Two $1-L$ beakers, A and $B,$ each containing a different aqueous solution of mannitol $($a nonvolatile sugar with $MW=182\mathrm{.}17\frac{g}{m}ol)$ are placed together in a box, which is then sealed. The temperature remains constant at $20C.$ Initially, there is $740mL$ of solution in A and $200mL$ of solution in $B.$ As the solutions stand in the sealed box, their volumes change slowly for a while. When they stop changing, beaker A contains $490mL$ and beaker $B$ contains $450mL.$ It is then determined that the solution in $A$ is $0\mathrm{.}867M$ in mannitol and has a density of $1\mathrm{.}05gm{L}^{-1}.$

$($a$)$ What is the molar concentration of mannitol in the solution in beaker $B$ at the end?

M

$($b$)$ Calculate the concentration of mannitol in the solution in A at the start.

M

$($c$)$ Calculate the concentration of the mannitol in the solution in B at the start.

M

$($d$)$ The vapor pressure of pure water at $20C$ is $17\mathrm{.}5$ torr.

What is the pressure of water vapor in the box at the end, after the volumes have stopped changing:

torr