Question

Consider an assay that involves a serial dilution as listed below. What is the total dilution factor for this assay?

• 0.5 mL of blood is pipetted into 1.0 mL of buffer.

• 0.05 mL of this sample is then pipetted into 1.0 mL of the assay solution.

please show work

Answer 1

Let, the concentration of the blood (initially) was y.

After first dilution (after adding to the buffer solution) if the concentration of the blood becomes S₁, we can write:

0.5 mL * y = (1+0.5)mL * S₁

or, S₁ = 0.5 y/1.5

After second dilution if the concentration of the blood becomes S₂, we can write:

0.05 mL * (0.5 y/1.5) = (1 + 0.05) mL * S₂

or, S₂ = (0.05 * 0.5 y/1.05 * 1.5)

Total dilution factor, f

= initial concentration/final concentration

= y / (0.05 * 0.5 y/1.05 * 1.5)

= (y * 1.05 * 1.5) / (0.05 * 0.5 y)

= 63