Learn about Advanced Placement Chemistry, Solutions 2, in this comprehensive video by bannanaiscool.
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Rob Lederer: Find the mass %, mole fraction and molality of an 11.9 M solution of HCL with a density of 1.38 gram per centimeter cube. This one is the hardest type of question you can be asked and if you get this one and get them all no kidding, so let's break down the information its got a 11.9 mol per liter HCL I mean moles of HCL per liters of solution and the density out that solution is 1.38 grams per cubic centimeter were is that coming just wait its coming up all you have to do break it down into the formula you know what you are looking for in terms of mass % mass of solute divide by mass of the total solution. So when you got that in your hand watch how it works you do cancellation all the way your mass % is going to equal now you got 11.9 moles of HCL and put it sure for HCL in moles of HCL times if I multiply the mole amounts of HCL and get the moles of HCL cancel left with your grams of HCL that's the mass of the solute but what's that mass of the solution. Well usually you know you got a liter of solution oh did you also know that there are over one thousand cubic centimeters in one liter that's just one cubic centimeters is what milliliter so If I've got one liter I've got a thousand milliliters or a thousand cubic centimeters, so there is your thousand cubic centimeters. Oh! and did you know the density of the solution 1.38 grams for every cubic centimeter then look at the you know the cancellation its beautiful and so one end you left with here grams of what this is grams of solution and so when you multiply all of this here by 100 you get yourself the answer and which is your 31.4 % HCL in the solution, now mole fraction okay. For the mole fraction the numerator is easy the denominator could look crazy but stay with me , so we is also 11.9 moles per liter okay so what's the Chi oh by the way that's Chi that's the symbol is Chi, which is mole fraction okay mole fraction mole solute so we don't most the solute this is 11.9 moles of HCL that's easy divided by the moles of solute plus the moles solvent that's moles of solution and now we cant just plug in the moles in the solution we know the volume of the solution in density other but we just cant plug in the moles we have to divide into moles of solute and moles of solvent here is the moles of the solute plus here is the moles of the solvent , here is not the explanation watch this. We have one liter of it correct this one liter of the solution okay we know that the thousand cubic centimeters are in one liter and so we've got a thousand cubic centimeters. When we multiply by the density again that will give us the mass of this solution. Now remember from the mass % question that 31.4% of it was HCL so that means that in 100 -31.4 that's the mass% of the water present, which is the solvent in HCL hydrochloric acid because they -- waters present. So 100 grams -31.4 is the 68.6 grams of water and that is grams of water grams of solution, grams of solution cancels the grams of solution there when we divide by the mole of mass of water we get the mass of water it looks complicated when we break it break it down and think about it you will be able to get the mole fraction of 0.185. You're always going to get a number for mole fraction less than one because the solute is always in lesser amount than the solvent so it's fraction out of one and which is the total its got to be less that one. Molality is moles of solute divided by kilograms of solvent here's the moles of solute the 11.9 moles now what is the kilograms of the solvent or the grams of the solvent first oaky lets go back we only got a liter of the solution cubic centimeters over liters one thousand of them that gives us the number of cubic centimeters of the solution and when we divide or multiply by 1.38 grams per cubic centimeter solution cubic centimeter cancel that the gram and done this couple of times already that's the grams in the solution. Isn't this again the % right here of the water. Well, its rea