in this video we're going to talk about how to calculate the molarity of the solution or the concentration of the solution so first you need the equation molarity is equal to the moles of solute divided by the liters of solution so it's moles divided by volume now you need to know what is meant by the term solute and solution so let's say if we dissolve salt and water individually the salt is the solute water is the solvent the solvent dissolves the solute and together the combination of the solute plus the solvent is the solution so keep that in mind so that'll help you to distinguish the solute from the solvent so now let's work on uh this example let's focus on part a point 25 moles of sodium chloride in 300 milliliters of solution what is the molarity of that solution so we're given everything that we need we have the moles of the solute sodium chloride dissolves in the solution and we have the volume of the solution however we need to convert it to the units liters and to convert milliliters to liters simply divide by a thousand one liter is equal to a thousand milliliters so 300 divided by a thousand it's point three another thing that you can do is move the decimal three units to the left so let's divide this by 0.3 liters and 0.25 divided by 0.3 that's about 0.83 so that's the concentration of the first solution in part a now let's move on to part b now keep this in mind molarity is moles of solute divided by liters of solution this will be helpful throughout parts b and c so for part b i'm going to do more of a conversion process let's start with 60 grams of sodium hydroxide now i need to get moles i want to have the unit moles on top and on the bottom the unit liters so let's convert grams to moles and we need to find the molar mass of sodium hydroxide to do that so we need to add up the atomic mass of sodium oxygen and hydrogen so sodium is about 22.99 oxygen is 16. hydrogen is 1.008 so this is 39 but for all practical purposes let's round it to 40. so we can say that one mole of sodium hydroxide has a mass of 40 grams so now we no longer have the unit grams of sodium hydroxide now all we need to do is take the moles and divided by the liters but we need to convert 250 milliliters to liters so if you take 250 and divide it by a thousand you'll get the volume in liters which is point 25 liters so notice that we have the unit moles on top and liters on the bottom whenever you have that your answer is the concentration in molarity so it's 60 divided by 40 and then take that result divided by 0.25 so the concentration is 6 molar or 6 moles per liter so that's the answer for part b part c let's find the molarity of the solution when 700 milligrams of potassium iodide is dissolved in 200 milliliters of solution so let's start with what we're given now we need to convert milligrams to grams and then grams to moles and then take the number of moles divided by the liters one gram is equal to a thousand milligrams and now we need the molar mass of ki the atomic mass of potassium is 39.1 and the atomic mass of iodine is 126 so the sum is 166 grams per mole so one mole of ki has a mass of 166 grams now the last thing we need to do is take the moles divided by the number of liters in the solution so 200 milliliters if you divide that by a thousand that's 0.2 liters and so that's going to give us the answer so it's 700 divided by a thousand divided by 166 divided by 0.2 so the concentration is 0.0211 so that's the molarity of the potassium iodide solution number two 50 milliliters of ethanol is dissolved by 400 milliliters of water what is the concentration of ethanol in the solution so which one is the solute and which one is the solvent the solute is dissolved by the solvent the solvent is water in this problem the solute is ethanol typically the solvent is usually and greater quantity than the solute we have a lot more water than ethanol so water dissolves ethanol in this case now in order to find the concentration we need to calculate the moles of the solute so we got to get the moles of ethanol and then divided by the liters of the solution now if you recall the solute plus the solvent combined makes up the solution so what is the volume of the solution we have 50 milliliters of solute 400 milliliters of solvent so therefore we have 450 milliliters of solution and if you divide that by a thousand that's 0.45 liters of solution so we're going to use that later so now we need to focus on finding the moles of the solute which in this case is ethanol so we have the volume and we have the density combined we can use that to get the grams of ethanol and then convert that into moles by the way here's the formula for ethanol c2h5oh so you can always look that up on the internet or something so let's start with the volume of ethanol we have 50 milliliters of ethanol and the density of ethanol is 0.79 grams per milliliter so now we have the mass of ethanol in grams so now we can convert that to moles but we got to find the molar mass so ethanol contains two carbon atoms six hydrogen atoms and one oxygen atom in a single molecule so this is two times 12.01 plus six times 1.008 plus 16. so this adds up to 46.068 grams per mole so that's the molar mass of ethanol so one mole is equal to 46.068 grams now the last thing we need to do once we have moles is to divide by the number of liters which we know it's 0.45 so once you have these two units moles divided by liters you now have the molarity of the solution so it's 50 times 0.79 divided by 46.068 and then take that result divided by 0.45 so the concentration is 1.905 so that's the molarity of the solution number three the concentration of aluminum sulfate is 0.3 moles per liter what is the concentration of the aluminum and sulfate ions well first let's write the chemical formula of aluminum sulfate aluminum is found in group 3a of the periodic table so it has a positive 3 charge and sulfate is one of those polyatomic ions that you should know by now it's so4 2 minus and so the chemical formula is going to be al2 so4 3 and the concentration is 0.30 moles per liter so based on that what is the concentration of the aluminum plus 3 cation so notice that we have a