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B) Using Raoult's law as the basis, derive an equation for the chemical potential of a liquid in an ideal solution...

Question

B) Using Raoult's law as the basis, derive an equation for the chemical potential of a liquid in an ideal solution

b) Using Raoult's law as the basis, derive an equation for the chemical potential of a liquid in an ideal solution



Answers

(a) What is an ideal solution? (b) The vapor pressure of pure water at $60^{\circ} \mathrm{C}$ is 149 torr. The vapor pressure of water over a solution at $60^{\circ} \mathrm{C}$ containing equal numbers of moles of water and ethylene glycol (a nonvolatile solute) is 67 torr. Is the solution ideal according to Raoult's law? Explain.

So this is Problem 39 Chapter 11. On the first question, A is asking us to write down the equation for the ideal Gasela. So the ideal gas law is the mathematical relationship among pressure volume temperature on the number of moles of the gas on it has the equation off P B equals and ah T where p iss pressure and it has units off atmospheres. B is volume, and it has units or Cletus on is the amount of moles and it has seen its a mole. Are is the ideal gas constant on the value that you're going to use in this book is 0.81 litres times atmospheres divided by mole times. Kelvin On the last is the temperature, which is always in the units off Calvin. So this is questioning. That's more want to question be on. It's asking us what is. The relationship is expressed in their ideal gas law. So from this equation, let me write this down again. You can see that pressure is directly proportional to temperature on the quantity of gas directly proportional means if the quantity off pressure will increase that temperature on the amount of malls will increase as well. Next, you can also see that pressure is inversely proportional to volume, and it means if you will increase the amount off pressure, the volume will decrease on the other way around so

Question 77 is a good question relating the parameters of a gas and how they are related to each other. Based on certain gas laws, the four parameters of a gas are its temperature, pressure volume and number of moles. In the case of the combined gas law, which is P one V one over t one equals P two V two over t to we need we would Onley use this if the moles of the gas are staying constant because moles air not part of the equation, we would use it if the moles of the gas or stay in constant. But the other variables are changing from one condition to another condition. In the case of the ideal gas law, we need to have moles stay constant and we need to know what the value of those moles are. This would be used if we knew three of the four variables and we were asked to solve for the fourth variable

As we know that the mole fraction of A. In the purpose is given by Why is equal to be in on multiplication X. A bye. We are not X A plus B. B. No acts and be which is equal to except by except for us. XB Maybe not by P. A. Not here. The value of P. N not is greater than B. B. Not. So I'll bring it further. I can right the expression at the V. A. But you actually He referred to one by except list XB. We be not by P. A. Not also I can write the expression is one is equal to Y is greater than Y. B. And let it be question # one. Similarly, similarly, the value of Y B is equal to be be not multiplication X. B. Bye being not XC. Yes B B no Xv which is equal to X B. By X B plus X. A. Maybe not by we're not. They did the question number two going forward, I can write the value live E. Y B is greater than the value of access B. So finally I can ride why by YB It's greater than X 80 X B. According to the given option. In this problem option C. It's correct siege. The depth of

So this question actually test our understanding on the vapor pressure of the mixture. So in a mixture yeah The partial pressure of the mixture actually equals two P. And actually equals to the more fraction of this And substance times it's actually it's vapor pressure. This is a partial pressure of the mixture. Mhm. So the question actually asked us about the solution right, what is a fraction more fraction of the liquid? A. In a solution? So here we can just set we can set the more fraction of A. In the solution in the solution. Yeah. Is actually X. Right again right down like this, it acts And then for B in the solution which simply be one -X. Because there are only two substance or liquid in the solution. And now we can use that right now we can calculate the partial pressure of the A. Is a mixture actually equals two. The more fraction and times the vapor pressure of the A. And the four B. We also know mhm equals two more fraction of the B. One minus X. Times the vapor pressure of the B. Yeah. And there's another important message in the question says the vapor has equivalent above the solution has the double. The more fraction of the substance A. That the solution does. So it says in the vapor face, the N. A minus M over MB. Right actually dartboard. The more fraction right actually, how can I stay here? Yeah. So it's doubled. So the double actually becomes like this, the more fraction of the N. A. Which equals to the N. A Plus MB. Which are in the vapor phase actually double the more fraction which equals to two X. This is uh what we get and how does that work? So from here now we can actually use the um we can actually kind of use the ideal gas law PV equals to NRT. Mhm. So then what we will know is the and a prime. We're simply equals two. The P. V. Which is A P. A. Over R. T. And same. And be prime also equals to the P. B. Be over Archie. And then we can just plug in this too into this aquarium. And what we get is so the video can regard as same since it's in the atmosphere. So what we can get is actually a P. A. Over the P. A. Plus PB Equals to the two X. So now we're going to do is the way combined this one, two and three together. So now let's just do a rearrangement. So here states p equals to two X. P. A plus PB. And the P. A. Here equals to the acts P A V. X. P A V. The plus the PB here is mhm. One minus X. P really be. Now we can try to do arrangement X. P. A V equals two two X square P A V plus two x -2 x square A P. B. B. Now that's just plugging the number. We don't know the acts And the PAV. 350. She 50 and two x square Times 350 And uh -2 x two at square PBB is just 100. So now what we do is now becoming 350 x Equals to 700 x square. The equals two two hundreds X. And miners 200 x squared. So it becomes 1 50 x Equals to around 500 x square. So either the x equals to zero. So because the or double there, so we can actually eliminate this one and then either another is x equals to 150 over 500. Which is yeah, around um Point sweetie. This is the answer. The answer is the more fraction is 30% and that's it.


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