$\overline{){\mathbf{ln}}\mathbf{\left[}{\mathbf{CH}}_{\mathbf{3}}\mathbf{NC}\mathbf{\right]}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{\left[}{\mathbf{CH}}_{\mathbf{3}}\mathbf{NC}\mathbf{\right]}}_{{\mathbf{0}}}}\phantom{\rule{0ex}{0ex}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{y}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{m}\mathbf{}\mathbf{x}\mathbf{+}\mathbf{}\mathbf{b}$

plot ln[CH_{3}NC] vs t

y = (-2.0775x10^{-4 }torr^{-1}^{ }s^{-1}) x + 6.2250 torr

**$\mathbf{-}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\mathbf{slope}\phantom{\rule{0ex}{0ex}}\mathbf{-}\mathbf{}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}\mathbf{.}\mathbf{0775}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$**

From the following data for the first-order gas-phase isomerization of CH_{3} NC at 215 ^{o}C, calculate the first-order rate constant and half-life for the reaction:

Time (s) | Pressure CH_{3}NC (torr) |

0 | 502 |

2000 | 335 |

5000 | 180 |

8000 | 95.5 |

12000 | 41.7 |

15000 | 22.4 |

Calculate the first-order rate constant.

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