Concentrations as Conversion Factors

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!