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A saturated solution is a mixture in which the maximum amount of a given solute has been dissolved into the solvent. You know you have a saturated solution as it will generally contain some undissolved solid solute. At this point adding more solute will not change the concentration of the solution; adding more solute will simply result in more solid at the bottom of the solution. A saturated solution is at equilibrium. The rate of dissolution and the rate of reforming the solid solute are equal. When the concentration is below the saturation concentration, then any solid will spontaneously dissolve. Once sufficient solute has dissolved and the system is at equilibrium, the net dissolution will stop. Adding further solid solute to the mixture will not change this and the solid will remain undissolved.