A saturated solution of naphthalene in chlorobenzene is prepared at a temperature of $293$K and a pressure of $1\mathrm{.}00$ bar. Under these conditions, the mole fraction of naphthalene is xsat$1.$ The pressure is raised to $600$ bar at constant temperature, and some naphthalene precipitates out. Derive an equation for the mole fraction of naphthalene still in solution at a pressure of $600$ bar $($we will call it x$).$ Your final answer should provide an equation for x in terms of x$\_$sat, the change in pressure, the molar volume of naphthalene solid $($V$\_$N$^$s$),$ and the partial molar volume of naphthalene in the liquid at $600$ bar.

Assume ideal solution behavior and that the molar volume of naphthalene in chlorobenzene is independent of pressure. $($HINT: show the work to get x $=$ x$\_$sat$*$exp$[(\backslash$Delta P$($V$\_$N$^$s $-$ V$\_$N$)/$RT$]$ where V$\_$N is partial molar volume$).$