10.21.2011 - Lecture 19 Today in Chemistry 260 x • ...

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Unformatted text preview: Lecture 19 Today in Chemistry 260 x •  •  •  Recap of Kinetic model, Maxwell-Boltzmann distribution Thermodynamics First law of thermodynamics x This Week in Chemistry 260 •  Reading: 12.3, 12.4; 12.6 (Oxtoby) •  Heat capacities, thermodynamics of gases Chemistry 260 Lecture 19 October 21, 2011 •  Thermodynaics studies the system from a macroscopic perspective • ClariHies the concept of chemical equilibria (chapter 14). 1 2 What is Pressure? Recap of Kinetic Model PV=nRT P= Rate of change of momenta Consider one molecule of mass m, with velocity vx, moving in one dimension, in a cube of dimension L Look at the momentum change per collision with the wall Connects microscopic properties (speed, # collisions, etc.) to macroscopic properties (volume, pressure, temperature, etc.) Based on ideal gas assumptions: •  Molecules very small, don't interact, have random motion, elastic collisions •  Pressure related to speed •  Temperature related to average kinetic energy force mass × acceleration = area area Pressure and speed of 1 ⇒ PV = Nms 2 molecules related 3 Etrans = 3 k BT 2 Temperature is essentially a measure of the average kinetic energy of the atoms/ 3 molecules in the gas Clarification on Maxwell Distribution of Speeds ⇒ urms = 1 2 To 2 RT M 8 RT πM 3RT M L L −mv x = 2mv x Δvx = |vf ‒ vi| For an elastic collision, vf=-vi Δvx =| -vx ‒ vx |=2vx All particles at vxΔt distance will hit the wall. This amount to volume of L2 vxΔt (N number density = N/V) Only half of the particles move at the right direction ½* N L2 vxΔt Total momenta change *= (momentum change per collision) m N L2 vx2Δt Rate of change of the momenta (Divide by Δt): m N L2 vx2 Pressure = Rate of momenta change / Area 3 Etrans = kBT ⇐ 2 1 PV = Nms 2 ⇐ 3 First P= Nm 2 × vx L3 4 a warning Definitions and Terminology: 3 ⎛ m ⎞ 2 2 − mu 2 2 kBT f ( u ) = 4π ⎜ ⎟ ue ⎝ 2π k BT ⎠ ⇒u = 1.  2.  3.  4.  5.  6.  ) mv x Thermodynamics The Maxwell Distribution of Speeds gives us information regarding how speed and temperature are related.  Developed specifically for IDEAL GASES  Similar expressions exist for other phases ⇒ ump = ( s = v2 + v2 + v2 x y z L velocity = vx System Surroundings State State Function Intrinsic Extrinsic Endothermic Exothermic Heat Maximum (peak) average root mean square 5 Work Adiabatic Diathermic Closed System Open System Isolated System Reversible Irreversible Kinetic Energy Potential Energy P-V Work Internal Energy Enthalpy Entropy Heat Capacity Specific Heat Free Energy Spontaneous Negative work is done by the system on the surroundings Positive work is done by the surroundings on the system 6 1 Lecture 19 Today: First law of thermodynamics, energy conservation Thermal equilibration Definitions and Terminology: Work System Adiabatic Surroundings Diathermic State Closed System State Function Open System Intrinsic Isolated System Extrinsic Reversible Endothermic Irreversible Exothermic Kinetic Energy Heat Thermodynamics Thermodynamics Consider a system - such as a piston dx Potential Energy P-V Work Internal Energy Enthalpy Entropy Heat Capacity Specific Heat Free Energy Spontaneous Negative work is done by the system on the surroundings Positive work is done by the surroundings on the system Opposing Force system CH 4 + 2O 2 ⎯⎯⎯ CO 2 + 2H 2O → The piston does work causing your car to move. 7 A Thermodynamic State How do we describe such a process? A Thermodynamic State The State of a thermodynamic system is defined by its properties (Defines the conditions of the MACROSCOPIC system that has EQUILIBRATED) The ideal gas law is an equation of state. PV = nRT The van der Waals equation is an equation of state. (P+an2/V2)(V-nb) = nRT P,V,T P,V,T Systems with the same properties are in identical thermodynamic states. Volume, Temperature, Pressure, and quantity (n) are examples of state functions. P,V,T State functions are path-independent, independent of the history of the system. The state is defined by the properties P,V,n, and T Constant mass and pressure 9 A State Function 8 10 Like altitude, it doesn t matter how you get up there. The key players in the first law of thermodynamics (conservation of energy): U=Q+W DU = q + w • U – internal energy (state) • Q – heat • W – work 11 14 2 Lecture 19 Work Work Mechanical work is done when a mass is accelerated. Definition: Work is defined as energy deposited into the uniform macroscopic motion of a large number of particles. NOT a state function ‒ path dependent 1.  