A pharmaceutical compound A is metabolized in human blood at

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

37\,^{\circ}\!\text{C}

. The process follows first-order kinetics with a rate constant

k=0.162\,\text{h}^{-1}

. Immediately after intravenous administration the concentration of the drug in the bloodstream is

8.0\,\text{mg}\,\text{L}^{-1}

. The minimum effective (therapeutic) concentration is

1.0\,\text{mg}\,\text{L}^{-1}

. (a) Calculate the concentration of A in the bloodstream 6.0\,h after administration. Include units with your answer. (b) Determine the time required for the concentration of A to decrease from

8.0\,\text{mg}\,\text{L}^{-1}

to the therapeutic threshold of

1.0\,\text{mg}\,\text{L}^{-1}

. Report your answer in hours to two significant figures. (c) Compute the half-life of A at

37\,^{\circ}\!\text{C}

and explain briefly how the value obtained in part (a) is consistent with first-order behavior.

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