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 Once the we know the value of k, we can then calculate the 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) = 0.63g/100ml = 6.3 × 10⁻⁴mg/100ml
The drug concentration after 4.5 hours is .
Additional explanation:
Radioactive decay is responsible for the stabilization of unstable atomic nuclei accompanied by the release of energy.
The half-life is the time after which half of the original sample has decayed and the other half is left behind. It is represented by .
The relationship between the rate constant and the half-life period for the first-order reaction is:
…… (1)
Here,
is the half-life period.
k is the rate constant.
Replace 90 min with in equation (1).
The radioactive decay formula is:
…… (of them)
here
A is the sample concentration after time t.
t is the time taken.
is the initial concentration of the sample.
k is the rate constant.
The duration of the process must be converted into min. The conversion factor for this is,
Therefore, the time spent can be calculated as follows:
Substitute 2 mg/100 mL for , for k and 270 min for t in equation (2).
Learn more:
Which nuclide will be produced in the given reaction?
Calculate nuclear binding energy: Answer details:
Series: High School
Subject: Chemistry
Chapter: Radioactivity
Key words: half-life, 0.25 mg/100 mL, 2 mg/100 mL, A, k, t, rate constant, 4.5 h, 270 min, radioactive decay formula.
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