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Reference Guide

Physical Chemistry - Reference Guides

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CHEM 11100

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permacha srtM PHYSICAL CHEMISTRY Basics Adiabatic process in which no heat is transferred into or out Internal energy The total kinetic and potential energy at the process of the system (U or E) molecular level Boiling point lowest temperature at which liquid under fixed Irreversible process Non-equilibrium process in which no small change pressure changes state from liquid to vapor in conditions could make the process go in reverse (vapor pressure = pressure on liquid) Isobaric process process in which pressure remains constant Carnot cycle system undergoing a cyclical process involving Isochoric process process in which volume remains constant two reversible isothermal processes and two reversible adiabatic processes Isothermal process process in which temperature remains constant Carnot engine The most efficient heat engine which follows the Mass amount of matter in an object carnot cycle Melting point The lowest temperature at which a solid under a Chemical Measure of a chemical system’s tendency to fixed pressure changes state from a solid to a liquid potential (μ) change (undergo a reaction, form a new phase) Pressure (p or P) The force acting on a unit area Critical point Temperature where liquid and vapor are identical Cyclical process a process which repeats a series of changes in the Quantity of heat Total kinetic energy of substance’s molecules system Reversible process process whose direction may be reversed by Enthalpy (H) The quantity of heat in a substance per unit mass small change in one force; system is always near equilibrium under constant pressure State function property of system which has a definite value Entropy (S) a measure of degree of randomness of a system (state variables) for each state, and does not depend on how Equilibrium state state in which state’s macroscopic properties the state is reached (such as temperature, pressure, volume) (such as temperature) are well defined and do not change with time Temperature (T) average kinetic energy of molecules of a substance (Note: Not to be confused with quantity of heat) Heat (q or Q) a form of energy; an energy transfer due to temperature difference between system and Triple point Temperature and pressure at which 3 phases surroundings of a substance (solid, liquid, vapor) co-exist in Heat capacity (C) Total amount of heat needed to produce a one equilibrium degree rise in temperature of a given substance Work (w or W) Form of energy transfer that may be represented Heat engine Device that converts heat into mechanical energy as a force acting through a distance ENERGY CONVERSION FACTORS TEMPERATURE CONVERSION FACTORS 1 J 1 Nm = 1kg m /s = 0.239 cal = 10 erg = 2.78 x 10 -7kWh T = 9/5 x T + 32 T = 5/9 (T – 32) -4 F C C F = 9.481 x 10 Btu T = T + 459.67 T = T + 273.15 -6 -3 7 R F K C 1 cal 1.163 x 10 kWh =3.968 x 10 Btu = 4.186 x 10 erg F = Fahrenheit; C = celsius; K = Kelvin; R = Rankine = 4.186 J 1 kWh 3.6 x 10 J = 8.601 x 10 cal = 3413 BTU = 3.6 x 10 13erg CONSTANTS 1 BTU 1055 J = 252 cal = 2.93 x 104 kWh = 1.055 x 10 10erg 23 Avogadro Constant (N ) A 6.0221367 x 10 molecules/mol -23 PRESSURE CONVERSION FACTORS Boltzmann Constant (k) 1.380658 x 10 J/K -8 2 4 5 5 -2 Stefan-Boltzmann Constant () σ 5.67051 x 10 W/m K ) 1 atm 1.01325 x 10 pa = 1.01 x 10 N m = 1.01325 bar = 760 Torr = 760 mm hg = 29.9 in hg Molar Gas Constant (R) 8.314510 J/(mol K) 0.082058 (l atm)/ (mol K) 1 Pa 9.869 x 10 atm = 7.5 x 10 cm hg = 1 N m 2 Molar Volume of an Ideal 22.41410 l/mol (273.15 K, 1 atm) 1 millibar 10 pa Gas (V m eQUiliBriUm constants c d  [] []  • For reaction, aA + b+B  cC dD CHEMICAL EQUILIBRIUM • At start of a reaction, QC=  a b  • At equilibrium, concentrations are concentrations are at  [] [] initial GAS EQUILIBRIUM a ratio at a fixed ratio • For gases, the equilibrium constant is • If C < C , then the reaction proceeds from expressed in terms of partial pressures [] []d  left to right KC=  a b  P c[] d Δn [] []  • If QC= KC, then the system is at equilibrium Kp=  C D Kp= K cRT)  equilibrium • If Q> K , then the reaction proceeds from [] [] b where Δ nc=+( ) d a−( ) b C C A B right to left 1 physIcal chEMIsTRy•1-55080-851-6 © 1998-2012 Mindsource Technologies Inc. permachasrtTM