The mixing of rock salt with ice would produce temperatures below zero degrees Celsius because the freezing point or the melting point of water has been lowered. This happens because the vapor pressure of the water is lowered which means the water molecules has less tendency to break from the bonds. At the molecular level, the salt molecules contribute to the overall interaction of the molecules so the breaking of the bonds of the water molecules in the melting process would not only be water molecules only, there would be other molecules that would take up the energy supplied. This is called the freezing point depression.