Molarity, Molality, Volume & Mass Percent, Mole Fraction & Density - Solution Concentratio

In this video we will focus on the

concentratio

n of the

solution

, we will talk about things like

mass

percent

age,

volume

percent

age,

mole

fraction

,

molality

,

density

and

molarity

, so before we start working on these practice problems, let's write down some notes that needs. To be familiar with the difference between the solute and the solvent in this example problem we have sodium chloride dissolved in water which of these is the solute and which is the solvent the solute is what is dissolving in this case that would be salt or sodium chloride, the solvent is what dissolves, so sodium chloride dissolves in water, so water is the solvent, the solute dissolves in the solvent.

Now when you combine these two, you get the

solution

, so remember the solute plus the solvent. is equal to the solution now the next equation you want to write is

mass

percent mass percent is equal to the mass of the solute divided by the mass of the solution multiplied by 100 percent now

volume

percent which you can write as v percent is very similar is equal to the volume of the solute divided by the volume of the solution multiplied by 100 now let's talk about the next topic, which is the

mole

fraction

, the mole fraction of substance a is equal to the moles of that substance divided by the total of moles, so let's say if we had two substances, let's say a and b, so the mole fraction of b will be the moles of b divided by the total moles, which is the moles of a plus the moles of b.

Now let's see if we have three substances a b and c the mole fraction of, say, substance c will be the moles of substance c divided by the total number of moles, so that's n a plus nb plus nc, so those are the formulas you need to calculate the mole fraction, now next we have to talk about

molarity

and I want to distinguish this with

molality

, so let's spell it out. This is molarity with an r. The molarity represented by the capital m symbol is equal to the moles of the solute divided by the liters of solution, so they are moles. about the volume, but the volume has to be in liters, not milliliters.

Molality, this is with l instead of r. Molality is equal to moles of solute, but here's how it differs from molarity: it's moles of solute divided by kilograms, not solute. solution but the solvent, so you have to keep that distinction in mind, so both molarity and molality have moles of solute on top, but for molarity you divide it by the volume of the solution and for molality the you divide by the mass of the solvent is in liters and this is in kilograms. Now the next thing you need to know, which you already know, is

density

.

Density is equal to mass over volume, so in chemistry density is usually represented in units of grams per milliliter. or sometimes you will see it as grams per cubic centimeter so what you need to know is that one milliliter is equivalent to one cubic centimeter and also one liter is one thousand milliliters and one kilogram is equal to one thousand grams so those are the most common conversions that you will use when working with solutions

concentratio

n problems. Now we have everything we need to know for the problems we're going to work on in this video, so let's start with number one, 15 grams of sodium.

The chloride was dissolved in 225 grams of water, what is the mass percentage of sodium chloride in the solution? So mass percent is equal to the mass of the solute divided by the mass of the solution multiplied by 100 percent, so we need to identify the solute and the solvent. and the solution too, the solute is sodium chloride, so we have 15 grams of solute, what is the mass of the solution? We are given the mass of the solvent, not the mass of the solution, so remember that the solute plus the solvent make up the solution. so we have 15 grams of solute, we have 225 grams of solvent, so 15 plus 225 means we have 240 grams of solution, that's what we're going to put here at the bottom, so let's divide 15 by 240 and then multiply that result by one hundred percent so the answer for this problem is six point two five percent so that is the mass percentage of sodium chloride in the solution now let's move on to number two 25 milliliters of methanol is mixed with 150 milliliters of water what is the percentage by volume of methanol and what is the mass percent of water, so let's start with one part, a volume percent is equal to the volume of the solute divided by the volume of the solution.

Note that both methanol and water could behave as solvents; however, in this example we have a greater amount of water than methanol, so methanol will be the solute, water is the solvent, so we can say that methanol will dissolve in water and we are also looking for the volume percent of methanol, so based on this question, the way it's worded 'We're going to treat methanol as a solute, but in part b we're looking at the mass percent of water, so based on the way it's worded Once the question is worded, we're going to treat water as the solute for the second part because we don't want the mass percentage of methanol, we want the mass percentage of water, so sometimes the way the question is worded tells you what substance should you treat as a solute because if we had a larger amount of methanol, we could say that water dissolves into methanol.

So this problem is a little complicated, but on the other hand methanol is chosen as the solute, so we have 25 milliliters of solute. Don't forget to put 100 here and then the volume of the solution, the solution is the solute plus the solvent. We need to add 25 plus 150 and we have 175 milliliters of solution, so the volume percent will be 14, so that's the answer for part a. Now let's move on to part b, what is the mass percentage of water? So this is going to be the mass of the solute divided by the mass of the solution multiplied by 100, so we want the mass percentage of water, so we're going to treat water as a solute based on the question: Now we don't have the solute mass. or the mass of the solution, so we need to use density to help us.

