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Thermodynamics III


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Standard State
The pure form of a substance at 1 bar.
Standard Value
The standard value for some property X is denoted
∆H°
Standard Reaction Enthalpy
Temperature and Standard State
Temperature is not part of the definition of standard states; however, 25°C i.e. 298.15 K is the most common temperature used in tables of data.
7.15 Standard Reaction Enthalpies Summary
Standard reaction enthalpies refer to reactions in which the reactants and products are in their standard state, the pure form at 1 bar; they are usually reported for a temperature of 298.15 K.
Hess' Law
The overall reaction enthalpy is the sum of the reaction enthalpies of the steps into which the reaction cab be divided.
Reaction Sequence
A series of reactions in which the products of one reaction take part as reactants in another reaction. The overall reaction is the net outcome of the sequence.
The process of using Hess' law
Finding a series of reactions with known reaction enthalpies that adds up to the reaction of interest.
7.16 Combining Reaction Enthalpies: Hess' Law Summary
According to Hess' law, thermochemical equations for the individual steps of a reaction sequence may be combined to give the thermochemical equation for the overall reaction.
Biomass
Energy generated from crops, plant waste and wood
∆Hc°
Standard Enthalpy of Combustion
Specific Enthalpy
The enthalpy of a combustion per gram; a practical measure of a fuel's value.
Enthalpy Density
The enthalpy of combustion per liter.
Biodiesel
The term for diesel fuel that comes from renewable, biological resources.
Fuels
Most fuels are hydrocarbons; after being combusted, CO₂ gas and liquid water remain, along with nitrogen as N₂ if it was present.
7.17 The Heat Output of Reactions Summary
The heat absorbed or released by a reaction can be treated like a reactant or product in a stoichiometric calculation.
∆Hf°
Standard Enthalpy of Formation
Graphite
The most stable form of carbon at normal temperatures; denoted as C(gr).
Null Reaction
The standard enthalpy of formation of an element in its most stable form is zero. ex. the standard enthalpy of formation of C(gr) is zero because C(gr)→C(gr) is a null reaction; i.e. nothing changes.
Combining standard enthalpies of formation to calculate a standard reaction enthalpy
The difference between the reaction enthalpies of the formation of the products and the reaction enthalpies of the formation of the reactants is the standard enthalpy of the reaction.
17.8 Standard Enthalpies of Formation Summary
Standard enthalpies of formation can be combined to obtain the standard enthalpy of any reaction.
Ionic Model
A model in which the principal contribution to the lattice energy was the Coulomb interaction between ions. Energy changes accompanying the formation of a solid could be estimated based upon this model.
∆H₋L
Lattice Enthalpy
Lattice Energy
The difference in energy between the ions packed together in a solid and the ions widely separated as a gas. A high lattice energy indicates strong ionic bonds. Similar to the lattice enthalpy.
Measuring Lattice Energy
Lattice energy cannot normally be measured directly; it is obtained by combining other measyrements and using Hess' law.
Born-Haber Cycle
A closed path of steps, one of which is the formation of a solid lattice from gaseous ions. The enthalpy change for this step is the negative of the lattice enthalpy.
17.19 The Born-Haber Cycle Summary
The strength of interaction between ions in a solid is measured by the lattice enthalpy, which can be determined by using a Born-Haber cycle.
∆H₋B
Bond Enthalpy
All bond enthalpies are positive
Heat must be supplied to break a bond.
Mean Bond Enthalpy
The bond enthalpies of a given bond vary depending on the neighboring atoms; these variances are small, so the mean bond enthalpy is used.
Gas Only
These rules and such for bond enthalpies are for gases only.
17.20 Bond Enthalpies Summary
A mean bond enthalpy is the average molar enthalpy change accompanying the dissociation of a given type of bond.
Enthalpy and Temperature
The enthalpies of both reactants and products increase with temperature. If the total enthalpy of the reactants increases more than that of the products, the reaction enthalpy of an exothermic reaction becomes more negative…
Kirchhoff's Law
∆H°(T₂) = ∆H°(T₁) + (T₂ - T₁)∆C₋p
The dependence of the reaction enthalpy on temperature
The difference between ∆H°(T₂) and ∆H°(T₁) is (T₂-T₁)∆C₋p, which is small because it depends on the normally small difference in the heat capacities of the reactants and products.
7.21 The Variation of Reaction Enthalpy with Temperature Summary
The temperature variation of the standard reaction enthalpy is given by Kirchoff's law in terms of the difference in molar heat capacities at constant pressure between the products and reactants.
Zeroth Law of Thermodynamics
An isolated system will evolve to equilibrium.
1st Law of Thermodynamics
Conservation of energy. dU = 0 for isolated system.
Constant Volume process
Isochoric and relate to first law
Constant Pressure process
Isobaric and relate to first law
Adiabatic and relate to first law
δQ = 0 so dU = -δW
Specific Heat
Amount of heat needed to raise the temperature of 1kg of material 1 degree Celsius.
Isothermal
Temperature is constant. dU = 0; dQ = dW
Entropy
the tendency toward disorder as predicted by the 2nd law of thermodanamics.
TdS ≥ dU + dW
Entropy and 1st law and 2nd law
pV = nRT
What is the ideal gas equation?
