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Practice questions for exam 2 in chemistry 1060, spring 2009. The questions cover topics such as entropy changes during phase transitions, gibbs free energy, entropy change during isothermal mixing, energy levels and configurations of particles, and industrial chemical reactions. Students are required to use given data and equations to calculate answers.
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Exam 2, PRACTICE Useful Information and Equations: € dG = dH − d ( TS ) €
( 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 ) €
( 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 €
( 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
Δ Hrxn = biDi i = react bonds breaking
j = prod bonds forming
change € dH = dE + d ( PV ) € Pi = XiPtotal € Δ Hrxn = ν (^) i Δ H ˚ i , f i = prod
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?