Chem152C2.pdf chem 152
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This 18 page Class Notes was uploaded by Shelby Logsdon on Monday February 9, 2015. The Class Notes belongs to chem 152 at University of Washington taught by munira khalil in Winter2015. Since its upload, it has received 166 views. For similar materials see general chemistry in Chemistry at University of Washington.
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Date Created: 02/09/15
Chem 152 C 222015 Spontaneous change A spontaneous process will occur in a system left to itself no action from the surroundings is necessary to drive the process A nonspontaneous process requires action from the surroundings to occur If a process is spontaneous as written the reverse is nonspontaneous and vice versa Spontaneous does not mean fast Spontaneous means thermodynamically favorable Entropy S First law of thermodynamics q E w 0 Energy is constant Second law of thermodynamics o Entropy of the universe is always increasing Any process that leads to an increase in the entropy of the universe is spontaneous quotheatquot refers to the amount of energy that ows in or out of a system Entropy is the term we use to describe how that energy is arranged or disbursed Dominant con guration 0 Con guration type of energy distribution 0 Microstate speci c arrangement of energy corresponding to a con guration 0 Largest of microstates dominant con guration 0 Dominant con guration has highest entropy Entropy and dominant con guration 0 Weight W or cap Omega of microstates associate w a given con guration 0 Connection between W and S is given by Boltzmann s formula S kblnW KbRNa 138 x 103923JK con guration Ex ideal gas expansion What is S for the expansion of a monatomic ideal gas from V1 to 2V1 Constant temperature process S Sf39Si SkbnW S kbln2W kblnW kbln 2WW kbln2 S For 1 mole of an ideal gas at constant temperature WfWi 2Na S kblnWfWi kbln2Na NaKbln2 Rln2 1 mole of ideal gas expanding volume where vf2vi Weight was directly proportional to volume S kblnWfWi for 1 particle S NKblnVfNi for n particles S RnVfVi for Na particles W scales linearly w V Enthalpy and Entropy Enthalpy keeps track of the heat energy coming in and out of the system and entropy keeps track of how that energy is arranged A spontaneous process is one that increases Sum Thermodynamic def of entropy o SqreVT qrev heat exchanged reversibly between system and surroundings Reversible vs irreversible processes In a reversible cyclic process the system and surroundings are both returned exactly to their original conditions In an irreversible cyclic process the system may return to original conditions but the surroundings are changed in a permanent way Isothermal process Isothermal means T 0 also E0 and H 0 Q W Isothermal expansion and compression 0 Consider a mass connected to an ideal gas contained in a piston o Piston is submerged in a constant T bath so that the T of the system and surroundings are the same and constant at all times 0 We can control the V and P of the gas by changing the mass on the plate Ex Work D 1 step 2 step reversible 1 step w Pextvfvi Pi44vivi 34 PiVi Q 34 PiVi W 2 step W1 39Pi22Vi39vi 3912Pivi W2 Pi44Vi 2Vi 3912 PiVi Wtotal 39PiVi Reversible Integral Wrev39nRT r1VfVi Wrev nrt n4vivi nRT n4 Thermodynamic de nition of entropy AS qreVT We can show that entropy is a state function by a 4 step thermodynamic o 1 isothermal expansion 0 2 isochoric cooling 0 3 isothermal compression 0 4 isochoric heating Step 1 TThigh from V1 to V2 0 T 0 E 0 and q w 0 Expansion is done reversibly then qrev wrev nrthighnV2N1 Step 2 T Tlow o nCVT q o V 0 therefore W 0 0 AT Tlow39Thigh Step 3 TTOW from V2 to V1 0 T 0 0 QB39WnRTlownV1V2 Step 4 T Thigh o V 0 0 Q4 nCVThigh39Tlow Q439q2 CltotalC1C2C3C4C1CI3 nRThighnV2V1 nRTIownV1V2 Calculating Entropy isothermal process 0 T 0 0 quev39dWrev o Idealgas queVdwreVPdv PdV dS dqreVT PdVT 39 S annV1Ni