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Exam 2, PRACTICE Useful Information and Equations: € dG = dH − d ( TS ) €
Δ G = Δ H − T Δ S
K =
( a (^) j , eq ) ν (^) j j prods
( ak , eq )^ ν^ k k reacts
( a (^) j − ν (^) j x ) ν (^) j j prods
( ak − ν (^) k x )^ ν^ k k reacts
G = G ˚+ RT ln( a ) €
Q =
( a (^) j ) ν (^) j j prods
( ak )^ ν^ k k reacts
Δ G ˚= Δ H ˚− T Δ S ˚= − RT ln K € Δ G = Δ G ˚+ RT ln( Q ) € S = kB ln W € ε = − wnet qin
qin + qout qin
Thigh − Tlow Thigh € dS ≥ d q / T €
W =
N!
( n (^) j )! j
Δ S = − ntotal R Xi ln( Xi ) i
dS ≥ d q / T
T ( K ) = t (˚ C ) + 273. € 4.184 J = 1 cal € 1 mL = 1 cm 3 € 1 atm = 760 torr ( mmHg ) € R = 1.987 (^) molcal • K € R = 8.314 (^) molJ • K € kB = R / NA = 1.38 × 10 − (^23) J K € R = 0.082 (^) molL^ • atm • K € 101.3 J = 1 L • atm € Δ Hrxn = Hproducts − Hreactants € 1 J = 1 kg ⋅ m^2 / s^2 € Xi = ni n (^) j
∑ j
Δ Hrxn = biDi i = react bonds breaking
∑ −^ b^ j Dj
j = prod bonds forming
∑ +^ Δ Hphase
change € dH = dE + d ( PV ) € Pi = XiPtotal € Δ Hrxn = ν (^) i Δ H ˚ i , f i = prod
∑ −^ ν^ j Δ H ˚^ j , f
j = react
Exam 2, PRACTICE PART 1 P1. As long as the temperature of the system is uniform, any phase change is reversible. What is the entropy change for the freezing of 2.50 moles of water? NOTE : Δ H ˚ for the process H 2 O( l ) → H 2 O( s ) is – 1.436 kcal/mol. P2. What is ∆ G ˚ at T = 303 K for the reaction N 2 ( g ) + 3H 2 ( g ) → 2NH 3 ( g )? NOTE : The ∆ H ˚f,298 for NH 3 ( g ) is – 11.0 kcal/mol and you will need the following data: compound S ˚ 298 (cal/K mol) H 2 ( g ) 31. N 2 ( g ) 45. NH 3 ( g ) 46. P3. The entropy change for reversible, isothermal mixing is € Δ S = − ntotal R Xi ln( Xi ) i
Calculate Δ S for the mixing of 0.75 mol of Ne and 0.50 mol of H 2. P4. Consider a sample of N = 10 molecules distributed among four non-degenerate energy levels with energies of 0, ε 0 , 2 ε 0 , 3 ε 0. The available energy E is 5 ε 0. How many unique configurations are possible? What is the number of arrangements ( W ) for each configuration? Which is the most probable configuration? It will help to draw the configurations, being mindful of N and E. P5. Suppose we have obtained the box of particle-in-a-box fame. Further, we find that there are four particles in this box with exactly 34 ε of total energy, where ε is the energy of the ground state of the box. Recalling that the particle-in-a-box energy levels increase as n^2 (that is, ε , 4 ε , 9 ε , …), what is the number of arrangements that are possible for these four particles?