Zeroth laW oF thermodynamics second laW oF thermodynamics • Two systems that are in thermal equilibrium with a third system are • heat spontaneously flows from a hotter object to a colder object, not the▯ also in thermal equilibrium with each other reverse REVERSIBILITY & ENTROPY First laW oF thermodynamics • entropy is a state function which is represented as S Memory Aid Law of energy Different forms of energy can interconvert; total • For reversible process, values of conservation remains constant state variables are always within an ΔQ ΔQ = ΔS xT • ΔU = Q + W infinitesimal step of equilibrium ΔQ • U is internal energy, Q is heat, and W is work • For a reversible isothermal process, ΔS =T ΔS T WORK & HEAT ΔS = ΔQ/T, where ΔS is change in S T =ΔQ • For a reversible process, ΔS • 2 quantities that result from energy transfer ΔS (system) = –ΔS (surroundings) • heat (Q or H) is energy in transit; work (W) is usually associated with and ΔS (universe) = ΔS (system) + ΔS the expansion or compression of gases (surroundings) = 0 • Total work done on a system is W = –P ΔV (by convention, • For irreversible process, ΔS (universe) > 0 ΔV = V – V ) TOTAl FINAL INITIAL Memory Aid THE CARNOT ENGINE P • By convention, when a system a works on the surroundings, W TOTAl W = P x ΔV Carnot Cycle Carnot is a negative quantity W • Reversible and consists of two reversibleTC Q H Cycle • For a more general pressure-volume W isothermal processes, at temperatures b change in which pressure is not P = ΔV TH> T C and reversible adiabatic d constant, assume an infinitesimal P ΔV processes,Q and Q TH volume change dV produces an ΔV W H C infinitesimal amount of work dW = P QC c V • dW = –P dV, where P is EXTERNAL EXTERNAL ❶ Path a→b Gas expands isothermally, at temperature T H, the pressure against which gas expands absorbing heat Q H • During this small volume change, pressure remains virtually constant • ΔU = 0 at PEXTERNAL ab b • Q H –W =1 a∫ pdv = n R THIn (V bV a • Then, work done in finite displacement is the sum of all such infinitesimals W = – ∫Vol2P dV Gas expands adiabatically until temperature Vol1 EXTERNAL ❷ Path b→c • since external pressure remains virtually constant, it comes outside the ▯ reaches TC integral sign • Q bc0 • W = – ∫VolP dV = –P (Vol – Vol ) = –P ΔV • –W = –ΔU = C (T – T ) (subscript bc indicates Vol1 EXTERNAL EXTERNAL 2 1 EXTERNAL 2 bc V H C Q or ΔU along b→c) Example: Find the work done along the P PV Diagram path b to c on the PV diagram ❸ Path c→d Gas is compressed isothermally, at temperature T C, Solution: 2 atm b c giving off heat Qc • ΔU = 0 W bc= –P(Vc– V b cd = –2 atm (0.05 m – 0.02 m ) 3 • Q C –W =3–n R T InC(V /Vc) d 1 atm a d = –2.02650 x 10 pa (0.03 m ) 3 ❹ Path d→a Gas is compressed adiabatically back to its initial = –6079.5 J state at temperature TH V • Q = 0 • Where W ibcthe work done along the 0.02m 3 0.05m 3 da path b to c, P is the pressure, and V and • –W 4 –ΔU = da (T V T H C c Vb are the volumes at points c and b, respectiveltely • The work terms in the two adiabats cancel each other out, so  V  V  APPLICATIONS W TOTAL H1 3n= RT l b −T Cln C   Va  Vd  Adiabatic process Q = 0; U2− U 1 ΔU = W • For a complete Carnot cycle, ΔS=0 Enthalpy (H) H = U + PV • Enthalpy is a state function Thermal Efficiency • Changes in enthalpy (ΔH) are directly related • a measure of how well a heat engine converts heat into work to the amounts of the substances involved in the process • For the carnot cycle, car (TH– T C/T Hwhere e caris the efficiency of a carnot engine and e = T /(T – T ), where e is the efficiency of a • ΔH changes sign when a process is reversed ref C H C ref carnot refrigerator (that is, a heat engine in reverse) Heat capacity heat capacity is dependent on conditions of • The carnot engine is a specific example of a heat engine (most (C or C ) heat transference; C = C + R p v p v efficient type) where where subscript subscript HEAT ENGINE Hot reservoir at temperaeHrT v indicates p indicates Q H dE  dH  Engine constant C v   constant C p   • W = Q INQ OUT = QH– Q C Heat pressure fdfv volume dT p • The efficiency of a heat engine is Engine W Q C Isobaric process W = pΔV; ΔU,Q, and W are not zero e = W/Q IN1– (Q /QC) H Isochoric process W = 0; U − U = ΔU = Q • For a refrigerator, e1– (Q /Q ) 2 1 H C Cold resevroir at temperCturTe Isothermal process ΔU = 0; Q = −W 2 physIcal chEMIsTRy • 1-55080-851-6
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