Thread: Dilution Calculation Problem Please Help!!!

Hello, I have been working in the science field for awhile now and I'm stumped by something :? . I'm sure there is a simple solution but I can't seem to figure it out

I have a 10 mL of a 0.5% solution and I want to make
an 0.8% solution by adding a volume of 20% solution to the .5% solution. What would this
volume be?

I can
easily calculate how to make 10mL of .8% from 20% stock but dont know how to
incorporate the .5% solution

I know the answer will be close to that given below but it is not accurate
because it does not account for the total volume.

20(stock)/.5(current) = 40(dilution factor)
10(mL total volume) / 40 Dilution factor = 0.25
Therefore add 0.250mL stock to (10mL total volume - 0.25 = ) 9.75mL diluent

AND

20(stock)/.8(desired) = 25 (dilution factor)
10(mL total volume) / 25 Dilution factor = 0.400
Therefore add 0.400mL stock to (10mL total volume - 0.400 = ) 9.6mL diluent

The difference between the amount used for a .5 and a .8 from the 20 is:
0.150mL (.400mL - .25mL) . Therefore, add 0.15mL of 20% stock to 10 (mL
total volume - .15 = ) 9.85mL 0.5% solution.

Thats pretty close but not correct as I want to add to the ten and if I am
removing .15mL from the 10mL, it wont contain the same amount of solute as
was in the full 10mL.

Your help would be most greatly appreciated if anyone knows that this formula would be!!!!!!!!!!!!!

Thanks!
Amb

It is an algebra problem. You see, concentration is the amount of something in the solution over the whole quantity and if these are concentrations by volume then it is the volume of the active liquid over the volme of the whole combined solution. So we have that,

.8% = (.5% of 10ml + 20% of quantity x)/(10ml + quantity x)

OR

.008 = ( .005 (10 ml) + .20 x ) / (10 ml + x)

Now you just need to solve for x. HINT: multiply both sides by (10ml +x).