Constant volume conditions 0 AS qrevT o S nCVnTfTi Constant pressure conditions 0 S nCplnT1Ti Phase change 0 Ice melting to water at 0 C 1 atm I AS qrevTn AHmeltT Ex what is S for the heating of a mole of a monatomic gas isochorically from 298K to 350K S nCVT1Ti 1 mol32Rln350K298K 2 JK Ex what is S for heating of 1 mol of water from 25 C to steam at 100 C at 1 atm pressue cph20 753 Jkmol cpsteam3376jIltmol AHVap4o99Iltjmol 2 AS nHT 1mo4099kjmol373K 109 JK 1 AS ncpT 1 mol75Kln373298 169JK Aston 126 JK Second law of thermodynamics Entropy of the universe is always increasing In any spontaneous process there is always an increase in the entropy of the universe Asuniv Assys l39 Assurroundings o Suniv gt 0 in spontaneous process 0 Suniv lt 0 in spontaneous process in opposite direction 0 ASuniv 0 process is at equilibrium Need to know S of system and surroundings to predict if a reaction will be spontaneous Entropy will keep increasing until equilibrium is reached Third law of thermodynamics Entropy of a perfect crystal at 0 K is 0 Allows us to calculate absolute entropies Standard molar entropy S is the entropy change associated w heating 1 mol of a substance from 0 K to 298 K at 1 atm The standard molar entropy change for a chemical process can be calculated via a Hess39 law type calculation using standard molar entropies S rxn sum nS prod summS react Entropy Changes in the surroundings Exothermic processes entropy of surroundings increase Endothermic processes entropy of surroundings decrease Assurr 39 AHsysT qsurr39qsys 39AHsys Asuniv Assys l39 Assurr Spontaneity and Temperature Sns 02g D Sn02s H 578 kJmol S 207 JmolK Determine spontaneity of rxn at 298K and 3000 K Ssurr 5780jmo 298 K 1940 JmolK ASuniV 207 1940 1730 Ssurr 5780kjmol 3000K 192 JmolK ASuniV 207 192 143 JmolK There must be a temperature when a reaction changes in spontaneity At what temperature does Suniv 0 Asuniv AssysSsurr 0 Assys39Ssurr Assys 39 39AHsysT T HsysSsurr T 2792 K Entropy and equilibrium processes At equilibrium AS 0 phase changes are the simplest equilibrium systems we can consider Consider water boiling at 373 K o Endothermic process with an increase in ngas o Ssurr and SSys have opposite signs What are the magnitudes of these values at 373K 0 SO H20L I H20G o 866 1959 0 Aern 0 At 373 K Hvap of water is 407 kjmol 0 ASsurr o ASuniv 1091 1091 0 Gibbs Free Energy G 2nCI law of thermodynamics ASSN HsysT Suniv39T Assys l39 39AHsysT 39T 39TASuniv 39TASsys l39 AHsys AGsys 39TASuniv 39TASsys l39 AHsys Gibbs free energy at constant P and T is G H TS all system quanUUes G spontaneous Phys 114 B 222015 Lecture Chapter 71 to 72 Systems and environments A system is a small portion of the universe It may be 0 A single object or particle o A collection of objects or particles 0 A region of space 0 Vary win time and space Work 0 The amount of energy transferred by a force acting through a distance o If the object does not move no work is done on it o The Si unit is Joule Nm the unit of force time distance Work done by constant force 0 Suppose a constant force displaces a box by d o W Fd o The work done by this force on the box given does not change even if there are other forces acting on it 0 Suppose a constant force displaces a box by d and the angle between F and d is th 0 The work done by the force on the box is W chosth Work as energy transfer o If a force external to a system displaces the system in the same direction as that of the force Work done on a system is positive and Energy is transferred to the system o If a force displaces the system in opposite direction Work done on system is negative Energy is transferred to the surroundings Ex water skiers often ride to one side of the center line of a boat as shown In this case the ski boat is traveling at V 15 ms and the tension in the rope is T 75 N if the tension does W 3500 of work on the skier in d 500 m what is the angel th between the tow