Density is mass over volume, so if we multiply both sides by volume we get that mass is density times volume, so this is the formula we should use, but we are. We're going to use it with a conversion process, so let's start with the volume of methanol, so we have 25 milliliters and the chemical structure of methanol is ch3oh. Now the density of methanol is 0.792 grams per cubic centimeter and note that one cubic centimeter is the same thing. as a milliliter, so if the density is reported as 0.792 grams per cubic centimeter, it is the same as 0.792 grams per cubic milliliter, so I'm going to put a milliliter at the bottom so that the unit of milliliters cancels out 25 times 0.792 and that's 19.8. we start with 150 milliliters of water and if we multiply by the density of water which is one gram per milliliter we will get 150 grams of water now to get the mass of the solution we need to add the solute and the solvent together so In this case we will deal with the water as solute, but regardless of which way you add them, it will be the same 150 plus 19.8 is 169.8 grams of solution, so now let's go ahead and finish the problem to get the mass percentage. of water will be the mass of water, which is 150 grams divided by the total, which is 169.8 grams, which is the mass of the solution multiplied by 100 percent, so now it will be 88.3 percent if the problem I was going to ask for the mass percentage of methanol. so we would put 19.8 grams on top if they said what was just the mass percentage of the solution and didn't specify methanol or water, then you need to identify which will most likely be the solute because both methanol and water can dissolve things, so Generally the solute will be the one that is generally in the smallest amount.

We have much less methanol than water, so if you have to choose, I would choose methanol as the cell, the solute, but in this case we specify what it is. The solute was for each part of the problem, so be careful with questions like that. Number Three. Two moles of potassium chloride are dissolved in eight moles of water. What is the mole fraction of kcl? To calculate the mole fraction of kcl, it will be the moles of kcl divided by the total moles, which is the moles of kcl plus the moles of water, so it will be 2 moles divided by 2 plus 8, so 2 over 10 and 2 over 10 is 0.2, so that is the mole fraction of potassium chloride for this problem now let's move on to number four 25 grams of sodium fluoride are mixed with 200 grams of water what is the mole fraction of fluoride of sodium in the solution?

So we'll use the same formula and find the mole. fraction of sodium fluoride and therefore we need to calculate the moles of the same fluoride and the moles of water, so we need to convert grams to moles, so let's start with 25 grams of sodium fluoride, let's convert it to moles, so we need find a molar mass. of sodium fluoride, if we look at the periodic table, sodium is about 22.99 and fluorine is 19. So if you want to round it up to 23, you could say 23 plus 19, we're going to say about 42 grams per mole. that's the molar mass of sodium fluoride, so we have one mole of naf over 42 grams, so we can cross out the unit of grams of naf 25 divided by 42 is .5952 moles.

Now let's do the same thing with the water, so let's get started. with 200 grams of water and let's convert it to moles, so for water we have two hydrogen atoms, so it's two times 1.008 and then oxygen is 16. So you get 18.016 grams per mole, so it's going to be one mole of water per 18.016 grams of h2o so we're going to divide 200 by 18.016 and we're going to get 11.1 moles of water, so now we can plug everything into our original equation so it's 0.5952 over 0.5952 plus 11.1. You can put this in parentheses if you want To write it as you see it, the mole fraction that I got is point zero five one, so that's the mole fraction of sodium fluoride in this solution number five. 15 grams of sodium bromide are dissolved in 400 milliliters of solution, what is the molarity? of the solution, the molarity is equal to the moles of the solute divided by the liters of solution, so for this problem we can do a conversion process to obtain the answer.

Let's start with 15 grams of sodium bromide over one and convert it to atomic moles. The mass of sodium is approximately 23 and that of bromine is 79.9, so the molar mass of nabr will be 102.9 grams per mole. What this means is that one mole of sodium bromide has a mass of 102.9 grams, so we can cross out the grams of nabr. so now we have moles of the solute and we need to divide it by the liters of solution. Let's convert 400 milliliters to liters to convert milliliters to liters. You need to divide by a thousand. A liter is a thousand milliliters.

Then you can divide by a thousand. or move the decimal three units to the left in either case you will get 0.4 liters, so we need to divide the moles by liters, so I will write 1 over 0.4 liters of solution, so this will give us the molarity that we have. at the top there are liters of solution at the bottom so it will be 15 divided by 102.9 which will give us the moles of nabr and then we will divide that by 0.4 liters of solution so the answer for this problem is 0.364 m, so that is the molarity of solution number six. 10 grams of sodium hydroxide are dissolved in 500 grams of water.

What is the molality of the solution? The lowercase m molality is equal to the moles of the solute divided by the kilograms of the solvent, so let's use the conversion process to get our answer something like what we did in number five now we need to identify the solute and the solvent the solute is sodium hydroxide the solute is typically a salt and water for most of these problems will usually be the solvent now when we mix methanol and water It could be tricky to determine which is the solvent and which is the solute so you may have to look the relative amounts of the two or, if the problem specifies, you know which is the solute, as we saw, the problem could say what is the volume percent of water or what is the mass percent of naoh or what is the volume percent of methanol sometimes the problem will specify which is a solute or which should be treated as a solute, but for this particular problem the solute can be easily identified, usually it is some type of salt such as sodium chloride, sodium hydroxide, potassium iodide , which is usually the solute, if you were to make sodium chloride with methanol, methanol will be the solvent, methanol can dissolve a small amount of sodium chloride, so here are some examples of common solutes and solvents, so most of the solutes are salts like sodium chloride, potassium iodide, sodium hydroxide etc., these are typical solutes, water is a solvent, methanol is a solvent, ethanol which is another solvent, so that if you were to combine these two, it becomes clear that methanol is a solvent, but If you were to mix two solvents, then we need to be careful.

