At 25 degrees Celsius, the second order reaction

At 25 degrees Celsius, the second order reaction NOCl (g) > NO(g) + 1/2 Cl2 (g) is 50% complete after 5.82 hours when the intial concentration of NOCl is 4.46 mol/L. How long will it take for the reaction to be 75% complete?

so we know the integrated 2nd order rate equation is
1/[At] = +kt + 1/[Ao]
right?

and we know that at
t = 5.82hr
[At] = 1/2 [Ao]

we were given that!

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rearranging..
k = (1/[At] - 1/[Ao]) / t
.. = (1/(1/2[Ao]) - 1/[Ao]) / t
.. = (2/[Ao] - 1/[Ao]) / t
.. = (1/[Ao]) / t
.. = (1/[Ao] / 5.82hr

and now we want "t" when the rxn is 75% complete.. i.e when [At] = 0.25 x [Ao]
so that..
1/[At] = +kt + 1/[Ao]
t = (1/[At] - 1/[Ao]) / k
t = (1/(1/4[Ao]) - 1/[Ao]) / k
t = (4/[Ao] - 1/[Ao]) / k
t = (3 / [Ao]) / ((1 / [Ao]) / 5.82hr))
t = 3 x ([Ao] / [Ao]) x 5.82hr = 17.5hr

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Questions?