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Nezavi [6.7K]
3 years ago
7

600 s after initiation of a first order reaction 48.5% of the initial reactant concentration remains present. What is the rate c

onstant for this reaction?
Chemistry
1 answer:
Ludmilka [50]3 years ago
8 0

Answer:

k=1.20x10^{-3} s^{-1}

Explanation:

For a first order reaction the rate law is:

v=\frac{-d[A]}{[A]}=k[A]

Integranting both sides of the equation we get:

\int\limits^a_b {\frac{d[A]}{[A]}} \, dx =-k\int\limits^t_0 {} \, dt

where "a" stands for [A] (molar concentration of a given reagent) and "b" is {A]0 (initial molar concentration of a given reagent), "t" is the time in seconds.

From that integral we get the integrated rate law:

ln\frac{[A]}{[A]_{0} } =-kt

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

ln[A]=ln[A]_{0} -kt

k=\frac{ln[A]_{0}-ln[A]}{t}

therefore k is

k=\frac{ln1-ln0,485}{600}=1,20x10^{-3}

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