Calculating Diluted Solutions: Understanding Decimal Notation | Helpful Guide

[rovaniemi]

I have a doubt that I would like to solve with your help.

The 1st solution I have is

10 mg/10 ml
from the above solution 1/10th is diluted that should be (0.1)
from the above 1/10th diluted solution another 1/10 is diluted again
from this once again diluted 1/10th solution 1/5 is again diluted
once again from this 1/5th diluted solution 2.5/5 is again diluted.

My question is is there any formula to calculate the decimal point. I mean 1/10th is denoted as 0.1th, but how to note multiple diluted solutions? from 1/10 to 1/10 to 1/5 to 2.5/5

Thanking you all in advance for your time and replies.

 

[tiny-tim]

hi rovaniemi!

10 mg/10 ml
from the above solution 1/10th is diluted that should be (0.1)

i'm not sure what you mean

do you mean that 10 mg/10 ml is diluted to 1 mg/10 ml ?

or do you mean that 10 mg/10 ml is diluted to 9 mg/10 ml ?​

in the first case, the concentration is multiplied by 0.1

in the second case, the concentration is multiplied by 0.9

if you perform several dilutions, you multiply those factors

for example, if the concentration is multiplied once by a factor of 0.1 and once by a factor of 0.5, then the combined concentration is 0.1 times 0.5, = a factor of 0.05 ​

 

[rovaniemi]

Hi Tiny Tim,

Thanks for the reply. Just need to confirm what I understood it correct.

I have used the first case where 10mg/10ml is diluted to 1/10

Now it is 0.1.

If I dilute it again to 1/10 .

Then the solution is now 0.1 times 0.1 , so 0.01

Hope this is how it is?

Thank you

 

[tiny-tim]

I have used the first case where 10mg/10ml is diluted to 1/10

Now it is 0.1.

If I dilute it again to 1/10 .

Then the solution is now 0.1 times 0.1 , so 0.01

Hope this is how it is?

yup!

you just keep multiplying! ​

 

[DeeNos]

Greetings,

Thank you for bringing your doubt to my attention. The formula for calculating diluted solutions is C1V1=C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume. In this case, the initial concentration is 10 mg/10 ml, and the final concentration is 2.5 mg/5 ml. By plugging in these values into the formula, we can calculate the number of dilutions needed.

To make the calculations easier, we can convert the initial concentration to 1 mg/ml. This means that for each 1 ml of solution, there is 1 mg of the substance. Now, for the first dilution, we have 1 mg/ml and we want to end up with 0.5 mg/ml. By using the formula, we can calculate that we need to dilute the solution by a factor of 2 (C1V1=C2V2, 1 mg/ml x V1 = 0.5 mg/ml x 1 ml, V1 = 0.5 ml). This means that we need to add 0.5 ml of solvent (such as water) to 0.5 ml of the initial solution to get a final concentration of 0.5 mg/ml.

For the second dilution, we have 0.5 mg/ml and we want to end up with 0.2 mg/ml. By using the formula, we can calculate that we need to dilute the solution by a factor of 2.5 (C1V1=C2V2, 0.5 mg/ml x V1 = 0.2 mg/ml x 1 ml, V1 = 0.4 ml). This means that we need to add 0.4 ml of solvent to 0.4 ml of the previous diluted solution to get a final concentration of 0.2 mg/ml.

We can continue this process for each subsequent dilution, always using the final concentration as the initial concentration for the next dilution. As for the decimal notation, it is simply a way to represent fractions in a more compact and convenient form. Each time we dilute by a factor of 10, we move the decimal point one place to the left. For example, 1/10 is equivalent to 0.1, 1/100 is equivalent to