At sea level atmospheric pressure is approximately $1\mathrm{.}00$atm and the composition of air is close to $20\mathrm{.}0\%$ oxygen $($actually around $21\%)$ and $80\mathrm{.}0\%$ nitrogen $($actually around $78\%).$ The Henry's law constants for oxygen and nitrogen in water at $20\mathrm{.}0C$ are approximately $1\mathrm{.}3{10}^{-3}\frac{M}{?}$ atm and $6\mathrm{.}7{10}^{-4}\frac{M}{?}$ atm, respectively. Determine the following:

a$.$ What are the approximate solubilities of oxygen and nitrogen gases in water at $20\mathrm{.}0C$ if the percent composition of air is around $20\mathrm{.}0\%$ oxygen and $80\mathrm{.}0\%$ nitrogen and atmospheric pressure is $1\mathrm{.}00$atm $?$

b$.$ What are the approximate solubilities of oxygen and nitrogen in water at $20\mathrm{.}0C$ if the pressure above the water is increased to $2\mathrm{.}00$ atm by adding $1\mathrm{.}00$ atm of helium gas to $1\mathrm{.}00$atm air?

c$.$ What are the approximate solubilities of oxygen and nitrogen in water at $20\mathrm{.}0C$ if the pressure above the water is increased to $2\mathrm{.}00$ atm by adding $1\mathrm{.}00$atm of nitrogen gas to $1\mathrm{.}00$atm air?

d$.$ What are the approximate solubilities of oxygen and nitrogen in water at $20\mathrm{.}0C$ if the pressure above the water is increased to $2\mathrm{.}00$ atm by adding $1\mathrm{.}00$atm of oxygen gas to $1\mathrm{.}00$atm air?

e$.$ Challenge question: Imagine that you wanted to make an oxygen$/$nitrogen gas mixture that resulted in both gases having equal solubility in water at $20\mathrm{.}0C.$ If the total pressure of the gaseous mixture was $1\mathrm{.}00$atm, what would be the percentages of oxygen and nitrogen?