# Homework 9: Kinetics and Nuclear

These homework problems are suggested and will not be turned in for review. However, answers will be available for them the following week by your class TAs. For more homework feel free to go to the Homework page.

1. Answer the following questions based on the potential energy diagram shown here:

1. Does the graph represent an endothermic or exothermic reaction?
2. Label the position of the reactants, products, and activated complex.
3. Determine the heat of reaction, ΔH, (enthalpy change) for this reaction.
4. Determine the activation energy, Ea for this reaction.
5. How much energy is released or absorbed during the reaction?
6. How much energy is required for this reaction to occur?

2. Sketch a potential energy curve that is represented by the following values of ΔH and Ea. You may make up appropriate values for the y-axis (potential energy).

ΔH = -100 kJ and Ea = 20 kJ

Is this an endothermic or exothermic reaction?

3. Hydrogen gas and oxygen gas react to form water, but water can also be broken down into hydrogen and oxygen gas; we typically write a reaction that can be reversed this way, using the double arrow symbol ( or ↔):

2 H2 + O2 ↔ 2 H2O

This reaction is exothermic in the forward direction:

2 H2 + O2 ↔ 2 H2O + 285 kJ

but endothermic in the reverse direction:

2 H2O + 285 kJ ↔ 2 H2 + O2

Consider a general reversible reaction such as:

A + B ↔ C + D

Given the following potential energy diagram for this reaction, determine ΔH and Ea for both the forward and reverse directions. Is the forward reaction endothermic or exothermic?

4. Sketch a potential energy diagram for a general reaction

A + B ↔ C + D

Given that ΔHreverse = -10 kJ and Ea forward = +40 kJ

5. Which one of the following reactions would you expect to be fastest at room temperature and why?

 Pb2+(aq) + 2 Cl-(aq) → PbCl2 (s) Pb(s) + Cl2 (g) → PbCl2 (s)

6. Consider the following reactions. Which do you predict will occur most rapidly at room conditions? Slowest?

 C2H6 (g) + O2 (g) → 2 CO2 (g) + 3 H2O(g) Fe(s) + O2 (g) → Fe2O3 (s) H2O(l) + CO2 (g) → H2CO3 (g) 2 Fe3+(aq) + Sn2+(aq) → 2 Fe2+(aq) + Sn4+(aq)

7. Consider the following reaction that occurs between hydrochloric acid, HCl, and zinc metal:

HCl(aq) + Zn(s) → H2 (g) + ZnCl2 (aq)

Will this reaction occur fastest using a 6 M solution of HCl or a 0.5 M solution of HCl? Explain.

8. Again consider the reaction between hydrochloric acid and zinc. How will increasing the temperature affect the rate of the reaction? Explain.

9. Based on the following kinetic energy curves, which reaction will have a faster rate - A or B? Explain. Also, which reaction, A or B, would benefit most in terms of increased rate if the temperature of the system were increased?

 A. B.

10. Phosgene, COCl2, one of the poison gases used during World War I, is formed from chlorine and carbon monoxide. The mechanism is thought to proceed by:

 step 1: Cl + CO → COCl step 2: COCl + Cl2 → COCl2 + Cl

a. Write the overall reaction equation.

b. Identify any reaction intermediates.

c. Identify any catalysts.

11.

We have typically been simplifying our potential energy curves somewhat; for multistep reactions, potential energy curves are more accurately shown with multiple peaks. Each peak represents the activated complex for an individual step.

Consider the PE curve for a two-step reaction on the left:

 a. What is ΔH for the overall reaction? b. What is ΔH for the first step of the reaction mechanism? c. What is ΔH for the second step of the reaction mechanism? d. What is ΔH for the overall reverse reaction? e. What is Ea for the first step? f. What is Ea for the second step? g. Which is the rate-determing step - step 1 or step 2? How do you know? h. What is Ea for the reverse of step 1? i. Is the overall reaction endothermic or exothermic?

12. If phosphorous-32 emits a beta particle, an isotope of what element is formed.
(a) sulfur (b) chlorine (c) silicon (d) aluminum

13. What element is formed by the following nuclear fusion reaction?

21H + 31H →

(a) beryllium
(b) lithium
(c) helium
(d) a new isotope of hydrogen

14. Complete the following nuclear equations and supply symbols or values for X and x:

1. x88Ra → 42X + 222xX
2. 14xC → xxN + 0-1e
3. xxNe → 19xF + 0+1e
4. 73xAs + 0-1e → x32X
5. 176xLu → xxX + x-1e
6. 235xU + 10n → x10n + 9436X + 139xX
7. 59xCo+ 21X → 60xCo+ xxX
8. 199X + 1xH → 168X + 4xX
9. 168X + 21X → xxX + 4xX
10. 26xMg + 10X → 4xHe + xxX

15. Write equations for each of the following nuclear processes:

1. positron emission by 12051Sb
2. electron emission by 3516S
3. α-particle emission by 22688Ra
4. electron capture by 74Be.

16. The decay of 23492U ultimately leads to 20682Pb. The process proceeds via the sequence of and Br decay steps: α, α, α-, α, β-, β-, β-, α, Write the symbol for each of the isotopes produced in the decay chain.

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## Homework#

17. (a) The heat of combustion of CH4(g) is -495.0 kJ mole-1. Calculate the mass equivalent of this energy in grams. (b) When 14C decays to 147N + 0-1e, a mass loss of 0.000168 amu occurs. How many moles of CH4(g) would have to be burned to produce the same amount of energy as would be produced from the decay of 1 mole of 14C?

18. When two 11H nuclei and two neutrons combine to form 42He, the mass of the product helium nuclei is not the same as the sum of the masses of the reactant particles. Calculate the energy, in joules per mole of helium atoms, that is equivalent to the change in mass during the reaction. lf the energy per helium atom were released as a single photon, what would be its wavelength? How does this wavelength compare with the approximate radius of the helium nucleus?

19. Calculate the binding energy per nucleon for the following nuclear species:

1. 126C (m = 12.0000 amu)
2. 3717Cl (m = 36.96590 amu)
3. 20882Pb (m = 207.9766 amu)
4. 3216S (m = 31.97207 amu)
5. 168O (m = 15.99491 amu)