Raoult's Law as a Special Case of Henry's Law; Ideal Solutions

Raoult's law for a volatile solute, $p_A = x_A p_A^{\circ}$, and Henry's law for a dissolved gas, $p = K_H x$, look different at first glance but are in fact the same underlying relationship, differing only in the value taken by the proportionality constant. Both laws state that the partial pressure of a volatile component above a solution is directly proportional to its mole fraction in the liquid; Raoult's law is simply the special case in which the proportionality constant equals the pure component's own vapour pressure, $p_A^{\circ}$, which happens precisely when the "solute" (component A, dilute or not) experiences essentially the same intermolecular environment in solution as it would in its own pure liquid. Henry's law constant $K_H$, by contrast, generally differs from $p_A^{\circ}$ because a dissolved gas experiences a very different molecular environment, surrounded almost entirely by solvent molecules of a different, usually much larger, size and polarity.

Solutions in which every component obeys Raoult's law across the entire range of composition, from pure A to pure B, are called ideal solutions. Two further conditions accompany this behaviour, both of which follow from the requirement that A–B intermolecular interactions be essentially indistinguishable from A–A and B–B interactions: the enthalpy of mixing is zero, $\Delta_{mix}H = 0$ (no heat is absorbed or released on forming the solution, since the strength of intermolecular attraction does not change), and the volume of mixing is zero, $\Delta_{mix}V = 0$ (the solution's volume is exactly the sum of the two pure-component volumes, since molecules pack together no more or less tightly than in the pure liquids). …