Question

A first order reaction is 38.5% complete in 480s.

Answer 1

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.

What is the first-order reaction?

The first-order reaction rate depends on the concentration of one reactant.

a. the rate constant

The equation for a first-order reaction

$t = \dfrac{2.303}{k} log \dfrac{a}{a-x}$

Where a = initial concentration

x = completetion

dt = 480 s

Reaction completed is 38.5%

$x = \dfrac{38.5\%a}{100} \\\\a - x = a (\dfrac{1-38.5\%}{100} ) = \dfrac{61.5 a}{100}$

$k = \dfrac{2- 303 }{480} log \dfrac{a}{(\dfrac{61.5a}{100}) } = 0.001$

b. Value of half-life:

$\dfrac{0.693}{k}= \dfrac{0.693}{0.001} = 693 s$

c. To reach 95% completion:

$x = \dfrac{95a}{100} \\\\\\a -x = a\dfrac{(1- 95)}{100} = \dfrac{5a }{100}\\\\\\t = \dfrac{2.303}{0.001}log\dfrac{a}{\dfrac{5a}{100}} = 2996 sec$

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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