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Question
How will you represent first order reactions graphically.
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Solution
i. The differential rate law for the first-order reaction A → P is 
The equation is of the form y = mx + c. A plot of rate versus [A]t is a straight line passing through the origin. The slope of straight line = k.
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| Variation of rate with [A] |
ii. The integrated rate law is
k = `2.303/t log_10 ["A"]_0/["A"]_"t"`
On rearrangement, the equation becomes
`(kt)/2.303 = log_10 ["A"]_0 - log_10 ["A"]_"t"`
Hence,
The equation is of the straight line. A graph of `log_10[A]_t` versus t yields a straight line with slope `-"k"/2.303` and y-axis intercepts as log10[A]0.
 |
| Variation of `log_10 [A]_t` with time |
iii. Rearranging the integrated rate law equation, we get
The equation has a straight-line form y = mx. Hence, the graph of `log_10 ([A]_0)/([A]_t)` versus t is a straight line passing through the origin.
 |
| Variation of `log_10 ([A]_0)/([A]_t)` with time |
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