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A first order reaction is 38.5% complete in 480s.
a) calculate the value of the rate constant.
b) what is the value of the half life.
c) how long will it take for the reaction to reach 95% completion​

Sagot :

Mahima6824soniidn

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

[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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