How are the digit mulipliers derived in digital titrator methods?
Explanation of how the digit multipliers are calculated
First step that is required to calculate the digit multiplier is to know the formula for the reaction taking place during the titration; here is a generic simplified one:
X sample analyte + Y titrant --> Products
Here is the equation that is used:
V= Volume of titrant to reach end point in mL
C= Concentration of the titrant in eq/L (N)
MW= Molecular Weight of analyte to be measured in g/mol
SA= Sample amount in mL
UF= Unit factor to convert units from g/L to the preferred unit (for example this would be 1000 to convert from g/L to mg/L because there are 1000 mg/L in 1 g/L. It would be 0.1 for % by Volume because 10 g/L=10,000 mg/L= 1%)
X= the coefficient from the formula
Y= the coefficient from the formula
If MW, UF, X, and Y are all the same regardless of the other remaining variables and are specific to the test and the result unit, that only leaves SA, C, and V to be the remaining variables. C is determined by the titration cartridge used, and SA varies to give the different ranges. Then for each applicable C and SA combination the rest of the formula can be simplified to a single factor to convert V in mL to final result. Lastly add in the extra factor of 800 digits = 1 mL (see: How many digits on a digital titrator are equal to 1 mL of titrant dispensed?) for V to get digits multiplied by factor to get the result instead of mL by factor to get result, and what's left is the digit multiplier.