Many drugs decompose in blood by a first-order process. 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) 4.0 h after it reaches its maximum concentration?

The half-life of a first-order reaction is determined as follows: 

t½=ln2/k

From the equation, we can calculate the first-order rate constant:

k = (ln(2)) / t½ = 0.693 / 90 = 7.7 × 10⁻³

When we know the value of k we can then calculate concentration with the equation:

A₀ = 2 g/100 mL 

t = 2.5 h = 150min

A = A₀ × e^(-kt) =2 × e^(-7.7 × 10⁻³ × 150) = 0.63 g / 100ml

   = 6.3 × 10⁻⁴ mg / 100ml

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