subscript of 2. so it turns out that to find it all you got to do is multiply the molarity by 2 so it's going to be 0.60 and in the case of sulfate there's three of them per formula unit so it's going to be .30 times three which is point ninety now for those of you who need to show your work here's what you can do the first thing you should do is write the dissolution of aluminum sulfate aluminum sulfate breaks down into two aluminum cations and three sulfate ions so you could say this is the solid phase and on the right the aqueous phase so i'm going to represent this as 0.3 moles of aluminum sulfate per liter because that's what it is molarity is moles per liter now we can use the molar ratio to convert from i'm going to use sulfate as an example so from aluminum sulfate to sulfate it's a one to three ratio so for every one mole of aluminum sulfate that dissolves three moles of sulfate ions are released into the solution so the unit moles of aluminum sulfate will cancel so now what you have left over is moles of sulfate per liter of solution so it's 0.3 times 3 and so this will give you 0.9 moles per liter which you could say that's 0.9 molar sulfate so that's the concentration of sulfate that's how you could show your work if you want to but the simplest way to get the answer is to take 0.3 and multiply by the subscript and that will give you 0.9 number four 15 grams of iron iii chloride is dissolved in 450 milliliters of solution what is the concentration of chloride so let's get the answer just completely using conversions and dimensional analysis let's start with 15 grams of fecl3 now in order to get the concentration we need to convert this into moles and at the same time we need to change the substance from fecl3 to cl minus so that's going to require an extra step but first let's calculate the molar mass of fecl3 so we have one iron atom and three chlorine atoms the atomic mass of fe is 55.85 and the atomic mass of cl is 35.45 so you should get a molar mass of 162.2 grams per mole so one mole of fecl3 has a mass of 162.2 grams so now let's change the substance from fecl3 to cl minus there's one chloride ion per formula unit of fecl3 so therefore we could say that one mole of fecl3 will release 3 moles of chloride ions in a solution it's a 1 to 3 ratio now that we have the moles of chloride ions all we need to do is divided by the liters of solution and that will give us the concentration of chloride so let's divide this by a thousand to convert it to liters so that's 0.45 liters so this is going to be 15 divided by 162.2 times 3 divided by 0.45 so the concentration of chloride in the solution is 0.617 moles per liter or capital m so that's the molarity of the solution of the chloride in the solution number five what mass of ammonium chloride is required to produce 250 milliliters of a 0.75 molar ammonium chloride solution so we're given the molarity and the volume how can we find a mass the best way is to convert it i'm going to start with the molarity of the solution so keep in mind capital m molarity you can represent it as moles per liter so a 0.75 molar solution means that we have 0.75 moles of ammonium chloride per liter of solution now we're not going to change the substance so we don't need to write nh4cl so i'm just going to write this .75 moles per liter now we have the volume of the solution 250 milliliters and if we divide that by a thousand that's 0.25 liters so you want to multiply the molarity by the volume because if you notice the unit liters will cancel and now we have the moles of ammonium chloride so all we got to do is change moles to grams and we can do that using the molar mass so in nh4cl we have one nitrogen atom four hydrogen atoms and a cl atom nitrogen is 14.01 h is 1.008 cl is 35.45 so the molar mass is 53.492 now because we have the unit moles on the top left we need to put the moles on the bottom so one mole of nh4cl has a mass of 43 point i mean 53.492 grams so this is going to be 0.75 times 0.25 times 53.492 so the answer that i got is 10.03 grams of nh4cl so if you're given the volume and the molarity and you want to find the mass you need to take the molarity and multiply it by the volume in liters and then multiply it by the molar mass of the substance that's going to give you the grams of the substance number six what a volume is required to dissolve 8.5 grams of potassium nitrate to produce a 0.15 molar potassium nitrate solution so this time we're given the mass of the solute the molarity of the solution and our goal is to find the volume we're going to find the volume first in liters and then we're going to convert it to milliliters so how should we begin now if we want to get leaders on top that means molarity has to be in the bottom we don't want to start with malaria because that's gonna be moles per liter however we need to flip it at some point because we want this unit to be on top just keep that in mind so let's start with the mass 8.5 grams of kno3 and here's the basic setup that i'm going to do i'm going to start with the grams and then using the molar mass of the substance this will give me the moles and using the molarity i'm going to get the liters on top which is what i want so that's just a blueprint of how i'm going to set up the conversion process and i don't like when the whole thing just disappears like that so we need to find the molar mass of kno3 potassium has an atomic mass of 39.1 n is 14.01 and o is 16. 3 times 16 that's 48 and 48 plus 14.01 that's 62.01 and then let's add 39.1 to that so this is 101.11 so there's 101.11 grams per 1 mole of substance now let's use the molarity of the solution so a point 15 molar solution means that there's point 15 moles of solute per one liter of solution in order to get the unit moles to cancel we need to flip this fraction so we're going to put the point 15 moles on the bottom and one liter on top so it's 8.5 divided by 101.11 and then take that result divided by 0.15 so it's 0.56 liters so that's the volume in liters and if you want to convert that to milliliters all you need to do is multiply by a thousand there's a thousand milliliters per liter so this is going to be about 560 milliliters you