Question

A volume of serum sample is diluted with equal amounts of buffer (1:1). Following this, a series of five dilutions is made of this first dilution by diluting it 1/10, rediluting 1/10, and then three times more, each resulting solution then being a 1/10 dilution of the previous one in the series. What is the concentration of serum in each solution made (6 in total)?

Answer 1

I'm assuming a percentage composition by volume (or volume percentage, % v/v) measurement.

Conc. of 1st sample = serum volume / total volume = [serum] / [one part serum + one part buffer] = 50%

Conc. of 2nd sample = concentration of [one part of 1st sample + nine parts of buffer] in total volume of ten parts

  = concentration of [two parts of 1st sample + 18 parts of buffer] in total volume of twenty parts

  = concentration of [one part serum + one part buffer + 18 parts of buffer] in total volume of twenty parts

  = serum volume of one part in buffer volume of nineteen parts = 1/20 = 5%

Continuing the same way, (or rather, by guessing the pattern,)

Con. of 3rd sample = 0.5%

Con. of 4th sample = 0.05%

Con. of 5th sample = 0.005%

Con. of 6th sample = 0.0005%