The relationship is nonlinear, which means it isn’t form a straight line when plotted on a graph. Now, there are three main factors, which affect solubility (besides pressure). Temperature will affect solubility. If the solution process absorbs energy then the solubility will be increased as the temperature is increased. If the solution process releases energy then the solubility will decreased with increasing temperature. Molecular size will affect the solubility. The larger the molecule or the higher its molecular weight the less soluble the substance will be.
Larger molecules are ore difficult to surround with solvent molecules in order to solvate the substance. In the case of organic compounds the amount of carbon “branching” will increase the solubility since more branching will reduce the size (or volume) of the molecule and make it easier to solvate the molecules with solvent. The polarity of the solute and solvent molecules will affect the solubility. Generally polar solute molecules will dissolve in polar solvents and non-polar solute molecules will dissolve in non-polar solvents.
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The polar solute molecules eave a positive and a negative end to the molecule. If the solvent molecule is also polar, then positive ends of solvent molecules will attract negative ends of solute molecules. This is a type of intermolecular force known as dipole-dipole interaction. All molecules also have a type of intermolecular force much weaker than the other forces called London Dispersion forces where the positive nuclei of the atoms of the solute molecule will attract the negative electrons of the atoms of a solvent molecule. This gives the non-polar solvent a chance to solvate he solute molecules.
I know all of this information is irrelevant, except for the bit about temperature, but I decided to include it anyway to give you (the reader) a wider perspective on the processes. In the case of potassium nitrate heat is absorbed to make the solution process more effective, thus making the solvate more soluble. This means that the higher the temperature, the more potassium nitrate can dissolve in distilled water. This proves my hypothesis to be correct. Errors: There are quite a few possible margins for error. The biggest one has to be human error.
It is up to the observer’s own judgment to decide when the crystals are forming, and the human eye can easily be deceived. For example, a person very eager to see crystals will probably see them before they actually appear, and take the temperature then. Human error can be reduced by having the same person take all the readings and observations. Another problem could be any water evaporating from the boiling tube, which could result in inaccurate readings. Unfortunately there is no way of eliminating this error that I can think of. One should simply state that the results are approximate.