rope and the center line of the boat W Tdcosth Costh Wtd th cos1WTd cos13500J75N 500 m 21 Net Work When more than one force acts on an object the total work is the sum of each work Or the total work can be calculated by 0 WtotalFtotaCOSthd Ex three forces are applied to a greased trunk that moves leftward by 3 m over a frictionless oor The force magnitudes are F15 n f29 n and f3 3 n what is the net work Nnetx F1 F2cos60 Wtotal Fnetx dcoslSO Fnetx H d Wtotal 39Fnetx d Flcmos60d 5 9cos603 150 Energy Energy of a system is a measure of its ability to do work Different types of energies based on different conditions or states 0 Kintetic associated w motion 0 Potential associated w con guration 0 Thermal associated w random motion of particles Energy is scalar SI unit isjoule Kinetic energy 0 K 12 mv2 o Faster objects have more kinetic energy 0 Kinetic energy is zero when the object is stationary and never negative Workenergy theorem 0 States change in kinetic energy is equal to total work done 0 Wtota 12 mV2f l2 mVZi 0 When Wtotal is positive KE increases 0 When wtotalon is negative KE decreases Ex a pne cone w mass 21 kg fall h 14 m to the ground where it lands w vf113ms a What as KE of pine cone before it landed l2 mv2 18 b What speed would the pine cone have landed if there was no air resistance Wbyearth Fgh mgh WE theorem W K Kf39Ki 12 mv12 Mgh 12 mv12 Vfsqrt 2gh 17ms c Did the air resistance do positive negative or zero work on the pine cone Negative air resistance opposes displacement 12 Ex a 1300 kg car coasts on a road w vi 18 ms after crossing a sandy stretch of road d 30 m long its speed decreases to Vf 15ms a What is work done on car WtotaK K Kf39Ki 12 mez 12 I39TlVi2 64X104J b Find magnitude of average net force on car in sandy section Wtota Fnetd anetl c If the sandy portion had been 15m long what is the average speed in this case AK Wtota Fnetd JZ mV239 JZ mVZi 2Fnetdm Vi2 Vf39 sqrt 221X103151300 17 ms Ex the minimum braking distance for a car traveling 40 mph to be 101 ft if the braking force is the same at all speeds what is the minimum braking distance for a car traveling at 65mph WK Fbdcos180 K Fbd 12 mvi2 D mvzi2Fb Let vi140 mph wdi 101 ft Vi265mph w d2 D2 d1V2i2vi12 Lecture chapter 73 to 74 Work done by variable force A variable force can be appx by a series or constant forces over short distances Lim FxX W Total work can be appx by adding the work from each segment Work done on a spring Work required to stretch or compress a spring by a distance x is given by W k2x2 Ex a block of mass m and speed v collides w a spring compressing it a distance x before the block momentarily stops a What is the compression of the spring if the force constant of the spring is increased by a factor of four WE theorem Wdone on block by spring WK W 12 kX2Kf39Ki Kf 0 x sqrt2Kik 1 x sqrt212mvi2k sqrtmv2k 2 New spring constant k 4k 1 X39 sqrt2Kik39 sqrt2Ki4k 12 sqrt2Kik 12 x Compression is reduced by factor of 2 b What is the compression of the spring if the mass of the block is halved and its speed is doubled 2 x39 sqrt12m2V2k sqrt2mv2k sqrt2 sqrtmv2k sqrt2 x Compression increases by factor of sqrt2 Ex a block of mass m12kg is on a frictionless surface and held against a horizontal spring of force constant k 10 x 104 Nm compressing it a distance of X 15 m how fast is the block moving after it is released and the spring pushes it away WE theorem Wby spring K 12 kX2K1Ki Ki0 12 kx212mv2 Kx2mv2 V2kx2m Vsqrtkmx 14ms Power Power is the rate at which energy is transferred lf work is done by a force on an object the average power is P WtFdt Fv Power is scalar SI unit is wattW Js Kilowatthour is the amount of energy equivalent to that transferred in 1h at 1kW Ex a new record for running the stairs of the empire state building was set The 86 ights w 1576 steps was run in 9 minutes and 33 seconds If the right gain of each step was 20 m and the mass of the runner was 700 kg What was