<u>Answer:</u> The time required for the conversion of benzoyl chloride to benzoic acid is 390 seconds.
<u>Explanation:</u>
The expression for the rate law of first order kinetics is given as:
......(1)
where,
= initial mass of isotope = 100 g
N = mass of the parent isotope left after the time = 100 - 25 = 75 g
t = time taken = 26 s
k = rate constant = ?
Putting values in above equation, we get:
![\ln \frac{75}{100}=e^{-k\times 26}\\\\k=0.011065s^{-1}](https://tex.z-dn.net/?f=%5Cln%20%5Cfrac%7B75%7D%7B100%7D%3De%5E%7B-k%5Ctimes%2026%7D%5C%5C%5C%5Ck%3D0.011065s%5E%7B-1%7D)
Now, we need to find the time when 99 % of the reaction is complete. Using equation 1 again, we get:
= initial mass of isotope = 100 g
N = mass of the parent isotope left after the time = 100 - 99 = 1 g
t = time taken = ? s
k = rate constant = ![0.011065s^{-1}](https://tex.z-dn.net/?f=0.011065s%5E%7B-1%7D)
Putting values in above equation, we get:
![\ln \frac{1}{100}=e^{-0.011065\times t}\\\\t=416s](https://tex.z-dn.net/?f=%5Cln%20%5Cfrac%7B1%7D%7B100%7D%3De%5E%7B-0.011065%5Ctimes%20t%7D%5C%5C%5C%5Ct%3D416s)
Time required for the conversion of benzoyl chloride to benzoic acid = 416 - 26 = 390 s
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