A large coal$-$fired powerplant burns $54$ kg of coal per second. The coal supply is $1\mathrm{.}6\%$ sulfur by weight. Sulfur dioxide is controlled by a scrubber that operates with $80\%$ efficiency $$ meaning it captures $80\%$ of the sulfur in the raw flue gas.

a$)$ What is the SO$2$ emission rate from this facility $($in kg$/$yr$).$

b$)$ Four kilometers directly downwind of the plume, a cloud forms at the same height as the effective plume height of the emissions. The cloud has a liquid water content of $2$x$10-6.$ Assume D class stability and use the Pasqual Gifford curves and a wind speed of $2$ m$/$s$.$ What is the SO$2($g$)$ concentration in ppbV$?$

c$)$ Determine the pH of the cloud given the conditions in $($b$).$ The gaseous concentration of CO$2$ is $410$ ppmV$.$ You do not need to consider any other gases. If you make any simplifications, clearly state and document these simplications.

d$)$ If $1\%$ of the SO$2($g$)$ is converted to H$2$SO$4($g$)$ during transport downwind, what is the pH of the cloud right when the cloud forms?