Problem $5$: Flux Balance. The CO$2$ scrubbers on a space mission have failed and an astronaut is

confined in a $20\backslash$times $20\backslash$times $10$ ft sealed room. Her lung capacity is about $0\mathrm{.}02$ ft and she's taking about

$18$ breaths per minute, exhaling completely each time. With each breath, she exhales at $4000$

ppm COz.

a$.$ If the room was initially at $0\mathrm{.}04\%$ CO$2,$ what is the initial concentration and partial

pressure of CO$2,($Cco$2,0[=]$mol$/$ft$\text{'}$ and Pcozol$=]$Pa$)?$

b$.$ What is the average total flux of COz exiting the astronaut's mouth? $($WA$=]$ mol$/$s$)$

c$.$ How long will it take to reach a dangerous level of CO$,?$ Justify dangerous' with

appropriate citation.

d$.$ Sketch the solution $($Cco$,($t$))$ from part c$.$ Label known initial and final

concentrations$/$times$.$

e$.$ If the astronaut gets one $3$x$3$ ft scrubber back online with a rating of $0\mathrm{.}1$ lb CO$2/$ft$?/$hr$,$ is

it sufficient