[Eensas]

Could someone please help me understand the thought process to the following question? I am conflicted between a 1:8 or 1:16 dilution. Thanks in advance!

In a test tube, we add 1.5mL of saline to 0.5mL of serum. Then from this, we remove 0.5mL for the next tube (tube 2) and keep 0.5mL in tube 1. Into tube 2, we now add 1.5mL of buffer.

What is the final dilution of the serum in tube 2?

A. 1:75
B. 1:4
C. 1:8
D. 1:16

[Babcock_Hall]

Can you explain your reasoning?

[jeffmoonchop]

Your initial tube has 2ml before the next dilution, did you mean to say you took 0.5ml out leaving 1.5ml in? Anyway, I like to think of dilutions as percentages. Or decimals. The first dilution is 1 in 4, the serum is 25% the concentration because it is now 1 part serum in 3 parts saline. If it was 1M it is now 0.25M. Try and figure out the next dilution from that.

[Eensas]

Hi, I’m not sure about the leftover in tube one because this is the exact wording of the question I got on my assignment.

My thinking was that since tube 1 contained 0.5mL of serum with 1.5 mL of saline, that would make the solution volume 2mL. So since the solution is 1 part serum, 3 parts diluent, it’s a 1:4 dilution. So then the subsequent dilution would be doubled because 0.5mL of tube 1 is again diluted in the same ratio of diluent, making tube 2 a 1:8 dilution.  But a recent discussion with my friend made me doubt my process of thinking and now we’re both confused and aren’t sure what answer is correct.

[Borek]

Your line of thinking is OK.

[mjc123]

No it isn't. If it is diluted 1:4 in tube 1, then a portion is diluted 1:4 again in tube 2, the final dilution is 1/4 x 1/4 = 1/16. You multiply successive dilutions, don't add. (Well, if you added, it would be 1/4 + 1/4 = 1/2, which is obvious nonsense.) But what I mean is if you do the same dilution twice, you don't double the dilution, you square it.

(On a pedantic point, I would say that the dilution in the first tube is 1:3, not 1:4 - i.e. 1 part sample to 3 parts diluent. That makes 1 part sample to 4 parts total, so the sample concentration is reduced by a factor of 4, so we call it a fourfold dilution. But when I spoke of multiplying, it is this factor that must be multiplied, so the second dilution gives a 16-fold diluted solution (1:15). It is not 1:9 i.e. 10-fold!)

[Borek]

Ah, my bad, he said "same ratio again" which was correct but then added instead of multiplying, missed that.