Thermodynamics 2 Flashcards
The 2nd Law of Thermodynamics
The entropy of the universe tends to increase
S > 0
Entropy
dS = dQ/T
S total
S total = Ssystem + Ssurroundings
Stotal = dSh + dSc = -Qc/Th + Qc/Tc = Qc(Th-Tc)/Th•Tc
The 3rd Law of Thermodynamics
Nernst heat theorem
The entropy S of all perfect crystalline substances is the same at absolute zero
Entropy change at the transition
dS = dH/T
Difference in entropy
S2 - S1 = dH/T = Cp(dT/T) = Cp(lnT)
Calculate absolute entropy
dS = n(Cp/T)dt at constant P
Debye Extrapolation
At low T, Cv = Cp = aT^3
Joule’s Law
The internal energy of a perfect gas depends only on the temperature
Ideal gasses and solutions
dUt = 0 (dU/dV) = 0
Joule’s Law
(dU/dV)t = (dU/dP)t = dU/dT
Gay-Lussac’s law
The volume of a given mass of gas is directly proportional to its temperature, if the pressure remains constant
Gay-Lussac’s Law
(V2/V1)p = (T2/T1)p
Boyle-Mariotte’s Law
The volume of a given mass of gas varies inversely with the pressure, if the temperature remains constant
Endothermic thermochemistry
If heat is absorbed during a reaction, dH and dU are positive, and the reaction is said to be endothermic.
Exothermic thermochemistry
If heat is given off, dH and dU are negative, and the reaction is exothermic
Hess’s Law
If a reaction can be broken down into a number of steps, dH of the overall process is equal to the sum of the enthalpy changes in each step
Standard heat of formation
The standard enthalpy of formation of compounds at 1 atm and 25 Celsius, and the substance is in a stable physical state under these conditions. It is 0 for elements
Standard enthalpy of reaction
The difference in enthalpy beteeen the products and the reactants, when both products and reactants are in their standard state at 298K
Gives free energy
G = H - TS
If dG < 0
Then the reaction is spontaneous
If dG > 0
Then the reaction is not spontaneous
If dG = 0
Then the system is in a state of equilibrium
If dS > 0 & dH <0
Spontaneous at all temperatures
If dS > 0 & dH > 0
Spontaneous at high temperatures
If dS < 0 & dH < 0
Spontaneous at low temperatures
If dS < 0 & dH > 0
Nonspontaneous at any temperatures
Standard free energy
dGrx = sum of dGproducts - sum of dGreactants
Chemical potential
u = dG/dn
dGb = (u)b•dnb
When phase equilibrium is achieved, the chemical potential of a component is the same in both phases.
Gibb’s phase rule
f = c - p + 2 c = # of components in the system p = # of phases present f = # of degrees of freedom of a system
1 component system Gibb’s phase rule I.e. Pure water
f = 3 - p
If p = 1( the system contains 1 of base), f = 2
The system is bivariant
1 component system Gibb’s phase rule
f = 3 - p
If p = 2(the system has two phases), f = 1
The system is univariant
1 component system Gibb’s phase rule
f = 3 - p
If p = 3(three phases), f = 0
The system is invariant
Bivariant
P and T can be modified independently without altering the # of phases
Univariant
Between two phases on phase equilibria diagram = along the line
For a given temperature, there is only one pressure at which two phases may exist
Invariant
A point at which all phases are simultaneously at equilibrium aka the triple point no degrees of freedom
Colligative properties
The physical properties of dilute solutions that depend only on the number of molecules in solution, not their chemical nature.
Colligative properties
Freezing point depression,
Boiling point elevation,
Osmotic pressure
Raoult’s law
When a solute is added to a pure solvent, the vapor pressure above the solvent decreases
Raoult’s Law
P1 = ix1•P1^o P1 = vapor pressure of the solvent with added solvent X1 = mole fraction of solvent P1^o = vapor pressure of pure solvent I = # of miles after the solution/# of miles before solution
Freezing point depression dTf
dTf = Kf•m(solute)•i K = constant m = mol solute/ kg of solvent
Boiling point elevation dTb
dTb = Akbar•m(solute)•i
Osmotic pressure (pi)
pi = CRT C = concentration of the solution T = temp in kelvin
