okay well welcome to another MedCram comm board vitals question this one
comes from our nap Plex Bank which is targeted to pharmacists and the question
goes like this how many MLS of a one to four solution of drug X is required to
produce four liters of a one to 20 solution and that w /v there is stating
that it's a weight divided by volume solution and they want the answer in
numeric value only rounded to the nearest whole number
okay so there's a lot of things to unpack here let's talk about this one of
the things that we've got to tackle here is this thing about ratio versus
proportion and I don't want it to trip you up here because this is not going to
go along with pure mathematics in a pure mathematical situation a one to four
ratio would indicate that in the whole that there is one part that is mixed
with four parts and so therefore the actual part that we're looking at would
not be 25 percent but actually 20 percent of the whole
that's if we were doing things perfectly mathematically but that is actually not
the case we know that a 1/4 is something that we
can all understand because 1/4 is 0.25 and we can all understand that right we
have a quarter of it we have one part taken up in the 4 so what is that going
on here is that we've got a solute being dissolved in a solution and because of
that what science does at least when it comes to a pharmacology is it likes to
use this terminology of a 1 to 4 solution to actually refer to this so
don't get tripped up with this : here when they say 1 to 4 solution they put a
colon in there 1 to 4 they're actually referring to one part
by weight in four parts this is actually not 20% like we would do it in pure
mathematics it's actually a 25% solution okay so so another example would be a 1
to 20 okay I'm not going to go 1 divided by 21 to figure what that is it's
actually 1 divided by 20 which is going to be 5% okay so that's the first thing
that you want to make sure that you don't get tripped up on so let's revisit
this question again how many MLS of a solution specific
solution a 1 to 4 that would be a 25% solution of drug X is required in other
words is needed at the beginning to be diluted out to produce 4 liters of a
solution which is more dilute so in other words we're going from a 25%
solution down to a 5% solution weight divided by volume and so the question is
is how many MLS are we going to need to make that happen and of course what
you're doing here is you're simply adding water to the solution to take a
known amount of solute of particles and simply have them at a less concentration
and so what's not changing here and this is the key here what's not changing is
the actual solute I can add water to something all day but it's not going to
change the number of molecules of solute so because of that we can actually
create an equivalent expression and let's show you that so this is the
expression that rules all of this and that's c1v1 equals c2v2 now why does
this work concentration remember the units of
concentration is going to be something like milligrams per liter and if I'm
going to be multiplying that by a volume which is a liter
what's going to be left is I'm going to be left with milligrams and if we're
dealing with the same substance milligrams can be moles right if you
know the formula mass or the atomic mass depending on what you're dealing with
and so what you have here is the certain amount of milligrams of
solute is going to be equal to the same milligrams of solute on this side
because over here we have milligrams per liter times liters and so what can
happen is is that the actual concentrations can change and the
solutions that they are in but what will never change in this situation is the
amount of solute so let's take a look at this obviously if we have something with
a high concentration in a low volume we can add volume to that and what will
happen is the concentration will go down and that's precisely what we have in the
situation here let's read the question again
how many MLS so the question here is looking for how much volume so we're
looking for a V here how much volume of a one to four solution that's a twenty
five percent solution of drug X is required to produce four liters of a one
to twenty weight by volume solution so what you've got to do is you've got to
look here is required to produce what they're going to do is they're simply
going to add water to the volume that you already started off with to make
this one in 20 solution so let's go ahead and write down what this looks
like so we're starting out with a one to four solution so number one to four we
said can be written just like 1/4 and that's the C coming down here the V is
what we're looking for we're looking for how much volume is going to be necessary
and we'll put that right here and continue that as the variable now what
staying the same here is the solute what's going to change is the
concentration and the volume so what's the new concentration the new
concentration that they're looking for is a one to twenty solution but as we've
already said that can be written as
1/20 and the new volume that we're looking for is if we're going to put it
in terms of milliliters is 4,000 okay there's four thousand milliliters in
four liters so if we do the math what we get here is this is equal to 200 and
this over here on this side is V 1 over 4 if we multiply both sides by 4 we get
the final answer which is V 1 is equal to 800 MLS so if we plug that back in
here we'll see now the final equation will say if I take 800 MLS of a 1 to 4
solution I can simply add enough water until I reach 4,000 MLS in other words I
will be adding 3,200 MLS and when I reach that point of 4000 my new
concentration will be 1 to 20 so once again and the answer is 800 MLS well
thanks for joining us