If the problem specifies what the volume percent of methanol is, then you want to treat methanol as a solute. If you specify what the mass percentage of water is, treat the water as a solute, if it's not specified then you have to look at the relative quantities, so if I dissolve it, let's say if you were to mix 10 milliliters of methanol with100 milliliters of water, I would treat it as the solvent, but now let's say that if I mixed 50 milliliters of methanol with 5 milliliters of ethanol, both are solvents, but in relation to each other I would select this one as the solvent because it exists in a much larger quantity than the ethanol, so I just want to clear that up for those of you who might be confused on that topic now let's go ahead and finish this problem, so we'll use the conversion process like we did in number five.

Let's start with the solute, so we have 10 grams of sodium hydroxide and let's convert that to moles for sodium. hydroxide, the molar mass will be 23 parana 16 for oxygen for hydrogen, you could use 1.008, but I'm going to use one because it gives us a nice round number of 40 for naoh, sometimes I have a habit of using 1.008 for h, but if you rounded to 40 your answer won't change much so we have one mole of sodium hydroxide for every 40 grams of naoh so we can cross out those units so now we have moles of solute all we have to do is divide by the kilograms of solvent so we have 500 grams of water, we need to convert it to kilograms, so let's convert it to convert from grams to kilograms, just divide by a thousand or move the decimal three units to the left, so 500 divided by a thousand is 0.5, so let's go. dividing moles of naoh by 0.5 kilograms of the solvent which is water, then moles over kilograms will give us the molality 10 divided by 40, that is 0.25 moles of naoh divided by 0.5 kilograms of water gives us a molality of 0 .5, so that is the molality of the solution now let's move on to some more difficult problems number seven the mass percentage of alcl3 in water is 15 the density of the solution is 1.17 grams per milliliter what is the molarity of the solution then what is the concentration of aluminum chloride in water so feel free to pause the video if you want to try this problem.

Now we are looking for molarity which means we need to find the moles of solute (the solute is aluminum chloride) and we also need to get the liters of solution to get For the moles of aluminum chloride we need the mass of aluminum chloride which is not we have and we do not have the volume of the solution. So how can we get these two things to calculate molarity? Well, let's go to the mass percentage that we know. That mass percentage is the mass of the solute divided by the mass of the solution multiplied by 100. The mass percentage can give us some numbers that we can use in this problem.

We have a solution of 15 by mass of aluminum chloride, so what that means is that out of 100 grams of solution there are 15 grams of aluminum chloride now what matters is not the individual number that we have here but the proportion is important because a solution of 15 to 15 could be 30 grams of aluminum chloride dissolved in 200 grams of solution and so we can have an infinite number of proportions, we can have 45 grams of aluminum chloride in 300 grams of solution, but to simplify things , I like to use 100 grams of solution because these two numbers are equal, so if I had, let's say a 30 percent solution I would have 30 grams of solute over 100 grams of solution, so if we select this number we have to use this number if We select 30 as grams of aluminum chloride we have to use 200 as long as the proportion is correct.

We're going to get the correct answer, so in this problem we could say that if we have 15 grams of aluminum chloride, then we have one hundred grams of solution, so now we could use this number to get the moles of aluminum chloride that we need now. to get the liters of solution, that's what we're missing, but we have the density of the solution, so let's start with 100 grams of solution and convert it to milliliters using the density, so one milliliter of solution has a mass of 1 .17 grams according to this value we can cancel the unit grams and then we can convert milliliters to liters, so there are one thousand milliliters per one liter of solution, so now we have the volume in liters, so it is one hundred divided by one point one seven divided by a thousand. and that is the zero point 0.8547 liters, so now that we have the volume of the solution we can calculate the molarity, so let's start with the mass of the solute which is 15 grams of aluminum chloride over one and let's convert it to moles, like this that we need the molar.

The mass of aluminum alcl3 has an atomic mass of 26.98 and chlorine. There are three of them, each of which has an atomic mass of 35.45. You can get those numbers using the periodic table, so it's going to be 133.33 grams per mole, which means one mole. of aluminum chloride has a mass of 133.33 grams, so we can cancel them out now that we have moles of solute at the top, all we have to do is put the liters of solution at the bottom, so that 15 divided times 133.33 is 0.1125 moles, divide it by 0.08547. and this will give you the molarity which is 1.316, this is how you can calculate the molarity of the solution if you are given the mass percentage of the solution and the density of it.