When impurities like salt is added to water, the boiling point of water increases because of what I think is vapour pressure, though I know very little about that too. However, with the same analogy, the freezing point should also increase. Instead, it decreases. Then why does it have to be added to ice-creams? Some websites included equilibrium but I couldn't quite grasp the concept.
Please give an intuitive explanation and an easy mathematical one if there is one. (I understand only those)
When salt is added to water, it affects the freezing and boiling points of the water due to a phenomenon known as colligative properties.
Boiling Point Elevation: When a solute (like salt) is added to a solvent (like water), it interferes with the ability of the water molecules to escape into the gas phase, which is what happens when water boils. The salt ions attract the water molecules and make it harder for them to leave the liquid phase and become a gas.
Freezing Point Depression: Conversely, salt decreases the freezing point of water. When salt is added, it disrupts the hydrogen bonding between water molecules, making it harder for them to connect in an ordered way to form ice crystals.
In the case of ice cream, salt is added to the ice used in the churning process. The salt lowers the freezing point of the ice, creating a saltwater slush that is colder than pure ice. This super-cold slush is able to freeze the ice cream mixture.
Mathematically, the change in freezing or boiling point can be calculated using the formula:
ΔT=Kf⋅m⋅i
where: (ΔT) is the change in temperature, (Kf) is the cryoscopic constant (for water it’s 1.86 °C/m), (m) is the molality of the solution (moles of solute per kilogram of solvent), and (i) is the van 't Hoff factor (number of ions the solute splits into in solution). For salt (NaCl), which splits into two ions (Na+ and Cl-), (i) would be 2. So, the more salt you add, the greater the change in the freezing or boiling point
Impurities (such as salt) readily dissolve into liquids (such as water), where they can circulate easily.
However, the impurities don’t boil away (their vapor pressure is low) and they tend not to be frozen into the solid (they don’t fit into the ordered crystal lattice).
So you have a situation where the concentration of the solvent is <100% in the liquid state but essentially 100% in the solid and gas states.
Now consider what the freezing and boiling points are: a balance between solid/liquid and liquid/gas, respectively. (The specific parameter that’s balanced is the chemical potential, which is like a sophisticated version of concentration.)
Reducing the concentration of the liquid upsets this balance and requires a temperature excursion past the original phase-change temperature, toward the temperature range of the more purer phase (colder for freezing, hotter for boiling) to drive the phase change to occur.
Another way to look it is that reducing the solvent concentration of the liquid from 100% to <100% lowers its Gibbs free energy curve:
The Gibbs free energy (which considers Nature’s favoring of both strong bonding in condensed matter and the many arrangements in a gas, as mediated by the temperature) is minimized for spontaneous processes and stable matter. The chemical potential is itself simply the Gibbs free energy per mole of substance.
Note how pushing the liquid curve down would push the intersections farther out. This provides a graphical explanation for why and how impurities depress the freezing while elevating the boiling point.
So why is salt used when making ice cream? It’s not added to the ice cream itself, of course; it’s added to ice surrounding the cream mixture we’re trying to freeze. Any salt touching the ice melts it, since—as described above—dissolved impurities make the liquid state more stable. But melting takes energy, quantified as the latent heat of fusion. This energy has to come from somewhere, and so the ice and ultimately the cream mixture tend to cool down, accomplishing our goal.
