Which of the following is correct for first order reaction?

1. t_100% = 2t_50%
2. t_90%  = 2t_40%
3. t_99% = 2t_90%
4. t_100% = 4t_25%

Dear Student,

Please find below the solution to the asked query:

option 3 is the correct answer
t_99% = 2t_90%
​Time required for 99% completion of reaction is two timess of the time required for 90% completion.
Let t₁ be the time required for 99% completion.
In this case initial value =100
Final value =(100-99) =1
Substituting these values in the equation for first order reaction we get
t₁=
         $$\begin{gathered} \frac{2.303}{k}\log \left[\frac{100}{1}\right] \\ \frac{2.303}{k}\log 100 \\ \frac{2.303}{k}\times 2 \end{gathered}$$

Again for 90% completion Initial value is 100
Final value =(100-90) =10
Substituting these values in the rate equation we get
t₂=
$$\begin{gathered} \frac{2.303}{k}\log \left[\frac{100}{10}\right] \\ \frac{2.303}{k}\log 10 \\ \frac{2.303}{k} \end{gathered}$$

Hence t₁= 2t_{2
   or} t_99% = 2t_90%

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