dilutions and ppm.... math exercise


Uploaded by mrphysh on 02.02.2011

Transcript:
A common mathematical calculation in laboratories is for dilutions
the formula is normality times volume equals normality times volume
this terminology relates to acid concentration but it could be anything
concentration times volume equals concentration times volume
the example I want use is ten microliters of 2000 parts per million
and we could call it ......
it doesn't matter ...let's call it benzene
we have 10 µL of 2000 parts per million benzene
and we add it to 500 µL and this will be in..a ,.....
methylene chloride or methanol or something like that
normality times volume equals normality times volume so
our original normality is 2000.... our volume is ten and
our ending normality is a variable so this is our variable
and our ending volume is the 500 plus the 10 or 510
so the normality.... you can quickly calculate this
and find that the normality is 39.2 ppm
if the analyst wanted 40 ppm
you have to run this as plus 490 instead of 500 and then that would make this a 500
and that would make this forty
my image of this is for an internal standard
and as an internal standard, you don't really care
what the concentration is and 500 µL
is a little easier to deal with than 490
Let's push this forward with just a little bit more detail
a microliter is a millionth of a liter and since there's 1000 mL it in a liter
and a thousand microliters in a milliliter so
thousand microliters in a milliliter and thousand milliliters in a liter
so there's 1 million microliters in a liter
a part per million is a milligram per liter is a part per million
a milligram per liter is a part per million
there's a million microliters in a liter
there is a million milligrams in a liter
you could look at this and say
"but a milligram is a measure of weight and a liter is a measure of volume"
but one of the definitions that we use... this been around a very long time
is that a cubic centimeter is equal to a milliliter and it weighs..... one gram
so, when we say that one part per million is a milligram per liter
there is an aspect of that as a definition
but there is also an aspect of that, that it is true and literally correct
the implication is that our liter is of water and in applications the liter usually is water
we're taking 10 µL of 2000 ppm, then and we're adding it to 500 µL
10 µL at 2000 ppm is how many milligrams?
okay, remember that parts per million is milligrams per liter
so that the concentration is 2000 milligrams per liter
we have 10 x 10-6 Liters
recall that a microliter is 10-6 liters... so, we have ten of them.
So it's 10 x10-6 ....and if we multiply this out ....the liters fall out
and we end up with 0.020 milligrams
and that is in 510 microliters
remember that parts per million is milligrams per liter
and the way I start this out is... I say
"how many 510s are there in one liter"
to find out how many 510 microliters there are in a liter we simply divide that into liters
the complication, of course, is that we got to make sure our units match
so we changed the 510 microliters to 5.1 x 10-4......
as you all know, the units all have to match
and we end up with 1960.
our 1960 times the milligrams in one of these (0.020) gives us 39.2 milligrams
I think the take-home lesson here might be "what is a part per million"
a part per million is 1 mg per liter
and the normality times volume
it's nailed into my mind as normality times volume
but it's just concentration times volume equals concentration times volume
and quickly note that it is all directly related
and that's it