A large volume of pure water at a temperature of $200K$ is flowing parallel to a flat plate of benzoic acid. The length of the plate in the direction of flow is $0\mathrm{.}14m.$ The velocity of water is $0\mathrm{.}1\frac{m}{s}.$ The concentration of benzoic acid at the surface of the plate $C_{A1}$ is its solubility in water and it is $0\mathrm{.}0245kg-mo\frac{l}{m^3}.$ The concentration of benzoic acid away from plate is practically zero $($owing to large volume flow of pure water$).$ It is given that the density of water is $997k\frac{g}{m^3}($mol$.$ wt$.18).$

$($a$)$ Determine the concentration of water on the surface of the plate in $kg-mol{m}^3.$

$($b$)$ Determine the mole fraction of benzoic acid $x_A$ on the flat plate.

$($c$)$ Determine $x_{B,m}$