At 25 o C, the second order reaction has a half life, t1/2, of 5.82 hours when t

Question

At 25oC, the second order reaction

has a half life, t1/2, of 5.82 hours when the initial concentration of NOClis 4.46 M. starting with a concentration of 4.46 M, how long (in hours) will it take for the reaction to be 75%.

The answer is 17.5hr i need the show work for how to get the answer

At 25 degreeC, the second order reaction has a half life, t1/2, of 5.82 hours when the initial concentration of NOClis 4.46 M. starting with a concentration of 4.46 M, how long (in hours) will it take for the reaction to be 75%. The answer is 17.5hr i need the show work for how to get the answer

Explanation / Answer

As we know that

Half Life = 1/(k*[NOCl]0)

k*[NOCl]0 = 1/5.82

k = 1/(5.82[NOCl]0) -----------------------------(1)

Also as we know

1/([NOCl]t) = kt +  1/([NOCl]0)

From Eq(1) , put the value of k , we get

1/(0.25[NOCl]0) = t/(5.82[NOCl]0) +  1/([NOCl]0)

1/0.25 = t/5.82 + 1

t = 17.5 hr

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