Pressure of air is measured Pressure Pressure with a BAROMETER Column height measures Column height measures pressure of the pressure of the atmosphere atmosphere •• 1 standard atm 1 standard atm = 760 mm Hg = 760 mm Hg = 760 torr = 760 torr (developed by Torricelli in 1643) = 29.92 inches Hg = 29.92 inches Hg = 14.70 psi = 14.70 psi Hg rises in tube until force = about 34 feet of water = about 34 feet of water of Hg (down) balances the •• SI unit is PASCAL, Pa, SI unit is PASCAL, Pa, force of atmosphere – where 1 atm = 101.325 kPa – where 1 atm = 101.325 kPa (pushing up). Aneroid Barometer In order to measure the pressure exerted by an enclosed gas, scientist use a device called an manometer. Two types of manometers: 1. Open-end manometer- used for gas pressures near 1 atm. 2. Closed-end manometer- used for gas pressures greatly over or under 1 atm. 1.The pressure of a gas is The Classical Gas Laws measured at 49.0 torr in an open-end manometer. Describe •Boyle’s Law this pressure in the units of atmospheres and describe the The volume of a mercury level in the manometer fixed quantity of gas at in respect to the pressure of the constant temperature is gas and the atmosphere. inversely proportional Robert Boyle to the pressure (1627-1691). Son of Earl of Cork, Ireland. 2 (L, atm) •Boyle’s Law The volume of a 2. Baby George was given a 4.53 dm3 V = 1/P fixed quantity of gas at helium filled metallic balloon on a constant temperature is VP = k inversely proportional to bright, sunny day when the the pressure barometric pressure was 768 torr. V1P1 = V2P2 That night a storm front moved in y=mx+b and the pressure dropped to 732 torr. 1 What is the expected volume of the V = m + b P balloon at these new barometric k conditions? or V = P (L, K) •Charles’ Law V = k’ T The volume of V1/ T1 = V2/ T2 a fixed amount of gas maintained at constant pressure is proportional to its Jacques Charles (1746- 1823). Isolated boron •Charles’ Law absolute and studied gases. The volume of a fixed amount of gas maintained at temperature. Balloonist. constant pressure is proportional to its absolute temperature. He 3. Baby George received a larger 6.19 Y=mx+b dm3 helium filled metallic balloon 5 V=mT+b CH4 on top of Pike's Peak at noon when 4 V = k’ T the temperature was 200C. That night, the temperature dropped to - V(L) 3 H2O 100C. What volume did the balloon 2 H2 occupy at that temperature? 1 N2O -200 0 200 T(0C) 3 Avogadro’s Law • The volume of a gas at constant temperature Avogadro’s and pressure is directly proportional to the number of moles of the gas. Hypothesis • Mathematically, this means V = kn At constant temperature and V1/ n1 = V2/ n2 pressure, equal volumes of gases contain equal number of particles It was found that one mole of any gas occupies a volume equal to 22.414 L at STP, or 0oC and 1 atm (Avagadro’s law) Y=mx+b Ideal-Gas Equation V=mn+b V = k’’ n • So far we’ve seen that V ∝ 1/P (Boyle’s law) V V ∝ T (Charles’s law) V ∝ n (Avogadro’s law) • Combining these, we get nT V∝ P n Ideal-Gas Equation “R” is the ideal gas constant describing the volume of one mole of a gas The relationship nT at 1 atm and 0oC V∝ L ⋅ atm P R = 0 . 0821 mol ⋅ K then becomes nT V=R L ⋅ kPa P = 8.314 mol ⋅ K or PV = nRT L ⋅ torr = 62.36 mol ⋅ K With the addition of a proportionality constant = 8.314 J (R). mol • K 4 4. A sample of hydrogen gas has Relevance of the Ideal Gas Law a volume of 8.56 L at a The Ideal gas law provides a temperature of 0oC and a constant set of conditions to which we pressure of 1.5 atm. Calculate can compare any gas sample. the mass of hydrogen present However, if any one variable is in the sample. held constant, the combined gas law can be utilized, where: P1V1/ n1T1 = P2V2/ n2T2 5. A sample of diborane gas (B2H6), a substance that burst into flame when exposed to air, has a pressure of 345 torr at a temperature of –15.0oC and a volume of 3.48 L. If the conditions changed the temperature to 36.0oC and the pressure to 468 torr, what will be the volume? 5