Question

Benzoyl chloride, C6H5COCl, reacts with water to form benzoic acid, C6H5COOH, and hydrochloric acid. This first-order reaction is 25% complete after 26 s. How much longer would one have to wait in order to obtain 99% conversion of benzoyl chloride to benzoic acid?180 s210 s290 s390 s420 s

Answer 1

Answer: The time required for the conversion of benzoyl chloride to benzoic acid is 390 seconds.

Explanation:

The expression for the rate law of first order kinetics is given as:

$\ln \frac{N}{N_o}=e^{-kt}$      ......(1)

where,

$N_o$ = 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:

$\ln \frac{75}{100}=e^{-k\times 26}\\\\k=0.011065s^{-1}$

Now, we need to find the time when 99 % of the reaction is complete. Using equation 1 again, we get:

$N_o$ = 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 = $0.011065s^{-1}$

Putting values in above equation, we get:

$\ln \frac{1}{100}=e^{-0.011065\times t}\\\\t=416s$

Time required for the conversion of benzoyl chloride to benzoic acid = 416 - 26 = 390 s