An adventurer has been bitten by a poisonous creature and has sought refuge in a shack. The adventurer is too weak to move from the shack and will die unless an anti-toxoid is administered. Luckily for the adventurer, the shack seems to be someone’s old abandoned home lab. One of the vials in the lab is precisely the quantity of anti-toxoid that the adventurer needs. Unfortunately, the anti-toxoid is dissolved together with a chemical preservative which the adventurer is highly allergic to. This preservative will kill the adventurer unless its levels are reduced by at least 150 times.
Besides 5 ml of anti-toxoid, the adventurer has also found reels of dialysis tubing and 25 ml of water. The adventurer thinks to himself: “I will arbitrarily divide the 25 ml of water into r portions and then use these portions to serially dialyze the anti-toxoid. If r is large enough, I will surely bring the lethal chemical preservative down by at least 150 times.” Is the adventurer correct?
Let us generalize with a starting sample volume Vs and a fixed dialysis buffer volume Vd with which to perform dialysis. If Vs is dialyzed against Vd, we get a dilution factor D where