Dilution Conundrum - (Dec/17/2018 )

This should be simple but I'm just not figuring it out :/

Chemical X has a concentration of 2000 U/mL. Chemical Y has a fixed volume of 100 uL and cannot be increased or decreased in the final volume. I want a final solution with a concentration of 2 U/mL.

I naturally tend to think this could be solved by simply doing C1V1 = C2(V2 + V1), however I notice this equation will asymptotically approach infinity if your initial concentrations are similar, which means it's probably not a proper equation. So how do I figure out how much of Chemical X to add to Y to achieve my desired concentration, while taking into account the volume of X that's being introduced? Or might I be thinking of this the wrong way entirely?

If you do the calculation - you will need to add 1 ul of X to the solution to make 101 ul of final... yes, this makes an asymptote if you then go and work out the extra decimals. It'l probably end up as something like 101.11111111111...etc. It is very difficult to measure volumes below 0.5 ul consistently with ordinary lab equipment, so the margin of error comes into play.

Also I note the question is ambiguous - it could either be saying that you must have 100 ul of Y initially and not change this volume at all, or it could be that Y needs to be 100 ul as a final volume (i.e. 99 ul Y + 1 ul X).

or that 100 ul of the final volume is y