User:Blackbombchu/sandbox/Rate of solution

Rate of solution is how quickly a solute dissolves in a solvent. Factors determining the rate of solution are surface area, stirring, saturation, and temperature. Diffusive dissolution is the dissolution of a solid into a liquid in an undisturbed system in the absense of gravity. For any solid of a given shape and any pure liquid at any given temperature, the amount of time it would take for that solid do undergo diffusive dissolution varies as the square of the size of the solid. For that reason, rate of solution will be defined for any given pair of a solute and solvent at a given temperature, and will be defined as the the square of the diameter of spherical sample of the solute in the pure solvent divided by the length of time it takes that sample to dissolve at a given temperature. This does not need to be defined in terms of size because size doesn't make a difference to this value. For dissolution by chemical reaction, the larger the activation energy for converting from crystal to soluble product, the slower the rate of solution will be.

For any given solute crystal in a pure given solvent at a given temperature, it will undergo convective dissolution if and only if its crystal is denser then the solvent and its solution is less dense than its solvent or if its crystal is less dense than its solvent and its solution is denser than its solvent. Sugar will not undergo convective dissolution but ice will which explains why people need to stir their tea to make the sugar dissolve fast but don't need to stir it to make ice cubes in it melt fast despite the much larger size of ice cubes. If the crystal is at a sufficiently large size for the given triplet of solute, solvent, and temperature, the solution layer around it will be thinner than the crystal diameter so the rate of change of its diameter with time will vary as the inverse of the thickness of the solution layer. For crystal sizes larger than that size, the length of time to dissolve varies as crystal size to the power of $5⁄4$. For a crystal smaller than that size, it can be treated like diffusive dissolution and the length of time for it to dissolve varies as crystal size to the power of 2.

Apple cider made from apple cider powder is so much denser than water that it has to be above about 50°C in order to be less dense than pure water at 0°C. For that reason, ice cubes in it will undergo convective melting until they lower the temperature down to 50°C with their latent heat of fusion then after that, they will undergo diffusive melting creating a layer of water at the top.