$7)$ A mixture of air and acetone vapor occupies a volume of $1$ m$3$ at $303$ K and a total pressure of $100$kN$/$m$2.$ The vapor pressure of acetone at $303$ K is $37\mathrm{.}9$kN$/$m$2,$ and the adsorption equilibrium data for acetone on carbon at $303$ K is given below: one kg Carbon $($a$)$ If the relative saturation of the air by acetone is $40\%,$ what mass of activated carbon must be added to the space so that, at equilibrium, the value is reduced to $5\%$ at $303$ K $?($b$)$ If $1\mathrm{.}6$ kg of carbon is added, what is the relative saturation of the equilibrium mixture assuming the temperature is unchanged?