  The phase diagram of the organic superconductor
$\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$Cl has been investigated by ultrasonic
velocity measurements under helium gas pressure. Different phase transitions
were identified trough several elastic anomalies characterized from isobaric
and isothermal sweeps. Our data reveal two crossover lines that end on the
critical point terminating the first-order Mott transition line. When the
critical point is approached along these lines, we observe a dramatic softening
of the velocity which is consistent with a diverging compressibility of the
electronic degrees of freedom.
