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?

Question

Chemistry

Gabriel Bailey

13 October, 17:39

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?

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Lana Mcgrath · Answer 1

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