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A 1.32 -g sample of a mixture of cyclohexane $\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)$ and naphthalene $\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)$ is dissolved in $18.9 \mathrm{g}$ of benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right) .$ The freezing point of the solution is $2.2^{\circ} \mathrm{C} .$ Calculate the mass percent of the mixture. (See Table 12.2 for constants.)

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$32 \%$, $68 \%$

Chemistry 102

Chapter 12

Physical Properties of Solutions

Solutions

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Lectures

03:58

In chemistry, a solution is a homogeneous mixture composed of two or more substances. The term "solution" is also used to refer to the resultant mixture. The solution is usually a fluid. The particles of a solute are dispersed or dissolved in the solvent. The resulting solution is also called the solvent. The solvent is the continuous phase.

05:06

In physics and thermodynamics, the natural tendency of a system to change its state is its tendency to increase the entropy of the system. It is a measure of the disorder in a system.

03:29

A 1.32 -g sample of a mixt…

05:49

A 1.60 -g sample of a mixt…

A $1.60-\mathrm{g}$ sample…

01:31

Calculate the freezing poi…

01:41

01:29

The freezing point of cycl…

All right. So for dis question, um, we're given the depression in the freezing point, and we can find through the the number of malls that exists in that mixture. Okay? Having the number of malls we can find, ah, set of equations that will determine how much in mass exists of each component of NAFTA lean and the cycle taxing. Well, um, so let's start in. The first step is to look up some later. This is what I found. So the baby for benzene, it's 5.12 in the normal prison point is 5.5. Okay, She used different numbers. You might get slightly different answers, but the procedure should be the same. All right, So the question says that this solution the freezing point of this solution ISS 2.2 Demings that we had the depression. That is the difference between the normal and this that is 3.3 sells us. Okay? And we can actually compute that using this form one K b times, morality times, I now, in this case, we we don't need to worry about I because both components that we have there are hydrocarbons. So we have the cycle hack sane, and we have the naturally Okay, so they have this form us right here, all right. And, uh, their molecules, they will not go through any type of ionization in solution. So the I did the eye for both is one. Okay, so I'll just ignore the event Half factor in this question because of that. All right, so we have this delta T We also have the constant so we can find the morality right school down here. The moral ality will be equal. Delta t divided by K b. Okay. And that will be 3.3 Celsius, divided by 5.12 Celsius. Poorer. Um, morality came. So the result of this should be 0.64. Okay. And morality is actually we can expend that in expresses mole per kilogram. All right, so from there's, we can now figure out number of moles. Now, this number of Moses, the total normal ramos the number most nafta lean, plus the number of moles off cycle vaccine. So how do we do this? Well, if we have 60.64 mol per one kilogram off benzene, we just have to multiply by the amount of beings in that we have. So we have 18.9 Grimm's of Amazing. So all we need. Here's to apply a conversion factor. One kilogram for 1000 grams and checking the units here. We get mold in the end, and this is 0.1 to 2 moles. Okay, so that's Ah, this is both the cycle. Heck, sing in. The Naftali gave both. All right, with that, we can set up one equation. That is just what I just wrote. So number off malls off cyclo, hexane and see, I'm representing right this way. And you have the number of moles of left wing. If you add in together, you should get point. Oh, want to know? I'm just gonna omit the units now because you will get a be messy. All right, so this is the first equation. We have to find another one because we have two variables. One equation that doesn't work out on. Actually, we do because we have the math, right? So we know that the mass off the cycle hexane plus the mess Naftali, if you add them together, that's our simple So is 1.32 crimps. Okay, again, I'm just gonna remove the units first. Implicit in the sparked. All right, but we can improve this because those air different variables. Right? But we can connect mass to number of malls. Right? How do we compute? Uh, number of malls, remember, Number of malls is the mass. This is mass. Okay. Divided by the molar mass. Which is I'm representing. Buy em capital with the little bar. This is the former, right? So if we want mass, all we do is multiply and byd enormous. Okay. All right. So what's Let's do that? So instead of having this, I'm going to write, uh, number of months off cycle axing times the Moeller mice off cycle haixing plus number of most in NAFTA lean times. The more mess left, a lean has to equal 1.32 There we go. And actually, you do have the masses, right? I can write. I'm gonna substitute you can look up or calculate the molar mass. So for the cycle hex, And that is approximately 84 And see in in this for NAFTA, lean is approximately 1 to 8. Okay. Put number of moles nationally in the is equal. 132 So there you go. You have a second equation. So the rest of the question is just mathematics. Remember how to solve a system of equations you have here two equations, and you can, for instance, isolate one here and then plug in here. Workouts is a little algebra. I'm not gonna go through this. You have to do yourself, um, or you can, You know, if you re lazy. There are, um, um, options out there off calculators that can solve this type of problem. Of course, if you haven't exam, that would not be helpful. So once you saw that, there's mathematical problem. Um, I got that the number of malls off you only need to solve for one. Okay, So sorry for the hype cycle, Hex. And I got to the number of Moses approximately. 0.55 most okay, Demings that the mass which blighted by the Mormons, you should get something about 0.46 grams. Okay. Now, to find a percentage, we just compare this number right here with the original mass off the whole simple 1.3 to take this divided by this multiplied by 100% and you will find that this is approximately 35% for the cycle. Hex ain't okay for this. Tom Pun here cycle axing for NAFTA. Lean. Not feeling right here will be the rest. Right. So that's 65%. You don't need to compute because it has to add to 100%. All right, that's it.

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