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For the reaction A -> B, the rate law is given by -d[A]/dt = k*[A]^(1/2). If the initial concentration of A is [A]0, which of the following statements is/are correct?

1. The integrated rate expression is k = (2/t)*([A]0^(1/2) - [A]^(1/2))
2. A graph of sqrt([A]) versus time t is a straight line with negative slope
3. The half-life is t_(1/2) = sqrt([A]0) / k
4. The time for 75% completion of the reaction is t_(3/4) = sqrt([A]0) / k

Correct answer: The integrated rate expression is k = (2/t)*([A]0^(1/2) - [A]^(1/2))

Solution

Integrating -d[A]/[A]^(1/2) = k dt gives 2*(sqrt([A]0) - sqrt([A])) = k*t. The integrated law matches option A. The half-life is t_(1/2) = 2*(sqrt([A]0) - sqrt([A]0/2))/k = 2*sqrt([A]0)*(1 - 1/sqrt(2))/k, which does not equal sqrt([A]0)/k; option C is incorrect. Option D: t_(3/4) involves [A]=0.25[A]0, giving 2*(sqrt([A]0)-0.5*sqrt([A]0))/k = sqrt([A]0)/k, which matches option D.

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