A $4$ cm$3$ mixture formed by adding $2$ cm$3$ of acetone to $2$ cm$3$ dibutyl phthalate is contained in a $6$ mm diameter vertical glass tube, which is immersed in a thermostat maintained at $315$ K$.$ A stream of air at $315$ K and $1$ atmosphere pressure is passed over the open top of the tube to maintain a zero partial pressure of acetone vapor at that point. The liquid level is initially $11\mathrm{.}5$ mm below the top of the tube and the acetone vapor is transferred to the air stream by molecular diffusion alone. The dibutyl phthalate can be regarded as completely non$-$volatile and the partial pressure of acetone vapor may be calculated from Raoult's law on the assumption that the density of dibutyl phthalate is sufficiently greater than that of acetone for the liquid to be completely mixed. Assuming the vapor is ideal and neglecting the effects of bulk flow in the vapor, calculate the time taken for the liquid level to fall to $5$ cm below the top of the tube. DATA: Vapor pressure of acetone at $315$ K$=60\mathrm{.}5$kN$/$m$2$ Diffusivity of acetone vapor in air at $315$ K$=0\mathrm{.}123$ cm$2/$s Density of liquid acetone $=764$ kg$/$m$3$ Density of liquid dibutyl phthalate $=1048$ kg$/$m$3$ Molecular weight of acetone $=58$ g$/$mol Molecular weight of dibutyl phthalate $=279$ g$/$mol