Mechanical Work: 2.  Surface Work: 3.  Electrical Work 4.  Expansion Work: dw=Fdx dw=ϒdA dw= εdQ dw=PdV F m (Force×distance ) (Surface tension×area) (electrical potential×charge) (external pressure×volume) A B x dw = Force × Distance dw = m ax dx Work – energy theorem: w = ΔKE, change in kinetic energy of the system 15 Work 16 Pressure-Volume (PV) Work Mechanical work is done when a mass is accelerated. surroundings m F m m B A dx y system x dw = -PEX dV Negative work is done by the system on the surroundings Positive work is done by the surroundings on the system Constant External Pressure: w = -PEX ΔV 18 Energy may be exchanged with the surroundings in the form of work Opposing Force Fx AREA By convention: Work – energy theorem: w = ΔKE + ΔPE ΔPE = m g dy w = change in kinetic energy plus change in potential energy of the system dx PEX = dw = -PEX A dx w = Force × Distance Work dw = -Fx dx 19 Heat Definition: Heat is defined as energy deposited into the microscopic random motion of the particles. NOT a state function ‒ path dependent Constant External Pressure: w = -PEX ΔV A diathermic wall is one that ALLOWS for heat transfer. system An adiabatic wall is one that DOES NOT ALLOW for heat transfer. But system or surroundings often get HOT… Heat Energy may be exchanged with the surroundings in the form of heat T1 T2 Amount of heat exchanged is q measured in energy units 20 21 3 Lecture 19 Equilibrium Thermodynamics (definitions) •  Open System mass, heat, energy flow freely •  Closed System heat, energy flow freely System ΔU = q + w •  Isolated System no mass, heat, or energy flow • U – internal energy (state) • Q – heat • W – work System System HEAT HEAT q>0 q<0 Exothermic Endothermic 22 U: ‒ KE of the molecules ‒ PE between molecules ‒ Bond energies Internal Energy 23 First Law of Thermodynamics/ energy conservation ETotal = KE + PE + U U = Sum Total Internal Energy U: ‒ KE of the molecules -- PE between molecules -- Bond energies The sum of all of the kinetic and potential energy contributions to the energy of all the atoms, ions, molecules, etc. in the system. He gas Methanol Gas ΔU = q + w for a closed system ΔU = 0 for an isolated system Conservation of Energy The change in internal energy (ΔU) of a closed system is equal to the sum of the heat (q) added to it and the work (w) done upon it. The internal energy of an isolated system is constant. Translational Energy Rotational Energy Electronic Energy Vibrational Energy Nuclear Energy Bond Energy Internal energy is a state function. - Quantity is independent of path. 24 25 First Law of Thermodynamics ΔU = q + w Summary of Thermodynamics closed system expansion against external pressure 0 -PΔV qv qp ΔU=w+q heat introduced Constant Pressure q q Constant Volume w=-PΔV closed system constant volume Process qv Constant Temperature Adiabatic Constant Nothing qp-PΔV Value T w = -PΔV = 0 no work done U ✓ ΔU = qv ΔU = q + w = q - PexΔV Heat energy is stored as internal energy and released as work. 26 27 4 Lecture 19 H =U + PV Enthalpy Enthalpy is a description of the thermodynamic potential of a system. It is frequently most convenient to carry out a process at constant pressure. H ≡ U + PV ΔH = Δ (U + PV ) ΔH = ΔU + Δ( PV ) At constant pressure: ΔH = ΔU + PΔV ΔH = ΔU + PΔV = qp •  synthesizing a compound in lab •  cooking dinner •  drying the laundry ΔU = q + w At constant pressure if only PV work is done: General statement Vf ΔU = q p − P ∫ dV Vi ΔU = q p − PΔV q p = ΔU + PΔV At constant pressure assuming only PV work: Change in Enthalpy is the heat transferred8in 2 the process H= U + PV Enthalpy Enthalpy is a description of the thermodynamic potential of a system. H ! U + PV U, P and V are all state functions  H is a state function In general: ΔH = ΔU + Δ( PV ) ΔU, P and V are all state functions  ΔH is a state function At constant pressure: ΔH = ΔU + PΔV q p = ΔU − w Amount of thermal energy being absorbed Change in internal energy Amount of energy going 29 into expansion work 5 ...
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