What is the Zeroth Law of Thermodynamics?
if system A is in thermal equilibrium with system B and system B is in thermal equilibrium with system C, then system A is in thermal equilibrium with system C
What is the 'written' definition for the First Law of Thermodynamics?
energy may not be greater nor destroyed, only transferred or changes from one form to another
What is the mathematical definition of the First Law of Thermodynamics?
∆U = q + w, where U is a state function
What is the 'written' definition of the Second Law of Thermodynamics as proposed by Carnot?
one cannot convert heat into work in a cyclic process without losing some heat to a low temperature reservoir
What are two mathematical definitions of the Second Law of Thermodynamics?
(dS)↓U,V >/= 0; (dA)↓T,V </= 0
What is the Third Law of Thermodynamics?
the entropy of all pure perfect crystalline substances is zero at zero kelvin
van der waals equation
P = (nRT/V-nb)-(n^2a/V^2) = (RT/Vm-b)-(a/Vm^2)
Redlich-Kwong Equation
P = (nRT/V-nB)-(n^2a/V(√T)(V+nB)) = (RT/Vm-B)-(A/Vm(√T)(Vm+B)
Boyle Temperature
temperature at which a gas behaves most ideally
equation fo boyle temperature
Tb = (a/bR)
state function
any property that can be determined by thermodynamic properties alone
intensive properties
thermodynamic properties that are not affected by the size of the system
extensive properties
thermodynamic properties that are affected by the size of the system
open system
energy and matter can be transferred from system to surroundings and vice versa
closed system
energy, but not matter, may be transferred
isolated system
neither energy nor matter may be transferred
adiabatic process
process that occurs in an isolated system, no conduction or transmission of heat
reversible process
a process that may be reversed at any moment by changing an independent variable by an infinitesimal amount
internal energy
delta U
internal energy
a state function, the sum of heat and work
thermodynamic efficiency
(of a carnot engine) is the ratio of the net work obtained (-w) to the fuel burned to provide heat (qz)
mathematical equation for enthalpy
H=U + PV
enthalpy
delta H
enthalpy
total heat content of a system, equal to the internal energy of the system plus the product of pressure and volume
Debye's T^3 Law of Heat Capacity
Cp(T) --> T³ as T-->0
Entropy mathematically defined
dS = (dqrev/T)
entropy
the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work
Gibbs Free Energy (mathematical equation)
G=H-TS
Helmholtz Free Energy (mathematical equation)
A=U-TS
Cpm/Cvm for an Ideal monatomic gas
Cvm = 3/2R, Cpm = 5/2R
Cpm/Cvm for an ideal diatomic gas
Cvm = 5/2R, Cpm = 7/2R
Activity
a=e^(µ-µ⁰/RT)
chemical potential
molar free energy
triple point
when all three phases are in equilibrium at a particular point
Gibbs-Helmholtz Equation
δ/δT(∆G/T)p = (-∆H/T²)
Clapeyron Equation
(dP/dT) = (∆Hm/T∆Vm)
Clausius-Clapeyron Equation
ln(P2/P1) = (-∆vapH/R)(1/T2-1/T1)
Van't Hoff Equation
ln(K2/K1)=(-∆rxnH°/R)(1/T2-1/T1)
joule-thomson coefficient
the derivative of the temperature with respect to the pressure at constant enthalpy
joule-thompson inversion temperature
the temperature at which uj-t = 0
critical temperature
the temperature, for a gas, above which it is impossible to liquify, regardless of pressure
law of corresponding states
the assumption that different gases have the same equation of state if each gas is described by reduced variables
Henry's Law
the vapor pressure of component A as Xa --> 0 is linear in Xa but the slope is not equal to Pa*
minimum boiling azeotropes
solutions which exhibit positive deviations from Raoult's Law
maximum boiling azetropes
solutions which exhibit negative deviations from Raoult's Law
law of mass action
the rates of chemical reactions = active masses of reacting species
molecularity
the sum of exponents in the rate law; tells how many species are coming together at the critical time in the reaction
half-life
the amount of time required for half of the initial concentration of the reactant to react
catalyst
a species that speeds up a reaction, without being consumed itself, by lowering the activation energy
transition state
chemical species found at the top of the activation barrier. it is an energy maximum in the direction of the reaction pathway, but an energy minimum in all other dimensions
activation energy
Ea
reaction intermediate
chemical species which lies somewhere along the reaction pathway and is a local energy minimum. However, such a species may or may not be able to isolated depending on the depth of its energy well
steady state approximation (mathematically)
(d[I]/dt) = 0
steady state approximation
the concentration of the intermediate does not appreciably change with time
Arrhenius Equation
lnK = lnA-(Ea/RT) or K = Ae^(-Ea/RT)
