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Reference Guide

# Physical Chemistry - Reference Guides

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University of Chicago

Chemistry

CHEM 11100

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Fall

Description

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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)
www.permacharts.com 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 www.permacharts.com
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 fdfv 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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