At one time, ozone $($O$3)$ generators were pitched as being safe and effective in controlling indoor air pollution $($these claims were widely refuted in the scientific literature$).$ Moreover, ozone can damage the lungs when inhaled; relatively low amounts can cause chest pain, coughing, shortness of breath and throat irritation. Suppose one of these so$$called $$air purifiers$$ which generates ozone at the rate of $50$mg$/$h is operated in an office $8$ft high by $14$ft wide by $25$ft long. The air exchange rate $($i$.$e$.,$ the loss rate$)$ in the room is $0\mathrm{.}5/$h$.(1$ ft $=0\mathrm{.}3$ m$)$

a$.$ What would the concentration of O$3$ be in the office at steady state?

b$.$ What would the removal rate constant need to be to keep the steady$-$state concentration below $0\mathrm{.}2$ mgc$/$ma$3?$

c$.$ Suppose the device is turned off after steady state at $($a$)$ is reached. How long will it take for the concentration to reach the National Institute of Occupational Safety and Health $($NIOSH$)$ recommended upper limit of about $0\mathrm{.}16$ ppmv under standard temperature and pressure?