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#### Question

(a) For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.

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Derive the relation between half life and rate constant for a first order reaction

The experimental data for decomposition of N_{2}O_{5}

[`2N_2O_5 -> 4NO_2 + O_2`] in gas phase at 318K are given below:

t(s |
0 | 400 | 800 | 1200 | 1600 | 2000 | 2400 | 2800 | 3200 |

`10^2xx[N_2O_5]mol L^(-1)` | 1.63 | 1.36 | 1.14 | 0.93 | 0.78 | 0.64 | 0.53 | 0.43 | 0.35 |

**(i) **Plot [N_{2}O_{5}] against *t*.

**(ii) **Find the half-life period for the reaction.

**(iii)** Draw a graph between log [N_{2}O_{5}] and *t.*

**(iv) **What is the rate law?

**(v) **Calculate the rate constant.

**(vi) **Calculate the half-life period from *k *and compare it with (ii).

Calculate the half-life of a first order reaction from their rate constants given below:

**(i)** 200 s^{−1} **(ii)** 2 min^{−1} **(iii)** 4 years^{−1}

The rate constant for a first order reaction is 100 s^{–1}. The time required for completion of 50% of reaction is _______.

(A) 0.0693 milliseconds

(B) 0.693 milliseconds

(C) 6.93 milliseconds

(D) 69.3 milliseconds

The integrated rate equation for first order reaction is A → products

(a) ``

(b) `k=-1/tl_n[A]_t/[A]_0`

(c) `k=2.303/t log_10 ([A]_t/[A]_0 )`

(d) `k=l/tl_n[A]_t/[A]_0`