We are being asked to determine the **rate constant** for the reaction given the following data:

Time (min) | Absorbance at 608 nm |

0 | 1.254 |

30 | 0.941 |

60 | 0.752 |

90 | 0.672 |

120 | 0.545 |

Recall: In chemical kinetics, a **reaction rate constant** or reaction rate coefficient, k, quantifies the rate of a chemical reaction.

For a **zero-order reaction**, the integrated rate law is given by

$\overline{){\left[\mathbf{A}\right]}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\left[\mathbf{A}\right]}_{{\mathbf{0}}}}$

where k = rate constant, [A]_{t} = final concentration, [A]_{0} = initial concentration, t = time. A plot of [A] versus time will be a straight line with **slope of –****k.**

For a **first-order reaction**, the integrated rate law is given by

$\overline{){\mathbf{ln}}{\left[\mathbf{A}\right]}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\left[\mathbf{A}\right]}_{{\mathbf{0}}}}$

where k = rate constant, [A]_{t} = final concentration, [A]_{0} = initial concentration, t = time. A plot of ln[A] versus time yields a straight line with a **slope of –****k***.*

A colored dye compound decomposes to give a colorless product. The original dye absorbs at 608 nm and has an extinction coefficient of 4.7 10^{4} M^{-1} cm^{-1} at that wavelength. You perform the decomposition reaction in a 1-cm cuvette in a spectrometer and obtain the following data:

Time (min) | Absorbance at 608 nm |

0 | 1.254 |

30 | 0.941 |

60 | 0.752 |

90 | 0.672 |

120 | 0.545 |

Determine the rate constant for the reaction.

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