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Il each of these substances costs lhe Samc anount per kilogram. which substance would be lhe most cost ellective way [0 lower the freezing point of waler? Assune al...

Question

Il each of these substances costs lhe Samc anount per kilogram. which substance would be lhe most cost ellective way [0 lower the freezing point of waler? Assune all ionic COmpcxinds completely clissocialeKBrC6llnO NalCaCl} Calz

Il each of these substances costs lhe Samc anount per kilogram. which substance would be lhe most cost ellective way [0 lower the freezing point of waler? Assune all ionic COmpcxinds completely clissociale KBr C6llnO Nal CaCl} Calz



Answers

If each substance listed here costs the same amount per kilogram, which would be most cost-coffective as a way to lower the freezing point of water? (Assume complete dissociation for all ionic compounds.) Explain.
$$\begin{array}{ll}{\text { a. } \mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}} & {\text { b. NaCl }} & {\text { c. KCl }} \\ {\text { d. } \operatorname{MgCl}_{2}} & {\text { e. }}
{\text { e. } \operatorname{SrCl}_{2}}\end{array} \quad$$

Hello, everyone. The freezing point depression formula is change in temperature. It cause k f times, M times I, where K f is the freezing point. Constant M is the morality, and I is the number of iron Spare Graham. For this question, K, F and M would not be the business of comparison because the K f of water is the same. Regardless, off the compound on the morality is going to be the same for the question because, he said kilogram, So it's our business of comparison would be the I. So we're looking at the ion spread. Graham. The compound with the most items for grandma give the most freezing depression for the first compound. The first compound is a coup violence compound on Thursday would not give ions in solution. Does the eye for that compound will be zoo. The next compound is sodium chloride any CL, and it will give two ions in solution. The any plus iron on the C l minus iron. So the ions program will be two irons and one more off any CL is 58.44 g, so that's two divided by 58.44 g and that should give us 0.342 The next compound is K C L, which would also give two ions in solution in the K plus iron on the C L minus iron. Now, one more of K C. L is 74.55 grants who also do two irons divided by the grandpa move, which is 74.5 fire. And this should give us 0.268 The next compound is M. D. C. L two. I'm just saying how to would give three ions in solution the M d two plus iron on the c l minus iron, but the c l minus I honest truth. So that's his three islands in solution. The more llamas off NGC l is 95.21 g. So we having 23 divided by 95.21 g and thats 0.0 t 15 and the last compound is S R C l. So which would also give three islands institution the S r two plus iron on the two c l minus iron. So that's three ions in solutions. So we have three, divided by the molar Mass is 1 58 point 53 and I should give us 0.0 189 Looking at the numbers we have, the highest number is 0.342 and that came from sodium chloride. The sodium chloride would be the compound I'll give the most freezing depression.

If we wanted to see which one of these four different substances would be able to lower our freezing point while being the most cost effective, we have to consider the Vantaa factor and the molecular weight for each of these substances. Now, if you calculate the molecular weight for each one of these substances, do you wait for A is 62.7 grams? Come on. For any CEO, that molecular weight is 58.44 grams per mole. For a part, see that molecular weight is 74.55 grams per mole, and the wait for the last substance strong to record is 158.53 grams per mole. So right off about we concede that an A C L is the most cost effective. But we don't know yet if that is going to lower our freezing point as much as maybe some of these other ones are. So let's take a look at this Van Hoff factor. So if you remember, Van Hoff says, you know, you look at the number of particles over the number of formula units. That's what they call it. So in the case of a van hot factor is just going to stay one when it dis associates or this will not disassociate one mixed with water, right, which is what you know, You lower the freezing point so that will not disassociate. That will not increase the number of particles in the solution. So the vacant home factor for a is going to remain One now for B is we know this is going to equal to write it dis associates in splits into in a a quiz form and then a c l Iona's well, now number C That is going to be to a swell of a how factor it is split into a positive potassium on the negative chlorine. Now this strange in chloride, this one van how factor is going to be three because it'll split into strontium right with two plus charge, and then it will split into two negative chlorine arms. So now if we take a look at this, this has the same Van Hoff factor. But it's heavier than this n a c l. So if it's heavier than any Theo, that means that if we just buy one kilogram of all of these four substances were going to get less moles of this potassium chlorate. So if you get less moles of the potassium cord and it disassociates informs two different I owns just like any CEO that is lighter than this Patasse employed, then this will not be the most cost effective, right? So we can cross See out now if you take a look at a the same thing, right, 62 grams promote that's heavier than HCL. And with the Van Hoff factor of just one, you're not really getting a lot for your money, so we can cross a up. Now. It is just between B and E and N C O, which weighs a lot less than the strong tomb chloride. So again, if you think about it, if it weighs a lot less, you're going to get a lot more moles. And because you get a lot more moles and this splits into two different particles per mole, you add, you are going to get a lot more and a CEO with your one killer room that you bought. Then you will get of this strong team chloride. Now the sergeant chlorate has a higher Van Hoff factor. But because you won't get the same number of moles, it will not be as effective as lowering the freezing point of you know you're solvent because you do not have simply the same quantity that you will have if you use an A C O.

