Rate constant, K for first order reaction has been found to be 2.54*10 to the power -3 per sec. Calculate its three-fourth life.

The integrated rate equation for a first order reaction is written as

(1)

where k is the reaction constant, t is the time in which reaction has occurred, [A]_{1} is the initial concentration and [A]_{2} is the concentration after time t. [A]_{2} is also written as

[A]_{2} = [A]_{1} - x

where x is the amount of reaction that has occurred.

Three fourth life means that 3/4 of the reaction has taken occurred. Let us assume that for the given reaction the initial concentration of the reactant is [A]_{1}. Let t be the time in which the concentration is reduced by 3/4. So [A]_{2} = 1/4 [A]_{1} = 0.25 [A]_{1}. We are given that k =2.54 X 10^{-3} s^{-1}. Substituting these values in equation (1), we get

t = {2.303 / (2.54 X 10^{-3})} log {[A]_{1} / 0.25 [A]_{1}}

Solving the above, we get

t = 546 s

Therefore the 3/4 life of the reaction is 546 seconds.

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