his average power W mgH 1 P Wt 2 H stepsstep height 157620m 3152 m T 9 min 33 s 960 33 573 s P mgHt 70kg981msz3152m573s 378 Watt 378W1 hp746W 506 hp Ex a kayaker paddles w a power output of P 500 W to maintain a steady speed of V 15 ms a Calculate the resistive force exerted by the water on the kayak Steady speed D Ff p Fv F Pv 500W15ms 333 N b If the kayaker doubles her power output and the resistive force due to the water remains the same by what factor does the kayakers speed change Resistive force f remains same so kayakers force F remains same as well V PF speed is doubled Ex a certain car can accelerate from rest to speed v in T seconds if power output of car remains constant a How long does it take for the car to accelerate from v to 2v P Wt WE theorem W Kt TKP KfKiP 12 mvf212mvi2P m2PVf239V2i t 1 In the 1St T secs 1 T m2P V202 T mv22P 2 While accelerating form v to 2v 1 t m2P2v2v2 m2P4v2v2 3mv22P 3T b How fast is the car moving at 2T seconds after starting 1 2T m2Pvf2 Vf24TPm 3 2PT mv2 PT12 mv2 4 vf24m12mv2 2v2 Vf sq rt2V Lecture 81 to 82 Conservative forces The net work done by a conservative force on a particle moving around any closed path is zero The work done by a conservative force on a particle moving between two points does not depend on the path taken by the particle Force of gravity and a force exerted by a massless spring are both conservative forces W chosth Nonconservative forces Any force that is not conservative 0 Kinetic friction o Tension in a rope 0 Force exerted by a motor Ex calculate the work done by gravity as a 52 kg object is moved from A to B along paths 1 and 2 W1 0 mgd 52kg981msz1 m 51 W2 mgd 0 51 B how do your results depend on the mass of the block Speci cally if you increase the mass does work done by gravity increase decrease or stay the same Work done by gravity depends linearly on the mass Potential energy PE is the energy stored in the con guration of a physical system 0 A single pointlike object cannot have potential energy since it cannot have any con guration Potential energy can be converted into other forms of energy such as kinetic energy and do work in the process Scalar quantity Measured in joules Graviational potential energy 0 Stored in at least two gravitationally attracting objects Elastic potential energy 0 Stored in a deformed spring or a similar object Electric potential energy 0 Stored in a con guration of at least two electrically interacting charged object PE functions 0 We de ne the potential energy function U that is associated w a conservative force as 39 U Uf39Ui39Wc 0 Where WC is work done by internal conservative force Gravitational Ug function o A system of an object and earth can store gravitational potential energy 0 Change in gpe depends only on difference in height Ugmgyry 0 only difference in gravitational potential energy that is independent of your choice of reference point is meaningful External work and U9 0 Consider a system of an object w mass m and earth A constant external force F is lifting the object a height of y wo any acceleration o The magnitude of the external force must equal to that of the gravitational force on the object o The work done by the external force on the object is 39 Wext FY Aug 0 Consider a system consists of an object w mass m only and excludes earth A constant external force F is applied to lift the object a height of y wo any acceleration 0 Work done by external force on object is E Ex as a cliff diver drops to the water from a height of 40 m the gpe of the man earth system decreases by 25000 how much does he weigh AUgmgy Mg 25000 40 m 630 N Ex at time t 0 s a box w mass m 200 kg is dropped from heigh 20 m above the ground a What is pe of box At t 0 s Vo0 Ugomgho 2kg981msz20m 392 b Find height and pseed at t 1 s H1ho Vot1th2 20 m l2 9811s 151 m V1gt 981 1 981 ms c Find pe of system and ke of box at t 1 s Uglmgh1 2981151 296 K112mV12 l2 29812 962 U91K1Ugo