Problem. 133 asks if each of the following substances listed here across the same amount per kilogram which would be the most cost effective way to lower the freezing point of water. So if your call, um, the equation to calculate the freezing point of water is this when we're considering, um, Saul Utes that our electrolytes or salts that can break apart into, um its components or their component ions and water Um, so this being event ha factor which tells you how many, um, how many particles result from dissolving a given substance in water? This is the mill ality of the solution here. And then we have the freezing point constant for water. So in general, what we want thio maximize wth e freezing point Depression of water is we want to maximize the number of ions, um, and that go into solution from dissolving whichever saw you, which use thereby making wth e van Hoff factor as high as possible. And we also want the, um, lowest molecular weight possible well, providing the most ions because, um, less substance would be required per mole of a solution. So just tow to go through. Kind of how? Ah, how I thought about this problem. I'm going to say that each substance here across $10 per kilogram, which is probably a bit generous because chemicals from suppliers like Fisher and Sigmar little bit expensive. Um, and let's say we want a two degree decrease in the freezing point. So the delta t Africa too. Okay, so going through this, um, here we have a molecular weight, Uh, 62.678 grams per mole. And because this is a non ionic compound, it's it's an alcohol. Um, the number of ions air particles in solution. When adding us the sol, you would just be one. So I'll take you through the math for this. Ah, this one substance. But I did it basically same for each one. Um, where I converted, Um, basically one kilogram of each of these substances to the number of moles you could get from purchasing just one kilogram so we can convert one kilogram, two crams, um, and then we can multiply by the conversion factor for the molecular weight here, and that tells us that we get 16 of 160.11 moles out of one kilogram of, um, of this alcohol here. That's what that means is, um, if we want see gonna race this really fast, somebody on space If we want a freezing point change of two, we can plug that into this equation. You only get one particle from dissolving us in water you want to solve for the mill ality here and then are freezing point constant for water is 1.86 That gives a similarity of 1.8 Allow, um, to make that two degree temperature change happen. So then I just sort of went through my own little my own little math equation to figure out how many sense it, uh, it would cost for each reaction, considering this is how much, Um, this is how much substance we need. So they have 1.8 moral or moles per reaction. If we just assume that run one kilogram of solvent. We know that one kilogram gets us 16.11 molds, and we know that it's $10 per kilogram. So what that tells us is this particular substance cross about 67 cents per reaction so you can go through the same sort of logic for, um, for each of the substances provided, Um, and I'll just give you the molecular weights and the number of ions for each. It's unlikely we wait for sodium chloride or, uh, regular table. Salt is 58.44 grams, and it breaks into sodium and chloride if it dissolves our associates completely, which the problem suggests that it does. So that's two ions. You go through the same sort of math that I just did, uh, for the substance over here, that would be 31 cents per reaction. We have potassium chloride here, which has molecular weight, uh, 74.55 grams per mole and it breaks again into two ions if it associates completely. And so if I go through that math, Um, what? This gives us ISS 40 cents per reaction and then for de magnesium chloride is actually free ions. If it's associates completely one magnesium and two core, I'd ions sorry, and then its molecular weight is 95.21 grams purple. This one gives you 51 cents for reaction and then strontium chloride here again, we have three ions on a molecular weight of 158 0.63 grams per mole. And here we have 0.85 since reaction. So based on going through all of this math, sodium chloride here is the winner. It's a good balance between the most ions and solution. Um, while still having wth e lowest, um, molecular weight to really get mileage out of that one kilogram purchased.

The expression for the lowering and the freezing point we have delta T. F. Is equal to K. F. Multiplied by em that is the morality of the solid for em multiplied by I, which is about half factor, which indicates the number of particles per formula unit of solid. So with this fast part in part a what we have is negative not .186°C. With part B We got negative 9.372° C. With parts see We got negative, not .4464°C. And finally with part D. We get negative not .2232°C. Using the equation at the top here. And so then what we can do is order them in decreasing order of freezing point. Yeah, A. D. B. And see


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