Question

(10 points) A basement (with volume V) in a residence is found to be contaminated with radon coming from the ground through the floor drains. The concentration of radon in the room is [Co] under steady-state conditions. The room behaves as a CSTR, and the decay of radon is a firstorder reaction with a decay rate constant of [k]. a. Now the condition changes: The source of radon is closed off but there is no ventilation. What is the equation that describes the concentration of radon in the basement with time [Ct]

Answer 1

`\mathbf{C_(Out) = C_o \ exp \Big [ - \Big ( (1)/((V)/(Q) ) + k \Big) t \Big ] }`

Step-by-step explanation:

The equation that describes the concentration of the radon in the basement with time Ct is;

`\mathbf{C_(Out) = C_o \ exp \Big [ - \Big ( (1)/(\theta) + k \Big) t \Big ] }`

where;

`C_o` = concentration of the radon

`C _ {Out}` = allowable radon concentration

k = decay rate constant

= theoretical detention

t = time needed to lower the radon concentration

The theoretical detention
`\theta =(V)/(Q)`

∴

`\mathbf{C_(Out) = C_o \ exp \Big [ - \Big ( (1)/((V)/(Q) ) + k \Big) t \Big ] }`