These problems are meant to compliment, not replace, the problems given in the book.
0) Starting with expressions for chemical potentials, show that when you add the two chemical equations A+B <==> C and D <==> E+F together that the overall equilibrium constant for the sum reaction is just the product of the two equilibrium constants for the individual reactions.
1) For the reaction A + B <==> 2C, starting with the expressions for the chemical potential of each species (A, B...) derive the expression for the equilibrium constant.
2) For the reaction in problem 1, the equilibrium constant is 10. If one started with 0.9 molal A, 1.9 molal B and 0.2 molal C what would be the initial reaction free energy for the reaction? How many moles of each component would be present if the reaction proceeded to equilibrium? The temperature is 25 C.
3) Given your answer to problem 2, what would happen if now an additional 1 mole of C was added to the system? What would be the final concentration of each component be after equilibrium is established?
4) Go back to problem two and consider the effect of temperature on the equilibrium. It was found that increasing the temperature of the reaction from 25 to 50 C changed the equilibrium constant from 10 to 2. What is the standard free energy change for this reaction at 50 C? What is the standard enthalpy change and entropy change for this reaction? (you can assume that the enthalpy and entropy changes are temperature independent)?
5) Compare a 0.1 molal aqueous solution of a buffer with a pKA of 7.0 to distilled water. Both solutions we will assume started at pH 7.0. What is the final pH of each solution after adding 0.01 M of HCl?
6) Consider the common buffer Tris-base. This is a weak base (an amine that can be protonated). It has a pKA of 8.0 at 25 C. (How can a base have a pKA? It is actually the pKA of the conjugate acid -- the protonated base.) It comes as a crystal entirely in the unprotonated form. When you add 100 mM of Tris-base to distilled water, what will be the pH of the solution? When you then add 30 mM NaOH (that is, add 30 millimoles of NaOH per liter of solution), what will be the final pH? What would be the pH if instead you added 30 mM of HCl? What would be the pH if you had added 100 mM HCl? How about if you had added 110 mM HCl?
7) What is the isoelectric pH of glycine? An isoelectric pH is the pH at which the molecule has no net average charge. Glycine is an amino acid with the neutral structure: NH2CH2COOH. The amine group on one side of the molecule is a weak base and can be protonated to form a quartinary amine cation R-NH3(+) and the carboxyl group on the other side can deprotonate to form the carboxylic anion R-COO(-). The pKA of the amine group is about 9.8 (this is for dissociation of the conjugate base -- the protonated amine). The pKA for the carboxylic acid is about 4.5. Show that the isoelectric pH is just the average of the two pKAs.
8) What is the reaction free energy for a reaction at equilibrium?
9) Does the expression
mean that the standard reaction free energy is the reaction free energy at equilibrium? Explain.
10) Will the equilibrium constant for the reaction A + B <==> C change when I add additional A to the reaction vessel? How about if I heat up the reaction vessel? Explain.
11) Finish the sentence: "For a weak acid, the pKA equals the pH when..."
12) Starting with an expression for KA derive the Henderson-Hasselbach equation: pH = pKA + log (Base/Acid). Use the reaction AH+H2O <==> A(-) + H3O(+) as an example.
13) How are KA and KB related to each other?
14) Explain in words why adding 10 mM strong acid to distilled water results in a much larger pH change than does adding 10 mM strong acid to a 100 mM solution of a weak acid at a pH equal to its pKA.
15) If the pKA of an acid is 4.0, what is the standard free energy for dissociation of the acid into the conjugate base and a solvated proton?
16) What is the standard state that we use to quote standard reaction Gibbs energies? Use the reaction AH + H2O <==> A(-) + H3O(+) as an example in your answer.
17) What are the meanings of exergonic and endergonic?
18) Using the Bronsted-Lowry classification, what is an acid and what is a base?
19) At 298 K, the standard reaction free energy of the reaction A <==> B is -5 kJ/mole. Assume all activity coefficients are 1.0 a) What is the equilibrium constant of the reaction at this temperature? b) What is the reaction free energy when there is 0.9 moles/kg A present and 0.1 moles/kg of B present?
20) Acetic acid has a pKA of 4.75. Assume that one starts with 0.2 moles of acetic acid in 0.9 kg (0.9 liters) of water at 298 K. Use activity coefficients of 1.0 for all calculations. a) What is the pH of this solution? b) What will be the pH when 100 mls (0.1 liters) of a solution of 1 mole/kg NaOH is added? c) when 100 mls of a solution of 3 moles/kg NaOH is added?
21) If you have a swimming pool in your back yard, you know that it is important to maintain the pool water at a constant pH (swimming pools work best at a pH of roughly 7.2). Let’s suppose you work for a swimming pool company and you have been charged with finding a good buffer to hold the pH of pools constant over extended periods. You decide to look into weak acids. Assume all activity coefficients are 1.0 for this problem. a) What would the pKA of a weak acid need to be in order for it to be an efficient buffer at pH 7.2? Explain. b) You know from experience that if the pH is not adjusted in a pool for a month in Arizona, the pH tends to rise to approximately pH 9. What is the OH- concentration at this pH? c) Given the pKA you determined in part (a) and the amount of OH- that enters a pool over the course of a month determined in part (b), what total concentration of weak acid (A- plus AH forms) would be required to keep the pH from rising above 7.4 in the pool during one month?
