Draw a log modulus–temperature plot for an amorphous polymer. What are the five regions of viscoelasticity, and where do they fit? To which regions do the following belong at room temperature: chewing gum, rubber bands, Plexiglas®?

1. A state has an energy  = 76.5×10−21 J and a degeneracy of 15. What is the free energyof the state at 25◦C and at 150◦C? Express your answer in kJ/mol.

2. A molecule has a bond that can rotate between the cis and trans states, both of whichhave zero entropy. It is found that the trans state is three times more common than thecis state when the temperature is 250 K. If the molecule is heated to 450 K, what is thenew ratio of trans to cis?

3. A system consists of two independent subsystems, A and B. Subsystem A has 1.3 × 106
allowed microstates and subsystem B has 4.6 × 107 allowed microstates. What is theentropy of the combined system?

4. Macrostate X consists of 5 microstates, each of which have an energy of x = 1.5×10−21
Joules. Macrostate Y consists of 150 microstates, each of which have an energy y =7.0 × 10−21 J. Calculate probability that the system is in state X if the temperature is25◦C.

5. A molecular system at room temperature (25◦C) is found with energy EA 95% of thetime and with energy EB 5% of the time. It is known that state A consists of an ensembleof 3 microstates while there are only 2 microstates in state B. Determine the differencein energies between the two states (EA − EB).

6. Chemical reactions are often described using a three state modelReactants → Transition State → ProductsIn most cases the energy of the transition state is much higher than the energy of the
reactant state. This means that the reaction cannot proceed until there is a randomthermal fluctuation large enough to ‘kick’ the reactant molecule(s) up to the transitionstate energy. Say we have a reaction in which the transition state is 9.0 × 10−20 J abovethe reactant state.
(a) Calculate the ratio of the probability the system is in the transition state to the probability that it is in the reactant state PTS/PR at 37◦C.

(b) Use your answer above to estimate the time it takes for the reaction to occurspontaneously at 37◦C. Assume that the system samples a new microstate everynanosecond (10−9 s).

(c) One way to speed up the reaction is to heat the system. If the temperature isincreased to 1000 K, how long does it take for the reaction to occur?

(d) In biological systems it is not feasible to accelerate reactions by heating them to1000 K. Instead, the reactions rely on enzymes that catalyze reactions by loweringthe energy of the transition state. If catalyzed reaction has a transition state energy2.0 × 10−20 J, what is the approximate reaction time? Use a temperature 37◦C.
1

(e) Finally, estimate the uncatalyzed reaction time if the transition state is not a uniquemicrostate, but actually an ensemble of 100 microstates. Use a temperature 37◦C.

7. A salt ion is dissolved in a large volume of pure water. The wall of the container has asingle defect that can bind the ion with an energy bound = −2.1 × 10−19 J.

(a) If the ion is only bound to the impurity site 2% of the time at room temperature(25◦C), what is the free energy of the ion in the unbound state? Assume that thefree energy of the bound state is equal to the binding energy (the state is non-degenerate).

(b) Calorimetry experiments reveal that the energy of the ion in the unbound state issolv = −5.1 × 10−20 J. Is the change in energy bigger or smaller than kBT at roomtemperature? [i.e. calculate (solv − bound)/kBT]

(c) What is the entropy of the unbound state?

(d) How many microstates are in the unbound ensemble?

The solubility of barium carbonate, BaCO3, is 0.0100 g/L. Its molar mass is 197.3 g/mol. What is the Ksp of barium carbonate?

Calculate the pH of a 0.51 M CH3COONa solution. (Ka for acetic acid = 1.8x10^-5)

Assume you are carrying out the titration of 50 mL of a 0.025 M solution of acetic acid with 0.1023 MNaOH. Acetic acid has aKaof 1.8×10−5.

(a) Calculate the pH of the solution at V= 0, V= 0.3Veq, V=Veq, and V= 1.2Veq. (Veq is the equivalence point volume)

(b) If a phenolphthalein indicator was used in this titration, where would the apparent endpoint occur? Assume the apparent endpoint would occur at the end of the color range of the indicator (pH’s of 8.0-9.6).

1)

A 1.0-L buffer solution is 0.125 M in HNO2 and 0.180 M in NaNO2.

Part A

Determine the concentrations of HNO2 and NaNO2 after addition of 1.5 g HCl.

Express your answers using three significant figures separated by a comma.

Part B

Determine the concentrations of HNO2 and NaNO2 after addition of 1.5 g NaOH.

Express your answers using three significant figures separated by a comma.

Part C

Determine the concentrations of HNO2 and NaNO2 after addition of 1.5 g HI.

Express your answers using three significant figures separated by a comma.

2)

A 1.0 L buffer solution is 0.250 M HC2H3O2 and 0.050 M LiC2H3O2. Which of the following actions will destroy the buffer?

A 1.0 L buffer solution is 0.250 M HC2H3O2 and 0.050 M LiC2H3O2. Which of the following actions will destroy the buffer?

What is the potential of a galvanic cell made up of Cd/Cd²⁺ and Ag/Ag⁺ half-cells at 25

Show the cationic poymerization of tetrahydrofuran, using phosphorous pentafluiride/water as catalyst.Prove, based on the mechanism, that phosphorous pentafluride/water is indeed a catalyst and not an initiator.

In the reaction MnO4- + 8H+ + 5e- Mn2+ + 4H20, the manganese in 3.95 grams of KMnO4 is reduced to Mn2+. How many coulombs of charge must have been transferred to the permanganate ion

Calculate the equilibrium constant for each of the reactions at 25 ∘C .

A.) 2Fe³⁺(aq)+3Sn(s)→2Fe(s)+3Sn²⁺(aq)

B.) O₂(g)+2H₂O(l)+2Cu(s)→4OH⁻(aq)+2Cu²⁺(aq)

C.) Br₂(l)+2I⁻(aq)→2Br⁻(aq)+I₂(s)

A rigid tank contains 61.5 g of chlorine gas (Cl₂) at a temperature of 77°C and an absolute pressure of 6.00 × 10⁵ Pa. Later, the temperature of the tank has dropped to 34°C and, due to a leak, the pressure has dropped to 3.90 × 10⁵ Pa. How many grams of chlorine gas have leaked out of the tank? (The mass per mole of Cl₂ is 70.9 g/mol.)

Suppose you made a copper-nickel cell where the copper was the cathode and the nickel was the anode. You add a 0.5000 M solution of copper nitrate on the cathode side and a 3.000 M solution of nickel nitrate on the anode side. What is the voltage of the cell under these conditions? The units are volts and use at least 4 significant digits in the answer. The error interval is 0.02 V.

ice at 0.0 degree C is used to cool water. What is the minimum mass of ice required to cool 325 g of water from 30.5 degree C to 4.0 degree C? (Heat of fusion= 333 J/g; specific heat capacities: ice= 2.06 J/g.K, liquid water= 4.184 J/g.K)

a. 108g b. 125g c. 325g d. 605g e. 1.75x10^4

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