The tea molecules (water + tea) are bouncing around inside the teacup. They are moving MUCH faster than the sugar molecules because they are in a liquid while the sugar is in a solid. Therefore, they have more energy.
When the tea molecules hit the sugar molecules they transfer energy into the sugar. This energy allows the the sugar molecule that obtained the energy to have enough energy to escape the intermolecular forces (attraction to other sugar molecules) that bind it into the solid.
This is the reason that the greater the surface area of something, the faster it'll dissolve. If the sugar was in a cube, it would dissolve slower because the sugar molecules on the surface would need to be dissolved first before the tea molecules could begin to transfer energy into the deeper down sugar. (aka, the water molecules would have less exposed sugar to transfer energy to by bouncing against it.)
This is the reason that the greater the surface area of something, the faster it'll dissolve. If the sugar was in a cube, it would dissolve slower because the sugar molecules on the surface would need to be dissolved first before the tea molecules could begin to transfer energy into the deeper down sugar. (aka, the water molecules would have less exposed sugar to transfer energy to by bouncing against it.)
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