Step 1

$\overline{)\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{{\mathbf{t}}_{{\displaystyle \raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}}}}\phantom{\rule{0ex}{0ex}}\mathbf{k}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{0}\mathbf{.}\mathbf{693}}{\mathbf{90}\mathbf{}\mathbf{min}}$

**k = 7.7x10 ^{-3} min**

Step 2

$\overline{)\mathbf{ln}\mathbf{\left[}\mathbf{A}\mathbf{\right]}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{kt}\mathbf{}\mathbf{+}\mathbf{}\mathbf{ln}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}}\phantom{\rule{0ex}{0ex}}\mathbf{ln}\mathbf{\left[}\frac{\mathbf{2}\mathbf{}\mathbf{mg}}{\mathbf{100}\mathbf{}\mathbf{mL}}\mathbf{\right]}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{(}\mathbf{7}\mathbf{.}\mathbf{7}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}{\mathbf{min}}^{\mathbf{-}\mathbf{1}}\mathbf{)}\mathbf{(}\mathbf{30}\mathbf{}\mathbf{min}\mathbf{)}\mathbf{}\mathbf{+}\mathbf{}\mathbf{ln}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}\phantom{\rule{0ex}{0ex}}\mathbf{ln}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}\mathbf{}\mathbf{=}\mathbf{ln}\mathbf{\left[}\frac{\mathbf{2}\mathbf{}\mathbf{mg}}{\mathbf{100}\mathbf{}\mathbf{mL}}\mathbf{\right]}\mathbf{}\mathbf{+}\mathbf{}\mathbf{(}\mathbf{7}\mathbf{.}\mathbf{7}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}{\mathbf{min}}^{\mathbf{-}\mathbf{1}}\mathbf{)}\mathbf{(}\mathbf{30}\mathbf{}\mathbf{min}\mathbf{)}\phantom{\rule{0ex}{0ex}}\mathbf{ln}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}\mathbf{}\mathbf{=}\mathbf{-}\mathbf{3}\mathbf{.}\mathbf{6810}\phantom{\rule{0ex}{0ex}}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}\mathbf{}\mathbf{=}{\mathbf{e}}^{\mathbf{-}\mathbf{3}\mathbf{.}\mathbf{6810}}$

**[A] = 0.02520 mg/mL**

Many drugs decompose in blood by a first-order process.

(a) Two tablets of aspirin supply 0.60 g of the active compound. After 30 min, this compound reaches a maximum concentration of 2 mg/100 mL of blood. If the half-life for its breakdown is 90 min, what is its concentration (in mg/100 mL) 2.5 h after it reaches its maximum concentration?

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