22) Consider a solution containing 0.02 mole/kg MgCl2, 0.01 mole/kg acetic acid (CH3COOH) and 0.01 mole/kg sodium acetate (NaCH3COO). a) What is the ionic strength of the solution? You can ignore the small contribution due to dissociation of CH3COOH. b) Calculate the activity coefficients of CH3COO-, H3O+, and CH3COOH using the Debye-Huckle limiting law. c) Using the activity coefficients determined above, calculate the pH of this solution. Note that pH is defined as the negative log of the H3O(+) activity, not the negative log of the H3O(+) concentration.
23) In the half reaction, Zn(s) --> Zn2+(aq) + 2e-, is Zinc being reduced or oxidized?
24) A common technique for separation of different sized DNA molecules is electrophoresis. One places a slab of agarose (rather like jello) inbetween two electrodes. The DNA molecules (which are negative ions) move through the agarose when a voltage is applied across the two electrodes. Small ones move fast, large ones are slowed down by the agarose. At the two electrodes, bubbles are formed. One electrode produces Hydrogen gas, the other Oxygen gas. These are formed by electrolysis of water. a) What is the half reaction at the electrode where the positive voltage is applied? b) What is the half reaction at the electrode where the negative voltage is applied? c) What is the standard electrochemical potential for this reaction? d) What is the standard reaction free energy for this reaction? e)What is the equilibrium constant at 25 C? Usually platinum is used as the material for the two electrodes. Platinum obviously was not choosen on the basis of price. f) Why not use copper electrodes?
25) Define the terms Anode and Cathode.
26) What are the units of reaction free energy in terms of Joules? What are the units of zero current potential in terms of Joules? How are these two quantities related to each other?
27) Starting with the expression,
,
derive the Nernst equation.
28) In the Nernst equation, what is Q for the half reaction Zn(s) --> Zn(2+) + 2e(-)?
29) What is the ratio between the oxidized and reduced species of a redox active solute when the E = E0? Why do you suppose that E0 is often referred to as the midpoint potential?
30) In photosynthesis (biological solar energy conversion) four photons of light are used to oxidize one water molecule to oxygen and protons. What must be the minimum oxidation potential of the oxidizing species formed by absorption of light?
31) Determine the standard zero point potential for the sum of the following half reactions:
Zn(s) <==> Zn2+ + 2e-
Cu2+ +2e- <==> Cu(s)
Is this a spontaneous reaction?
32) Fill in the table using 0.1 M for all initial conditions and 1 s-1 or 1 M-1s-1 or 1 M-2s-1 as appropriate for all rate constants
| Reaction | Differential rate equations | Initial rates (M/s) | Final concentrations |
| A --> B |
dA/dt = dB/dt = |
dA/dt = dB/dt = |
A = B = |
| A + B -- > C |
dA/dt = dB/dt = dC/dt = |
dA/dt = dB/dt = dC/dt = |
A = B = C = |
| A <--> B |
dA/dt = dB/dt = |
dA/dt = dB/dt = |
A = B = |
| A+B <--> C |
dA/dt = dB/dt = dC/dt = |
dA/dt = dB/dt = dC/dt = |
A = B = C = |
| A --> B -->C |
dA/dt = dB/dt = dC/dt = |
dA/dt = dB/dt = dC/dt = |
A = B = C = |
| A <--> B+C --> D |
dA/dt = dB/dt = dC/dt = dD/dt = |
dA/dt = dB/dt = dC/dt = dD/dt = |
A = B = C = D = |
| 2A +B <-->C-->D |
dA/dt = dB/dt = dC/dt = dD/dt = |
dA/dt = dB/dt = dC/dt = dD/dt = |
A = B = C = D = |
| A+B<-->C<--> D |
dA/dt = dB/dt = dC/dt = dD/dt = |
dA/dt = dB/dt = dC/dt = dD/dt = |
A = B = C = D = |
33) Consider the simple first order reaction, A --> B. If you start with 1 M A and 0 M B and it takes 10 seconds to go to 0.5 M A and 0.5 M B, what is the rate constant for this reaction?
34) Consider the reaction A<-->B --> C. Let the first reaction have a forward rate constant of 1 s-1 and a reverse rate constant of 50 s-1 and let the second reaction have a rate constant of 5 s-1. If I initially add 1 mole of A to one liter of solvent (no B or C added), how long will it take before the concentration of C is 0.5 M using a) the equilibrium approximation and b) the steady state approximation?
35) At 298 K the first order rate constant for the conversion of A to B was measured to be measured to be 10 s-1. At 330 K, the first order rate constant was measured to be 20 s-1. What is the activation energy (in joules per mole) for this reaction?
36) For the reaction A + B<--> C <--> D, the forward rate constant for the first reaction is 10 M-1s-1, the reverse rate constant for the first reaction is 1 s-1, the forward rate constant for the second reaction is 5 s-1 and the reverse rate constant is 0.1 s-1 at 298 K. What is the standard reaction free energy for the overall reaction A + B <--> D?