Dilution:

METHOD 1:

First, consider that the number of colonies on each plate indicates the number of bacterial cells that were in the final 0.1 mL aliquot that was spread on the plate.  Each of the three plates shown above were spread with the same volume of liquid (0.1 mL) from bottle 3 so we can average the number of colonies on the three plates:

90 + 106 + 98 = 294 colonies

294 / 3 = 98 colonies

Remember, this is also the average number of cells per 0.1 mL of fluid taken from bottle 3.  Thus the concentration (titer) of bottle 3 can be calculated:

98 cells / 0.1 mL = 980 cells/mL in bottle 3

In order to figure the titer of bottle 2, we must recall General Chemistry and the equation C₁V₁ = C₂V₂, where C₁ is the concentration of the more concentrated solution, V₁ is the volume taken out of that solution, C₂ is the concentration of the more dilute solution and V₂ is the final total volume of the more dilute solution.  Let’s manipulate this equation to apply to our current situation and allow us to calculate the concentration of bottle 2:

C_bottle2V_{removed from bottle2} = C_bottle3V_{final in bottle3}

C_bottle2 (11 mL) = 980 cells/mL (110 mL)

C_bottle2 = 9.8 X 10³ cells/mL

We can used this same equation to determine the titer in bottle 1 and finally in culture A:

C_bottle1V_{removed from bottle1} = C_bottle2V_{final in bottle2}

C_bottle1 (1 mL) = 9.8 X 10³ cells/mL (100 mL)

C_bottle1 = 9.8 X 10⁵ cells/mL

C_cultureAV_{removed from cultureA} = C_bottle1V_{final in bottle1}

C_cultureA (1 mL) = 9.8 X 10⁵ cells/mL (100 mL)

C_cultureA = 9.8 X 10⁷ cells/mL

Rachel Watson, M.S.
AG 5010
766-3524
Cell: 307-760-2942
rwatson@uwyo.edu