The experimental data for the decomposition of `N_(2)O_(5)[2N_(2)O_(5)to4NO_(2)+O_(2)]` in gas phase at 318 K are given below :
`{(t//s,,0,,400,,800,,1200,,1600,,2000,,2400,,2800,,3200),(10^(2)xx[N_(2)O_(5)]//molL^(-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 time.",,,,"
(ii) Find the half-life period for the reaction.")
("(iii) Draw a graph between "log[N_(2)O_(5)]" and t.",,,,"
(iv) What is rate law ?"
(v) Calculate the rate constant.
(vi) Calculate the half-life period from k and compare it with (ii).

Explanation

To solve the problem step by step, we will follow the instructions given in the question and the video transcript. Let's break it down:

### Step 1: Plot [N₂O₅] against time
1. **Data Preparation**: We have the following data:
- Time (s): 0, 400, 800, 1200, 1600, 2000, 2400, 2800, 3200
- Concentration of N₂O₅ (mol/L): 1.63, 1.36, 1.14, 0.93, 0.78, 0.64, 0.53, 0.43, 0.35

2. **Graph Plotting**: On a graph paper, plot the time on the x-axis and the concentration of N₂O₅ on the y-axis. The points will be plotted as follows:
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