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Following data are obtained for reaction :

N_{2}O_{5} → 2NO_{2} + 1/2O_{2}

t/s | 0 | 300 | 600 |

[N_{2}O_{5}]/mol L^{–1} |
1.6 × 10^{-2} |
0.8 × 10^{–2} |
0.4 × 10^{–2} |

1) Show that it follows first order reaction.

2) Calculate the half-life.

(Given log 2 = 0.3010, log 4 = 0.6021)

In a pseudo first order hydrolysis of ester in water, the following results were obtained:

t/s | 0 | 30 | 60 | 90 |

[Ester]mol L^{−1} |
0.55 | 0.31 | 0.17 | 0.085 |

**(i) **Calculate the average rate of reaction between the time interval 30 to 60 seconds.

**(ii) **Calculate the pseudo first order rate constant for the hydrolysis of ester.

For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.

t (sec) |
P(mm of Hg) |

0 | 35.0 |

360 | 54.0 |

720 | 63.0 |

Calculate the rate constant.

The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table:

Experiment | A/ mol L^{−1} |
B/ mol L^{−1} |
Initial rate/mol L^{−1} min^{−1} |

I | 0.1 | 0.1 | 2.0 × 10^{−2} |

II | -- | 0.2 | 4.0 × 10^{−2} |

III | 0.4 | 0.4 | -- |

IV | -- | 0.2 | 2.0 × 10^{−2} |