### Define the rate formula and the integrated reaction rate equation for zero and first order kinetics.

Chemistry

**Homework set 10 – Total points: 100**

*Instructions: Type your answers to the following questions and submit an electronic copy of your completed assignment on Canvas. Points for each question are indicated in front of the question. Name your file as **CHEM151_HW10_FirstNameLastInitial*

*Question 1: Theoretical understanding of reaction kinetics (10pts)*

After studying the slides, your notes from lecture and your readings, answer the following questions in 2-3 sentences for each part:

- Explain what reaction kinetics describe and how the study of kinetics is different from the study of a reaction at equilibrium.
- How does temperature affect reaction rates?
- How can it be explained that the reaction slower as time goes by? In other words, why does the slope of the concentration over time becomes smaller over time in a reaction? What kinetics does this indicate?
- Define the rate formula and the integrated reaction rate equation for zero and first order kinetics.
- The reaction between methanol and ethyl acetate is a reaction similar to the reactions involved in producing biodiesel. The reaction is first order with respect to methanol and zero order with respect to ethyl acetate. Write the reaction rate law for this reaction.

CH3OH + CH3CH2OCOCH3 ⟶ CH3OCOCH3+CH3CH2OH

*Question 2 (5pts)*

After doing the readings from section 20.1 of Van Loon and Duffy and/or the slides, answer the following questions in 2 sentences for each part:

- What is mineralization of organic compounds?
- True/False When an organic compound degrades the products are always less toxic
- Photolytic degradation of organic compounds: Under what conditions is it possible? What is required for such a reaction to occur?
- Indirect photolysis reactions can often be described by pseudo first order reaction. What is the reaction rate dependent on in such a case?
- Non photolytic reactions: what does it mean that a reaction is biotic versus an abiotic reaction? Give an example of a biotic reaction of an organic compound that you learned in this class (before Midterm 2).

*Question 2 (5x5pts) Basic calculations of rates*

- [11.24 – Dimensional analysis] Concentrations in atmospheric chemistry are most often reported in molecule/cm3. As a result, second-order rate constants used in modeling atmospheric chemistry are commonly reported in units of cm3 molecule–1 s–1. Convert the rate constants 3.5 x 10-14 cm3 molecule–1 s–1 to L mol–1 s–1. Is that unit conversion the same for all chemical compounds? What would you need to convert to L g-1 s-1?

- [11.27 – Dimensional analysis] Show that if the units of rate are mol L−1 s−1, then the units of the rate constant for the following second-order reaction are L mol−1 s−1:

H2(g) + Br2(g) à 2 HBr rate = k [H2][Br2]

- [11.25 – Rate laws] For each of the rate laws below, what is the order of the reaction with respect to the hypothetical substances X, Y, and Z? What is the overall order?
- Rate = k[X][Y][Z]
- Rate = k[X]2[Y]1/2[Z]

- [11.29 – word problems to equations – rate laws]

The hypothetical reaction, A + B à C, has the rate law: Rate = k[A]x[B]y

When [A] is doubled and [B] is held constant, the rate doubles.

The rate increases fourfold when [B] is doubled and [A] is held constant.

What are the values of the exponents x and y?

- [11.32 – tabular data to equations – rate laws]

The following experimental data were obtained for the reaction

2 A + 3 B à C + 2 D

Determine the reaction order for each reactant and the value of the rate constant.

[A] (mol/L) |
[B] (mol/L) |
Rate = d[C]/dt (mol/L/s) |

0.127 | 0.15 | 0.033 |

0.127 | 0.30 | 0.132 |

0.255 | 0.15 | 0.066 |

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**Question 3: Basic calculation of half-life for 1****st**** order reactions ***(15 pts)*

- The pesticide Carbaryl has a half life in soil of 19 days. Assuming its degradation follows first order kinetics, calculate the reaction constant. Then, write the kinetics equation as a rate law and as an integrated law.

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*The pesticide Heptachlor has a reaction 0.006 /day.*Assuming its degradation follows first order kinetics, calculate the half-life of heptachlor and interpret its meaning.

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- The concentration of a chemical was measured at 15 mg/L. 20 hours later it was measured at 10 mg/L. Assuming the chemical degrades with first order kinetics, what is the reaction rate of the chemical and its half-life?

*Question 4: Using the equation for first order kinetics – exponents/logarithms practice (15pts)*

Consider dieldrin, a pesticide in the category of organochlorines. It has a half-life of 934 days. After calculating its reaction rate constant, assuming first order kinetics, calculate the following:

- For an initial concentration of 12 ppm in water, calculate the concentration after 10 hours, after 1 month, and after 1 year.
- Considering a water that has 40 ppb of dieldrin in it, how long will it take for the concentration to drop below 5 ppb.
- How long will it take for the concentration to reach 10% of its initial value, regardless of the starting concentration
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*Question 5 – Determining order of reaction and reaction rate from exp data (10pts)*

[EXCEL NEEDED] A new organic compound is tested to determine its kinetics and reaction rate. Concentrations of the chemical were measured under the same conditions for 50 hours, starting at a concentration of 14 ppm. The data from the experiment is given below:

time (hr) |
C (ppm) |

0 | 14 |

5 | 10.03 |

10 | 6.85 |

15 | 5.3 |

20 | 3.47 |

25 | 1.9 |

30 | 1.71 |

35 | 0.76 |

40 | 1.1 |

45 | 0.27 |

50 | 0.29 |

- Is the degradation of the compound following zero or first order kinetics? Use an appropriate quantitative metric to justify your answer.
- Assuming first order kinetics, determine the reaction rate of the compound by linearizing the integrated rate law for first order kinetics and determine the first order reaction rate and the corresponding half-life.

*Question 6 [11.49] Determining order of reaction and reaction rate from exp data (15pts)*

[EXCEL NEEDED] The rate of photodecomposition of the herbicide picloram in aqueous systems was determined by exposure to sunlight for a number of days. One such experiment produced the following results, (Data from Hedlund, R.T., Youngston, CR. “The Rates of Photodecomposition of Picloram in Aqueous Systems,” Fate of Organic Pesticides in the Aquatic Environment, Advances in Chemistry Series, #111, American Chemical Society, (1972), 159–172.)

- Determine the order of the reaction that best fits this data by checking if the best model is zero, first or second order kinetics.
- Then for the best model, determine the rate constant, and the half-life for the photodecomposition of picloram.

time (days) |
C (umol L-1) |

0 | 4.14 |

7 | 3.70 |

14 | 3.31 |

21 | 2.94 |

28 | 2.61 |

35 | 2.30 |

42 | 2.05 |

49 | 1.82 |

56 | 1.65 |

*Question 7 [11.57] – Arrhenius relationship for k dependence on temperature (5pts)*

[EXCEL NEEDED] The table below presents rate constants measured at three temperatures for the following reaction, which is involved in the production of nitrogen oxides in internal combustion engines.

* O(g) + N2(g) à NO(g) + N(g)*

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Determine the activation energy of the reaction in kJ/mol.

k (L/mol/s) |
Temperature (K) |

4.4E02 | 2000 |

2.5E05 | 3000 |

5.9E06 | 4000 |