d Find ke and speed of box just as it reaches ground V22V022gh V22Zgho V2sqrt2gho 198 ms K 12 mV22 12 m2gho mgho 392 Elastic Us function A system of an object attached to a deformed spring sotres elastic potential energy Choosing uS to be 0 at X 0 when spring is not compressed or stretched the elastic pe is given by 0 kX2 Ex a spring w k 3200 nm is stretch until us 144J what is change in epe if the initial stretch is changed to a A stretch of 20 cm Us 12 Iltx2 3200Nm02m2 64 AU 64 144 08J b Compression of 2 cm U 12 3200Nm 02m2 64 U 8J c Compression of 4 cm U 12 3200 Nm 04m2 2541 u 2541 144 11 Lecture chapter 83 Mechanical energy The sum of kinetic energy and potential energy Conservation of mechanical energy o If there is no external work done on the system and there is no work done by nonconservative force mechanical energy is conserved 0 WtotalK O KiUiKFUF o KU0 You can de ne gpe to be zero anywhere you want as long as you are consistent Ex a block of m 16 kg slides w an initial speed of v0 950 ms on a frictionless surface until it encounters a spring w a force constant of k 902Nm the block comes to rest after compressing the spring by x 4 cm nd spring U K and total mechanical energy of blockspring system E for compressions of 0 cm 1 cm and 4 cm System block and spring K 12 mv2 U 12 kx2 E KU 0 cm compression V 0950 ms K 12 16kg950ms2 0722J U0J E722J 1 cm compression U 12 902 Nm01m2 045 E722J K 722 0451 677 4 cm compression K0J E722J LJ722J Ex at an amusement park a swimmer starts at rest slides wo friction and descends a vertical height of h 231 m what is her speed at the bottom of the slide UiKi UfKf UiK1 Mgh l2 mv2 V sqrt2gh 673 ms Ex suppose the pendulum bob in gure has a mass of m33 kg and is movig t the right w a speed of vb24ms a What is the change in gravitational potential energy of the bobearth system when it moves from point B to point A Height at pos A L costh L L costh L1 costh Ha Ua mg I 1costh 033kg981msz1cos35 07 B what is the speed at point A KbUbKaUa l2 mvb2 l2 mva2 mg l1costh Va sq rtVb22gl1costh 1 2ms Ex the two masses in the atwoods machine are initially at the same height moving w a speed of Va with m2 moving upward How high does m2 rise above its initial pos before momentarily coming to rest M1 37 kg m2 41 kg and v0 20 ms Ki Uf l2 mlvo2 12 m2V02 m1gh m2gh H m1m2V02 2m2m1g 039 m Lecture chapter 84 to 85 Work done by nonconservative forces WncKU E WtotaK K E theorem WcU def of potential energy Work done by kinetic friction Suppose a book is sliding on a tabletop slowing down due to the friction between he book and the table surface the book eventually stops The work done by friction on the table is positive since the point of application of friction moves w the book Surface does not have kinetic energy Positive work by friction warms up the surfaces Energy associated w temp of a system is its internal energy If an object is sliding on a rough incline pe as well as ke of the earth object system changes Then AEmechK U fkd Other types of work by nc forces Air resistance Wnc to deform an object result in increase of thermal energy f chemical reaction takes place within the system change in chemic al energy occurs Law of conservation of energy States the total energy of an isolated system is constant Within the isolated system energy can be converted from one form to another or transmitted from one region to another but energy can never be created or destroyed 39 AEsys Ein 39 Eout Gravitational potential energy curves A ball on a frictionless track starts at rest The ball earth system has the least potential energy and the most kinetic energy at the lowest point in the track The ball turns around at highest point and repeats process Elastic potential energy curves A mass attached to a spring is pulled by distance A from equilibrium position and released The mass undergoes an oscillatory motion
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