Answer to Question #164127 in General Chemistry for kyle

Question

1.     Radon 222 is released from the earth and can become trapped in buildings. Suppose the concentration measured in a college classroom building is 1500 pCi/m³, which is significantly above the recommended remedial action level of 4 to 8 pCi/m³ if all leaks into the building are sealed (i.e., no more radon enters the building), how long will it take for the concentration of radon to reach the recommended level?

show complete solution and explanation, step by step

Answer 1

Given

A₀ = 1500pCi/m³

A = 8 pCi/m³

(Rd-222)t_1/2 = 3.8 days

Req'd:t

solution

$\frac{-dA}{dt}$ = kA

integrating

ln[$\frac{A}{A_0}$ ] = - kt

t_1/2 = $\frac{ln 2}{k}$

3.8 days = $\frac{ln 2}{k}$

k = 0.1824/days

solve for time

ln[$\frac{8}{1500}$ ] = - [0.1824/days](t)

t = 20.7 -days