How does antifreeze make it less likely for water in a radiator to freeze or boil?

Freezing

Freezing Point - The temperature at which the solid and liquid phases of a substance are in equilibrium at atmospheric pressure.

When a solute is dissolved in a solvent, the freezing point of a solution  is lowered according to the equation:

T = change in temperature
i = the van't Hoff factor, which is the number of particles into which the solute dissociates
m = the molality, which is the moles of solute per kilograms of solvent
K_f = the molal freezing point constant (for water, K_f = 1.853 C/m)

When a substance freezes, a few molecules cluster together, forming a tiny amount of the solid.  As more liquid molecules move toward the surface of the cluster, the solid grows.  As each molecule is added to the solid cluster, heat (equal to the heat of fusion of the substance) is released.  As this heat energy is lost to the surroundings, the freezing continues.

In a solution, the solute particles hinder the solvent particles from colliding, effectively forcing the solvent particles to move away from the freezing solid cluster and remain in the liquid phase.  In order for the liquid solvent molecules to collide with the cluster, the temperature must be lowered.  Lowering the temperature lowers the kinetic energy of the solvent molecule, thereby lowering their velocity (KE = mv²).  At lower temperatures, the solvent molecules are slowed from moving away from the cluster and are allowed to reach the cluster to add to the solid.

Boiling

Boiling Point - The temperature at which the vapor pressure of a liquid is equal to the pressure on the liquid (generally atmospheric pressure).

When a nonvolatile solute is added to a pure solvent, the vapor pressure of the solvent decreases.

• Vapor pressure - The pressure over a liquid or solution that results when molecules escape the liquid and enter the gaseous phase.

In order for a molecule in the liquid phase to enter the gaseous phase, the molecule must be at the surface of the liquid and have enough kinetic energy to break the surface.  The addition of a nonvolatile hinders this situation in two ways:

1. The solute particles occupy space at the surface.
2. The solute particles introduce a new set of attractive forces with the solvent molecules.

As shown in the picture above, the solute causes the vapor pressure or the solvent to decrease.  Since boiling point is the temperature and at which the vapor pressure of the liquid is equal to the the pressure on the liquid, the boiling point of the solution is higher that the boiling point of the pure solvent according to the equation:

T = change in temperature
i = the van't Hoff factor, which is the number of particles into which the solute dissociates
m = the molality, which is the moles of solute per kilograms of solvent
K_b = the molal boiling point constant (for water, K_b = 0.515C/m)

A higher temperature is required in order to increase the vapor pressure of the solution to atmospheric pressure.  The increase in boiling point temperature is shown in the phase diagram below:

Next:  "Phase Diagrams"