# Homework 3 (Due 4/11/16)

- Page ID
- 47371

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

## Q3.1

Describe how graphical methods can be used to determine the order of a reaction and its rate constant from a series of data that includes the concentration of *A* at varying times.

## Q3.2 (New)

A study of the rate of the reaction represented as \(2A⟶B\) gave the following data:

Time (s) | 0.0 | 5.0 | 10.0 | 15.0 | 20.0 | 25.0 | 35.0 |

[A] (M) |
1.00 | 0.952 | 0.625 | 0.465 | 0.370 | 0.308 | 0.230 |

- Determine the average rate of disappearance of
*A*between 0.0 s and 10.0 s, and between 10.0 s and 20.0 s. - Estimate the instantaneous rate of disappearance of
*A*at 15.0 s from a graph of time versus [*A*]. What are the units of this rate? - Use the rates found in parts (a) and (b) to determine the average rate of formation of
*B*between 0.00 s and 10.0 s, and the instantaneous rate of formation of*B*at 15.0 s.

## Q3.3

Compounds A and B both decay by first-order kinetics. The half-life of A is 20 minutes and the half-life of B is 48 minutes. If a container initially contains equal concentrations of compounds A and B, after how long will the concentration of B be twice that of A?

## Q3.4

Nitrosyl chloride, NOCl, decomposes to NO and Cl_{2}.

\[\ce{2NOCl}(g)⟶\ce{2NO}(g)+\ce{Cl2}(g)\]

Determine the rate equation, the rate constant, and the overall order for this reaction from the following data:

[NOCl] (M) |
0.10 | 0.20 | 0.30 |

Rate (mol/L/h) |
8.0 × 10^{−10} |
3.2 × 10^{−9} |
7.2 × 10^{−9} |

## Q3.5

Hydrogen reacts with nitrogen monoxide to form dinitrogen monoxide (laughing gas) according to the equation:

\[\ce{H2}(g)+\ce{2NO}(g)⟶\ce{N2O}(g)+\ce{H2O}(g)\]

Determine the rate equation, the rate constant, and the orders with respect to each reactant from the following data:

[NO] (M) |
0.30 | 0.60 | 0.60 |

[H_{2}] (M) |
0.35 | 0.35 | 0.70 |

Rate (mol/L/s) |
2.835 × 10^{−3} |
1.134 × 10^{−2} |
2.268 × 10^{−2} |

## Q3.6

Use the data provided to graphically determine the order and rate constant of the following reaction:

\[\ce{SO2Cl2 ⟶ SO2 + Cl2}\]

Time (s) |
0 | 5.00 × 10^{3} |
1.00 × 10^{4} |
1.50 × 10^{4} |
2.50 × 10^{4} |
3.00 × 10^{4} |
4.00 × 10^{4} |

[SO_{2}Cl_{2}] (M) |
0.100 | 0.0896 | 0.0802 | 0.0719 | 0.0577 | 0.0517 | 0.0415 |

## Q3.7

Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of 3 × 10^{4} g/mol that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalyzed reactions can be complex, at low concentrations this reaction can be described by a rate equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 µg (0.15 × 10^{−6} g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.

[Penicillin] (M) |
Rate (mol/L/min) |
---|---|

2.0 × 10^{−6} |
1.0 × 10^{−10} |

3.0 × 10^{−6} |
1.5 × 10^{−10} |

4.0 × 10^{−6} |
2.0 × 10^{−10} |