Solubility and Henry's law

Why does salt dissolve in water but not in petrol? The rule is 'like dissolves like'. A polar or ionic solute dissolves in a polar solvent such as water; a non-polar solute dissolves in a non-polar solvent such as benzene or hexane. The forces between solute and solvent must be similar to the forces each already has. It is like making friends at a new school: you first get along with someone like you. Sugar and water are both polar, so sugar dissolves well; naphthalene is non-polar, so it dissolves in benzene but hardly at all in water.

Keep adding sugar to a glass of water and stirring, and at some point no more will dissolve: the solution is saturated. Before that point it is unsaturated. A saturated solution is not still inside: sugar particles keep dissolving and others keep coming back out at the same rate. This is a dynamic equilibrium. The amount that dissolves in a saturated solution at a given temperature is the solubility; for solids it is usually given per 100 g of solvent, so that every substance is compared on the same amount.

Temperature and solids. It depends on the heat of dissolving. If dissolving takes in heat (endothermic), warming pushes the equilibrium towards dissolving, so solubility rises with temperature. If dissolving gives out heat (exothermic), solubility falls as the temperature rises. This is Le Chatelier's principle at work. Pressure has almost no effect on solids and liquids dissolving, because they hardly compress.

Gases dissolve in liquids too: the fizz in a soda drink is carbon dioxide dissolved under pressure. Henry's law says that the partial pressure of a gas above a liquid is proportional to its mole fraction in the solution:

p = K_H x

K_H is Henry's law constant, and it is different for each gas. Look at it carefully: for the same pressure, a larger K_H gives a smaller x. So a gas with a large K_H is less soluble.

Two simple shortcuts follow from the law:

• If the pressure goes up, more gas dissolves, in the same proportion: double the pressure, double the amount dissolved.
• For a gas in water, x = moles of gas ÷ (moles of gas + moles of water). The water is about 55.5 mol per litre, and the gas is only a tiny amount, so we can leave the gas out of the bottom. It is like adding ₹1 to ₹100 crore: the total hardly changes.

Temperature works the other way. Dissolving a gas gives out heat, so warming the liquid lowers the solubility of the gas. That is why a cold drink keeps its fizz longer, and why fish find less oxygen in warm water.

Henry's law in daily life:

• Soda bottles are sealed under high pressure so that more carbon dioxide dissolves; open the bottle and the bubbles escape.
• Scuba divers breathe air at high pressure, so more nitrogen dissolves in their blood. If they come up too fast it bubbles out and causes the painful bends. Their tanks use air diluted with helium, which dissolves far less.
• At high altitude the partial pressure of oxygen is low, so less oxygen dissolves in the blood. Climbers become weak and unable to think clearly: this is anoxia.

For salts that dissolve only a little, the solubility product K_sp is used to work out how much dissolves.