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The value of the rate constant is 0.001
The value of half-life is 693 sec.
Time taken to complete 95% reaction is 2996 sec.
The first-order reaction rate depends on the concentration of one reactant.
a. the rate constant
The equation for a first-order reaction
[tex]t = \dfrac{2.303}{k} log \dfrac{a}{a-x}[/tex]
Where a = initial concentration
x = completetion
dt = 480 s
Reaction completed is 38.5%
[tex]x = \dfrac{38.5\%a}{100} \\\\a - x = a (\dfrac{1-38.5\%}{100} ) = \dfrac{61.5 a}{100}[/tex]
[tex]k = \dfrac{2- 303 }{480} log \dfrac{a}{(\dfrac{61.5a}{100}) } = 0.001[/tex]
b. Value of half-life:
[tex]\dfrac{0.693}{k}= \dfrac{0.693}{0.001} = 693 s[/tex]
c. To reach 95% completion:
[tex]x = \dfrac{95a}{100} \\\\\\a -x = a\dfrac{(1- 95)}{100} = \dfrac{5a }{100}\\\\\\t = \dfrac{2.303}{0.001}log\dfrac{a}{\dfrac{5a}{100}} = 2996 sec[/tex]
Time taken is 2996 secsecondsond.
Thus, the value of the rate constant are 0.001
The value of half-life is 693 sec.
Time taken to complete 95% reaction is 2996 sec.
Learn more about the first-order reaction
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