zeroth order reaction
half-life is direction proportional to initial concentration concentration versus time is linear
Integrated Rate Law of Zeroth Order Reactions
[A] = -akt + [A₀]
Half-Life of Zeroth Order Reactions
t1/2 = [A₀]/2ak
first order reaction
natural log of concentration versus time is linear half life is constant
Integrated Rate Law of First Order Reactions
ln[A] = -akt + ln[A₀]
Half life reaction of first order reactions
t1/2 = ln2/ak
second order reaction
reciprocal concentration versus time is linear half life doubles
Integrated Rate Law of Second Order Reactions
1/[A] = akt + 1/[A₀]
half life reaction of second order reactions
t1/2 = 1/ak[A₀]
william thomson
lord kelvin
william thomson
rediscovered Carnot's work, corrected it to conform with the first law of thermodynamics
rudolf clausius
worked with Thomson to correct Carnot's work to conform with the first law of thermodynamics
Sadi Carnot
french engineer who most likely would have discovered the first and second laws of thermodynamics had he not died of cholera at age 36
James Prescott Joule
proved heat is a method by which system exchange energy, showed that the same change in state (a certain rise in temperature) can be accomplished either by doing work on a body or heating it
Peter Debye
a Dutch chemist who was the first to show that for non-metallic solids, Cp(T) --> T3 as T-->0, this T3 temperature dependence has been shown to be valid experimentally
max planck
first postulated the third law of thermodynamics
walther nernst
first postulated that the entropy of any reaction approaches zero as the temperature approaches 0 Kelvin
Raoult's Law
Pi = XiPi*
fugacity -for an ideal gas -for a real gas
a = P/Po, a = f/Po
Trouton's Rule
states that the entropy of vaporization is almost the same value, about 85-88J, for various kinds of liquids at their boiling point
Le Chatelier's Principle
increase [A] shifts...
decrease [A] shifts...
increase pressure shifts...
decrease pressure shifts...
increase temperature shifts...
decrease temperature shifts...
to products
to reactants
to side with fewer molecules
to side with more molecules
to side with more molecules
to side with fewer molecules
Reduced Temperature
Tr = T/Tc
Reduced Pressure
Pr = P/Pc
Reduced Molar Volume
Vr = V/Vc
Hess's Law
path independence means that the enthalpy change for any sequence of reactions that sum to the same overall reaction is identical
van der waals constant a
addresses the intermolecular forces the coefficient of thermal expansion related to the attractive forces between molecule Constant in that takes into account the attractive forces for a pure substance
van der waals constant b
addresses the actual volume of the gas particles related to the repulsive forces between molecules A constant that takes into account the repulsive forces for a pure substance, minimum
joule expansion
two moles of an ideal monatomic gas expand adiabatically into an evacuated container (vacuum), tripling the original volume this type of expansion is a
swamping
using the excess of everything except one reactant
Svante Arrhenius
Swedish chemist who proposed molecular definitions of acids and bases
isothermal process
thermodynamic process in which the temperature of the system remains constant
isobaric process
a process occurring at constant pressure
isochloric process
thermodynamic process taking place at constant volume
temperature
intensive property state function a measure of the average kinetic energy of the particles that make up a substance
heat (q)
energy transferred due to a temperature difference extensive property not a state function the energy of the random motion of the particles that make up a substance
work (dw)
the energy transferred by virtue of a mechanical link between systems dw=-PdV for a compression, reversible work (on system) is minimum work for an expansion, reversible work (by system) is maximum work
internal pressure
the rate at which the internal energy changes with volume at constant temperature
Joule-Thomson expansion
a method of expansion in which a gas or liquid at pressure P1, without a considerable change in kinetic energy, flows into a region of lower pressure P2
dew point curve
the temperature at which the vapor starts to condense
bubble point curve
the temperature at which the liquid starts to vaporize
Sir James Dewar
British chemist and physicist known for his invention of the vacuum flask which he used in conjunction with research into the liquefaction of gases
Carl von Linde
German scientist, engineer, and businessman who discovered a refrigeration cycle and invented the first industrial-scale air separation and gas liquefaction processes, which lead to the first reliable and efficient compressed-ammonia refrigerator in 1876