In a container filled with air at $35\backslash$deg C and $101$ kPa, a block of dry ice $($solid CO$2)$ with a mass of $14\mathrm{.}7$ kg is introduced. After sealing the lid, the pressure of the container gradually increases until it reaches $912$ kPa. Assume that the transfer occurs isothermally $($T $=$ constant$).$ a$)$ What is the initial number of moles of air in the tank? Disregard the volume occupied by solid$-$ state CO$2$ and assume a negligible amount of CO$2$ escape before sealing the tank. Mw of CO$2$ is $44$ g$/$mol$.$ b$)$ Calculate the final density of the gas mixture in the tank in a unit of g$/$L$.$ Mw of air is $29$ g$/$mol$.$