γ = Cp/Cv
Ideal gas: γ, and adiabatic Work
Hess's Law
If a reaction can be described as a series of steps, then ΔΗ for the overall reaction is the sum of the ΔΗ values for all of the steps.
v_i
stoichiometric coefficients
Standard Enthalpy of formation
∆H⁰₂₉₈ = ∑v_i*∆H⁰₂₉₈(i) - ∑v_i*∆H⁰₂₉₈(i)
Standard Enthalpy of reaction
∆H⁰_T = ∆H⁰₂₉₈ + ∫₂₉₈ ∆Cp*dT
and heat of reaction at constant pressure
H = U + pV = U + nRT
good job
Draw Heat engine P-V diagram
Efficiency of a heat engine and why.
η = W / |Q_h| = (|Q_h| - |Q_c|) / |Q_h|
Thomson's postulate
There cannot be a closed path through p_V space where all Q_h results in Work.
Clausius's postulate
Heat cannot flow spontaneously from a cooler to a hotter system
Carnot Cycle
A reversible process in which the system is alternately in contact with two heat reservoirs at constant temperature. paths are isothermal, adiabatic, isothermal, adiabatic.
Carnot Efficiency
since |Q_h| / T_h = |Q_c| / T_c
Second Carnot theorem
the efficiency of any machine cannot be larger then the efficiency of the Carnot machine with same heater and cooler
Entropy: isobaric, isothermal, ∆S_phase transition , isothermal and ideal gas
dS = ∫Cp*dT/T ; ∆S = ∆Q/T ; ∆S_p.t. = ;
Entropy of mixing two gases.
∆S = n₁R*ln(V/V₁) + n₂R*ln(V/V₂)
Third Law of Thermodynamics
states that the entropy of a system approaches a constant value as the temperature approaches zero
Helmholtz free energy
δW ≤ -(dU - TdS) ≤ -d(U-TS)
Will a spontaneous process occur, and work
If W_nonmechanical > W_mechanical then it will occur.
Free energy Conditions of equilibrium.
dA = 0 at const T,V
dH = TdS + Vdp
Entropy and Helmholtz and Gibbs free energies
G_T = G⁰_T + nRT*ln(p)
dependence of Gibbs free energy on pressure for an ideal gas
dU = TdS - pdV + ∑ µ_i * dn_i
Internal energy of an open system and Chemical Potential. Define chemical potential.
H, G, and A with respect to chemical potential.
dH = TdS + Vdp + ∑ µ_i * dn_i
µ = G/n
Chemical potential of pure materials.
µ_i = µ⁰_i + RTln(p_i)
Chemical potential of component i in an ideal gas mixture.
Conditions for equilibrium
T₁ = T₂
Triple point
the temperature and pressure conditions at which the solid, liquid, and gaseous phases of a substance coexist at equilibrium
Critical Point
point of inflexion on the P-V diagram
Degrees of Freedom, F
Number of independent parameters that must be set to fully determine the state of a system in equilibrium.
Number of components, C, of a system
The number of substances minus the number of independent equations describing the chemical reactions relating the substances. ie CO, CO₂, O₂, Fe, FeO (5)
Gibbs Phase Rule
F = C + 2 - P (the 2 is for temp and pressure)
dp/dT = ∆S/∆V
Clausius-Clapeyron equation for phase transition
Solution
Mixture of one or more substances dissolved in another substance. The molecules of each of the substances disperse homogeneously and do not change chemically. A solution may be a liquid, gas, or solid.
Molar Fraction
x_i = n_i / n
Weight fraction
ratio of mass's
Molarity
Expresses the number of moles of solute per liter of solution
Molality
mol of solute/kg solvent
Partial molar values of Extensive properties(F)
(with bar over the top)F_i = dF/dn_i
Excess values or ∆F_mix
F^M = F - ∑n_i * F⁰_i
Relative partial molar value
(with bar over top)(F_i)^M = d∆F_mix / dn_i
Gibbs-Duhem relation: general and binary solu.
∑[(dF_i(bar) / dn_j) *n_i] = 0
Ideal Dilute Solutions
Solution where the solvent molar fraction approaches unity.
Henry's law and constant
In ideal dilute solution the saturated vapor pressure of the solute is proportional to the solute concentration in the solution. p₂ = h*c₂ and h = k↑ / k↓.
Applies to diatomic gases in metals.
Sieverts law and how different from Henry's
µ₂ = µ₂_vapor
Condition for vapor in equilibrium with solution.
µ = µ⁰ + RT*ln(p)
Chemical potential of solute vapor in a solution.
Standard state of the Solute
if c₂ = 1 then RT*ln(c₂) = 0 and µ₂ = phi₂
µ₂ = phi_x + RT*lnx₂
Chemical potential of solute of vapor in an IDEAL DILUTE solution.
Chemical potential of solvent
µ₁ = µ⁰₁ + RT*lnx₁
Raoult's law
p₁ = p⁰₁*x₁
entropy, enthalpy, and volume
S₁(bar) = S⁰₁ - R*lnx₁
Macroscopic point of view
the gross or overall behavior
Microscopic point of view
statistical behavior of particles