# Concentrations as Conversion Factors

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Concentration of solutions is used to distinguish between two solutions
that may have the same solute and solvent.
And concentrations can be used in calculations and can be converted
into conversion factors, which is what I'm going to show you today.
So, concentration is expressed as a percentage.
15% if it's a mass/mass concentration of sodium chloride
if you're going to take - if you're given that - percent in concentration
you can turn it into a fraction.
So any percentage is a fraction over 100 right?
So, 15 percent would mean that you have 15 out of 100.
Since it is mass/mass we understand that it's 15 grams of our solute sodium chloride,
in our 100 grams of whole solution.
If it was mass/volume it would still be the same numbers
15% so 15 over 100, but it would be grams of solute over 100 milliliters of solution. Okay?
For conversion factors it's just writing your relationship as a fraction.
So for conversion factors we can always turn a fraction into two different fractions.
We can have grams of solute on top and the grams of solution on the bottom.
But we can also flip it over,
and write the fraction upside down.
So we will always have two conversion factors for any fraction
that we can write. In terms of concentration - molarity - is also used
and it's the moles of solute per liter of solution.
So if you're given a concentration that is 3 molar
of potassium hydroxide
that means that you have 3 moles of your solute in every 1 liter of your whole solution.
Okay. This is not a fraction of 100 because it's not a percentage.
So it is the moles for every 1 liter.
Anytime you can write a fraction, we can flip it over and make a second fraction.
And this time we put the liters on top and the moles on the bottom.
So this is how we can take our concentration percentage and molarity
and turn them into fractions. It is the fractional form that we will use
when we're doing math problems when we're using those concentrations to convert
Okay, I have some examples up here that we're going to through so you can see how those
percentages, those concentrations, are converted into fractions and used in these problems.
The first one says: How many milliliters of a 35% NaOH solution
can be made with 75 grams of NaOH?
So, first step -
these are our numbers, okay?
Notice that the 35% since it's a percent it's a concentration.
If you see a concentration, if it's a percentage or a molarity, go ahead and
write it as a fraction because that's the way you're going to use it in the problem.
So 35% NaOH means that we have 35 grams NaOH
we'll assume that it's mass/mass - since uh -
sorry - mass/volume
there we go! So that's grams of NaOH
if it's mass/volume, for every 100 milliliters of the solution.
And we'll designate mass/volume here.
Okay, so our percentage I've written as a fraction
and just understand that you can flip it over and make two fractions
I'm just going to write 1 for now.
Then to start the problem you have to evaluate the two numbers that were given
in the problem. Never start with the number that you can write as a fraction.
The fraction is going to be your conversion factor that you're going to use
to convert one unit to another so you don't want to start with the fraction.
So if we don't start with the fraction that means we're going to start with our
75 grams of sodium hydroxide.
Basically we are trying to convert our grams of sodium hydroxide into milliliters of solution.
And we're going to use this fraction as our conversion factor to make that conversion.
Our units have to cancel out - whatever unit we're given
that unit - grams of NaoH - has to be on the bottom of our conversion factor
so with my fraction here, I'm going to have to flip it over
and put the 35 grams of NaOH on the bottom
and the 100 milliliters of solution on the top
So that my units will cancel out.
Now it's just a matter of doing the math so you get your calculator
And you have 75 divided by 35 times 100.
And I get 214.2857 and several other digits
again your answers to a math problem have to be expressed
in the correct number of significant figures.
We have two significant figures in the number given here,
two in this number, the 100 is considered exact so we don't count
significant figures for that.
So our answer can only have two so I'm going to round this to 210 milliliters of solution.
Okay. And that's how we used our percent concentration as a conversion factor to
convert from grams of sodium hydroxide to milliliters of the whole solution.
Likewise we can use molarity as a conversion factor as well.
In this question it states: How many grams of sulfuric acid
are in 150 milliliters of a 2 molar sulfuric acid solution? Okay?
So again, first step - evaluate your numbers. You have 150 milliliters of your solution,
the solution is 2 molar.
Can you write any of those numbers as a fraction? Yes.
Anything that's a concentration we're going to go ahead and write as a fraction.
So 2.0 molar H2SO4
means that you have 2 moles of H2SO4 in every 1 liter of your solution.
Alright? So, of your 2 numbers, you have to pick which one you're going to start
your math problem with.
Again, my rule is don't start with the fraction. So you're not going to start with
the 2 molar because we're going to use that as a conversion factor.
So I'm going to start with my 150 milliliters of solution.
150 milliliters of H2SO4, okay?
First step, I have to get rid of, or convert, my volume of H2SO4
to another unit. I'm not going to be able to go right to moles
or right to grams in one step, but I can use this information to convert it to moles.
So, I need to have milliliters on the bottom.
This fraction has liters in it. You can also convert that
then you could say 2 moles of H2SO4 in every 1000 milliliters of solution,
because a liter is equivalent to 1000 milliliters.
So I'm going to use it in this form
that cancels out my milliliters so my milliliters of my sulfuric acid cancel out
now I have moles of sulfuric acid -H2SO4.
I need grams so this is where you go the periodic table
you add up the molar mass: you add up two hydrogens, one sulfur, four oxygens -
and that should be 98 grams.
So for every 1 mole of H2SO4 it weighs 98.0 grams.
I had to put moles on the bottom so my moles cancel.
And that leaves me with grams of H2SO4.
So this is where you pull out your calculator again,
you have 150 milliliters
times 2 divided by 1000 times 98.
And I get 29.4 on my calculator.
So again, we need to look at significant figures.
We had 2 significant figures here, 2 here - that means our answer can only have 2.
So I'm going to round it to 29 grams H2SO4.
Alright, so this is an example of how you can use
your concentration of molarity as a conversion factor
to convert between volume of your solution and moles of your solution
and then, of course, we went one step further and converted our moles to grams
using the periodic table.
So these are examples of how you can use concentration as conversion factors in your math problems.
The first step, or the most important step, I would say
is picking out the concentration from the question and writing it as a fraction.
Do that first when you have a concentration in your question
and then you will use that as a conversion factor in the problem.
So doing more examples of these will improve your ability to complete these kinds of questions.
And I suggest lots of practice!