In a serial dilution, 0.1 mL of serum is added to 1.9 mL of saline in the first tube. The next tubes contain 1.5 mL of saline, and 0.5 mL from the previous tube is added to the next tube. How do we calculate dilution in the next tubes?

Question

In a serial dilution, 0.1 mL of serum is added to 1.9 mL of saline in the first tube. The next tubes contain 1.5 mL of saline, and  0.5 mL from the previous tube is added to the next tube. How do we calculate dilution in the next tubes?

HIX Tutor · Accepted Answer

undefined First, we need to calculate the dilution factor for each step:

Step 1: 0.1 mL serum + 1.9 mL saline = 2 mL total volume
Dilution factor = Total volume / Serum volume = 2 mL / 0.1 mL = 20

Step 2: 0.5 mL from the previous tube + 1.5 mL new saline = 2 mL total volume
Dilution factor = Total volume / Previous volume added = 2 mL / 0.5 mL = 4

Each step dilutes the serum further by the dilution factor calculated.

Naomi Aronson · Answer

Here's how you do it.

You can see the general method of calculating dilution factors in this Socratic answer. The general method for calculating serial dilutions is in this answer The general formula is for calculating a single dilution factor is #"DF" = V_f/V_i# Here you have two dilution factors, one for the first dilution and another for the other dilutions. First dilution : #V_f = "aliquot volume + diluent volume" = "(0.1 + 1.9) mL" = "2.0 mL"# #"DF"_1 = V_f/V_i = (2.0 cancel("mL"))/(0.1cancel("mL")) = 20# You have diluted the sample by a factor of 20. The dilution factor is often used as the denominator of a fraction. Thus, a #"DF"# of 20 means a 1:20 dilution. The other dilutions: #V_f = "(0.5 + 1.5) mL" = "2.0 mL"# #"DF"_2 = V_f/V_i = (2.0 cancel("mL"))/(0.5cancel("mL")) = 4# For each step, the dilution factor is 4 or 1:4. The Serial Dilutions The formula for serial dilutions is #"DF" = "DF"_1 × "DF"_2 ×"DF"_3 × …# We can generalize this formula as #"DF"_n = "DF"_1× ("DF"_2)^(n-1) = 20 ×4^(n-1)#, where #n# is the number of dilutions. Thus, #"DF"_1 = 20 × 4^(1-1) = 20 × 4^0 = 20 × 1 = 20# or #1:20#. #"DF"_2 = 20 × 4^(2-1) = 20 × 4^1 = 20 × 4 = 80# or #1:80#. #"DF"_3 = 20 × 4^(3-1) = 20 × 4^2 = 20 × 16 = 320# or #1:320#, etc.

Noah Aldrich · Answer

undefined In the next tubes, the dilution factor is calculated by dividing the volume of the previous tube by the total volume of the next tube. This accounts for the volume of serum added in the previous tube, which contributes to the overall dilution.