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The vapor pressure of ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ at $20^{\circ} \mathrm{C}$ is $44 \mathrm{mm} \mathrm{Hg},$ and the vapor pressure of methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ at the same temperature is $94 \mathrm{mmHg} . \mathrm{A}$ mixture of $30.0 \mathrm{g}$ of methanol and $45.0 \mathrm{g}$ of ethanol is prepared (and can be assumed to behave as an ideal solution). (a) Calculate the vapor pressure of methanol and ethanol above this solution at $20^{\circ} \mathrm{C} .$ (b) Calculate the mole fraction of methanol and ethanol in the vapor above this solution at $20^{\circ} \mathrm{C} .$ (c) Suggest a method for separating the two components of the solution.

$$0.672$$ and $$0.328$$

Chemistry 102

Chapter 12

Physical Properties of Solutions

Solutions

Carleton College

University of Maryland - University College

University of Toronto

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.

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in this question. We've been asked to determine the overpressure of methanol and ethanol contempt. So we've been given the vapor pressure 22-3 soldiers. And we've been given a certain amount of each of those substances at that temperature. So we've been asked to determine the vapor pressure of the amounts that we've been given this temperature. So all you have to do to take her mind the separation the same pressure of X. This is going to be equal to the more fraction of acts, multiplied by the favor pressure of X. Few of this just call this pure with the pressure of that sub. So what we can do here is to teach your mind the number of moles of each and then teach your mind more. Cause remember the mole fraction of I is the courtroom moles. I divided by total malls in that mixture. So let's first of all determine the number of moles of each of these substances but are making up that mixture. Remember number of moles is called mass of the substance divided by its Malema's. So if we are to look at martin off the number of moles of methanol are going to be equal to 30 g of methanol divided by 3. 2 Instead of four claims. Malls proclaims claims for more of Method which is the Mamas. So this is going to be equal from 7.936. Yeah. and then the number of moles of ethanol. This is the mass which is 45 divided by The molar mass of was 6.07. So this is going to be 7.977 models of ethanol. Now that we have these, we can get my mp total. Go to malls. Nt this is going to be equal to 7.93 C Plus 7.977. So the mole fraction of methanol is going to be equal to 4936 Divided by 0.936 plus 2.977. And the more fraction of ethanol. This is going to be equal to observe 1,936 0.977 divided by 4936 Plus 0.97 seven. So these are the more facts but we can also do here. This is a similar to one minus the mole fraction of maybe. So making this calculation, this gives us 0.4 89 and this gives us 7.511. Now that we have more fractions, we can then teach a mind the the preparations of these or the vapor pressure of Methanol. This is going to be 0.4 age nine Multiplied by 9 4 millimeters of mercury. And this gives us all six which is in millimeters of making it. Then moving on to ethanol. The favor pressure of ethanol is going to be 0.55, multiplied by 44. and this gives us 2, 2 and the units are also in millimeters of Thank you. No Moving on. If we are to assume a bogus behavior of these gases, what we can do is know that tv is equal to end team. That is the number of malls is equal to tv divided by our team. And the VT is the same for both. That is we are operating under the same conditions of pressure and temperature in the volume. So these are the same. So what we can do here to look into the number of moles of each substance, we can write this in terms of more from that is if we look at this, we have the same volume and separation and this is also constant. So number of moles is directly proportional to patient. So what we can do here is to look into the more fractions in terms of pressure. Remember the more fraction of methanol is equal to the number of moles of methanol divided by the number of moles of methanol plus the number of moles of get them. So since we have this expression here, this is going to be he of methanol divided by he of methanol plants that off ethanol and making this substitution here we have What? six divided by what six plus 22. So X. M. This is going to be equal to 0.68. And then moving on to X. G. I don't know this is going to be one minus X. M and this is one minus 0.68 and this gives us 0.32. Right now we are dealing with alcohol. So what we can do to separate these two is to use functional distillation, which depends on the difference in the boiling point of methanol. And yeah.

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