Choosing Dilution Factor

         Always you are faced with whether to run an unknown sample at full strength, or whether to dilute it before analyzing it.  You might do that because too strong a response/signal could either put your readings off-scale, or make a test run an inordinatly long amount of time.  You might also get interference effects due to changing the bulk properties of your solvent matrix by changing viscosity, density, surface tension, etc.

These matrix effects are an obvious reason for diluting to a concentration below that of your highest-concentration standard.  Another reason is subtler.

Most analytical techniques graphically or mathematically fit a curve through the standard samples.  The way least-squares modeling works, you can be sure the curves come close to or (if there are only two) pass through the data points from the top and bottom standard solutions.  But then, if you give the curve-fit some degrees of freedom, the rest of the curve can wriggle around quite a lot in an unreasonable way.  This wriggle represents the uncertainty in the curve fit.

The deviation from the “true” curve should be relatively small inside the range of the standards since the curve must return to these points.  Outside that range, the curve could run off in any direction and so the errors can get quite large as you get further outside the range of the standards.

For this reason, you should always, at the very least, make sure your unknowns fall within the range of concentrations defined by your standards.  If the first pass shows that the unknown is outside of this range, you should rerun the sample at a different dilution factor.

You must also always be aware of whether or not the mathematical origin (0,0) is being used in the data fit.  If it is, and you really get a zero response either naturally or because you subtract a blank, then you can consider the bottom end of the range as being zero.  Otherwise, the relative error you get, as the concentration of the unknown goes to zero, diverges to infinity – definite positive response with zero analyte present.