Mathematical explanation of blank titration in Mohr method for argentometry

Question

In my book it is written that in order to minimize systematic error in Mohr method for argentometry it is a common procedure to conduct a blank titration with $ \mathrm{Ag^+} $ against a $\mathrm{CrO_{4}^{2-}}$ solution (with the same concentration of the original solution).

The book then suggests to subtract the $ \mathrm{Ag^+} $ volume needed to observe precipitation (in the blank solution) from the volume obtained as a result of the 'standard' titration.

I don't understand why I have to subtract that number, specifically I do understand that there is a systematic error but I don't get why it is the volume of $ \mathrm{Ag^+} $ obtained by the blank titration.

Answer 1

$\ce{AgCl}$ ppts before $\ce{Ag2CrO4}$. But in order to visually detect the $\ce{Ag2CrO4}$ you must add a slight excess of $\ce{Ag^+}$. Hence you use a "blank" with no $\ce{Cl^-}$ to account for the amount of $\ce{Ag^+}$ needed to get enough of the $\ce{Ag2CrO4}$ ppt to form so that it can be detected visually.