Can you please help me with this chemistry question?

Consider a certain type of reaction has a rate constant of 2.95 × 10–2 min–1. Calculate the time required for the sample to decay to one-fourth of its initial value.

a) 2.95 min

b) 0.0590 min

c) 23.5 min

d) 29.4 min

e) 47.0 min

2 Answers

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  • 2 months ago

    Integrated form of the first order rate law:

    ln [A] = –kt + ln [A]_o

    ln 0.25 = –(2.95 × 10–2 min–1) (t) + ln 1

    -1.3865 = –(2.95 × 10–2 min–1) (t)

    t = -1.3865 / –2.95 × 10–2 min–1

    t = 47.0 min

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  • 2 months ago

    t½ = (ln 2) / k =  0.693147 / (2.95 × 10^–2 min^–1) = 23.5 min

    It takes two half-lives to reach one-fourth of its initial value. 

    2 × 23.5 min = 47.0 min

    So answer e)

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