As well as changing the total amount of each compound that can be dissolved (the solubility), the brew temperature also affects how fast each compound will dissolve. This is called the rate of dissolution, and it is related to, but distinct from, solubility.
Solubility is the end point — the maximum amount that can dissolve, no matter how long you leave it. The dissolution rate tells us how fast we get there. A substance may have low solubility but a high dissolution rate, meaning that only a small amount can dissolve, but that it will dissolve quickly — or vice versa (Smith, 2015).
The rate of chemical reactions, such as dissolving a compound in water, can be described by a mathematical formula known as the Arrhenius equation. This equation is based on the idea that in order to react, molecules must have a certain minimum amount of energy, known as the activation energy. This principle explains why gas in a lighter doesn’t spontaneously combust in air, but needs to be lit. A spark from the lighter provides enough energy to overcome the activation energy and start the reaction. Once the flame is burning, the heat of the flame itself supplies the activation energy.
The Arrhenius equation describes how at higher temperatures, more molecules will reach the activation energy required, and the reaction will therefore take place more quickly. This principle applies to nearly all chemical reactions, including compounds dissolving in water. As a rule of thumb, increasing the temperature by 10° C (50° F) approximately doubles the rate of most reactions, so increasing the brewing temperature from 90–100° C (194–212° F) will approximately double the initial rate of extraction.
Increasing the temperature will also increase the rate of diffusion,