Thermodynamics II

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Thermodynamics II
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Review Sample Problem

• 40.0 g NH4NO3 dissolved in 500. g water in
  insulated cup, what is the final temperature of
  the solution, given same specific heat as water,
  and standard enthalpies of formation
• ?Hof NH4NO3(s) -365.6 kJ/F NH4(aq) -132.5 kJ/F
• NO3-(aq) -205.05 kJ/F
• NH4NO3(s) ? NH4(aq) NO3-(aq)

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ENTROPY S

• Measurement of randomness or disorder
• Greater disorder ? larger S
• Second Law of Thermodynamics
• Entropy of universe always increasing
• Nature favors increase in disorder
• For any process ?S SPRODUCTS SREACTANTS
• ?S 0 products favored by entropy
• ?S
• Energy must be expended to give a more ordered
  state

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One liter of an ideal gas is allowed to expand to
two liters at constant temperature. What is the
?S of the process? -- of the reverse process?

• For system ?S Rln(Vf/ ?S i)
• In general
• Units of ?S J/K or J/FK
• S is a STATE FUNCTION
• ?S 0 favors spontaneous
• ?S
• S alone does not determine spontaneity

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?So for reactions and phase changes

• So ABSOLUTE ENTROPY of one mole of a substance
  at 1.00 atm pressure and T 298 K
• Can be calculated and tabulated
• So 0 for a perfect crystal at 0 K
• ?So SSo(products) - SSo(reactants)
• Hesss Law holds for ?So

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Find ?So forCaCO3(s) 2H(aq) ? Ca2(aq)
CO2(g) H2O(l)
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Predict Signs for ?So

• ?So always positive if more gas is produced
• ?So always positive for phase change to state
  with more freedom.
• ?So usually positive if more moles of products in
  solution

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Gibbs Free Energy G H - TS

• G is a state function
• Absolute Go of a substance cant be determined
• ?Go difference in total free energy between
  reactants and products in thermodynamic standard
  states.
• ?Go ?Ho - T ?So at constant T
• Hesss Law works for ?Go
• ?Gof can be tabulated (defined like ?Ho)

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Find ?Go (at 25o) forCaCO3(s) 2H(aq) ?
Ca2(aq) CO2(g) H2O(l)

• From ?Gof
• Or from ?Ho ( -15.17 kJ) and ?So ( 141.7 J/K)

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?Go -RTlnK K ? products/reactants

• ?Go 1 ? spontaneous
• ?Go 0 ? K
• ?Go 0 ? K 1
• Find K (at 25oC) for
• CaCO3(s) 2H(aq) ? Ca2(aq) CO2(g) H2O(l)
• ?Go -57.36 kJ/F

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?G ?Go RTlnQat equilibrium, ?G 0, Q K
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Temperature Dependence of ?Gofor reactions and
phase changes, reactants products at same T

• ?Ho does not depend on temperature ?HoT ?Ho25
• ?So does not depend on temperature ?SoT ?So25
• ?GoT ? ?Go25 ?GoT ?Ho25 T?So25

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Temperature Dependence of K

• ?Go ?Ho - T?So -RTlnK
• lnK -?Ho/RT ?So/R vant Hoff
• Plot lnK vs 1/T, straight line
• Slope - ?Ho/R
• Intercept ?So/R
• Given K at two different T
• lnK1 -?Ho/RT1 ?So/R
• lnK2 -?Ho/RT2 ?So/R
• ln(K1/K2) (?Ho/R)(T1 T2)/T1T2

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Find K (at 50oC) forCaCO3(s) 2H(aq) ?
Ca2(aq) CO2(g) H2O(l)?Go -57.36 kJ/F ?Ho
-15.17 kJ/F ?So 141.7J/FK

• Method I, vant Hoff K25 1.1E10
• Method II from ?Go25

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Temperature Dependence of Phase Changeexample
H2O(l) ? H2O(g)

• K P(H2O) in atm
• Plot of lnK vs 1/T see back page

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PHASE CHANGES - generalizations

• To state with more freedom
• ?Ho positive
• ?So positive
• ?Go positive at high T
• ?Go negative at low T
• ?Go 0 at To normal temperature of phase
  transition
• For vaporization ln(P1/P2) (?Hovap/R)(T1
  T2)/T1T2

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N2(g) 3H2(g) ? 2NH3(g)

• Find ?Ho, ?So, ?Go, K at 25oC, and 250oC. Find T
  range for spontaneous. Why run at 250oC?