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puteri [66]
3 years ago
15

The half-life for the first-order decomposition of a is 355 s. how much time must elapse for the concentration of a to decrease

to
a.one-fourth
Chemistry
1 answer:
Eva8 [605]3 years ago
4 0

Given the half life of the first order decomposition reaction is 355 s

Rate constant of the first order reaction is related to the half life by the equation,

k = \frac{0.693}{t_{\frac{1}{2}}}

k = \frac{0.693}{355 s}

k = 0.00195 s^{-1}

The concentration of the substance is decreased to 1/4 th.

If we start with 1 M solution, after time t the concentration becomes 1/4th = 0.25 M

First order rate law:

[A] = [A]_{0} e^{-kt}

[A] = 0.25 M

[A]_{0} = 1 M

k = 0.00195 s^{-1}

Plugging in the values to solve for t,

0.25 M = 1 M (e^{-(0.00195s^{-1})t})

ln(\frac{0.25}{1}) = - (0.00195 s^{-1})(t)

t = \frac{ln(0.25)}{0.00195} s

t = 710 s

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