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As the salt KNOz dissolves in methanol, the number z(t) of grams of the salt in _ solution after seconds satisfies the differential equation0.8r 0.Q01z'What th...

Question

As the salt KNOz dissolves in methanol, the number z(t) of grams of the salt in _ solution after seconds satisfies the differential equation0.8r 0.Q01z'What the MAximur arnount of the sult that will ever dissolve in the methanol? (b) If € 50 when how lcng ` will it take for an additional S0g of salt to dissolve?

As the salt KNOz dissolves in methanol, the number z(t) of grams of the salt in _ solution after seconds satisfies the differential equation 0.8r 0.Q01z' What the MAximur arnount of the sult that will ever dissolve in the methanol? (b) If € 50 when how lcng ` will it take for an additional S0g of salt to dissolve?



Answers

A soluble salt, $\mathrm{MX}_{2}$, is added to water in a beaker. The equation for the dissolving of the salt is: $$ \mathrm{MX}_{2}(s) \longrightarrow \mathrm{M}^{2+}(a q)+2 \mathrm{X}^{-}(a q) ; \quad \Delta H>0 $$ a) Immediately after the salt dissolves, is the solution warmer or colder? b) Indicate the direction of heat flow, in or out of the beaker, while the salt dissolves. c) After the salt dissolves and the water returns to room temperature, what is the value of $q$ for the system?

So when one substance dissolves into another, a solution is fond and so a solution is a homogeneous mixture made up of a solid dissolved into a solvent. So firstly, what we need to do here is determine the moles of solute. Using the definition for polarity and then using the molar mass, we can calculate the mass. So much clarity is equal to the number of moles divided by the mass of solvent. That's what we do is take not point not 50 moles per kilogram, Multiplied by 500 grounds, Multiplied by one kg divided by 1000 g. We got 9.9- five moles. So now we can determine the mass of methanol. Using the molar mass of methanol, We simply take the moles, multiplied by 32.0416 g per mole. We got 9.80 g. So therefore we need 9.80 g of methanol to dissolve in 500 g of water. To make a 9.950 miles per kilogram. A queer solution of methanol

Hello Today we'll be talking about Chapter 14 Question 34 which requires us to make a zero 0.5 Moeller solution of ammonium N H four c l ammonium chloride, and we want to make 2.5 liters of it. And so we need to know how much ammonium chloride we need Ingrams And so to start, let's just think about what the units of polarity are. Polarity. Big M has three units of moles of Saul. You'd over leaders of solution the volume of this solution and that's the total volume of the solution. So if we have 0.5 Moeller ammonium chloride, that's the same as having 0.5 moles and h for C l ammonium chloride. They were making licorice or something, and that's in one leader of solution. And so if we just multiply this number by the volume of the solution that we have, we confined how many total moles are in that solution, and then get the mass most wise by 2.5 leaders, our leaders will cancel out and we'll be left with one 0.25 moles of ammonium chloride. And so if we then no, the molecular weight of ammonium chloride. We confined them ass pretty easily. The molecular weight of ammonium chloride can be found on by adding up the constituent parts from the periodic table. And, sir, if we add nitrogen for Hydra Jin's and a chlorine, we can get the molecular weight as being 53 0.491 grams per mole. So if we take our 1.25 moles of ammonium chloride times 53.491 grams, her mole ammonium chloride are moles will cancel and we'll be less with grams of ammonium chloride. So are correct units. And what we get out is 66 0.86 grams. And we have to condense this because we have a limited number of significant figures. So since we only have 0.5 Moeller to go off of, we have to condense our units two seven times 10 to the first grams of ammonium chlorate. So hopefully this makes you a little bit more comfortable with the concept of using polarities to calculate amounts of compounds in solution. Thank you

Okay, so we know that the rate of change is equal to the input rate minus the output rate. So therefore we can write t x of T d. T is equal to 0.3 k G's per minute kg per minute, minus 0.12 times except T kg per minute. So now we have DX of tea is equal to zero point. We can actually rewrite this to make our lives easier. The except E plus 0.12 times X is equal to 0.3. So this is a linear equation so therefore has an integrated factor Where pft you can write p off T is equal to 0.12 on we can if we take the integral of both sides of the integral of peer to use equal to 0.12 t so we can write New of T is equal to eat the power of the integral off P of tea which is equal to eat the power of zero point toward to t eso multiplying this'd equation here by U of t. We end up with the derivative derivative with respect ity of eat the power of 0.12 tee times Acts is equal to 0.3 e to the power of 0.12 t integrating both sides with respect to t, we end up with E to the power of zero point. Want your tea? Times X is equal to 2.5. Retake the integral of this integral. This this ends up being 2.5 e to the power of 0.12 t plus, of course, see dividing both sides by E to the power of 0.1 TV we end up with Except T is equal to 2.5 plus C e to the power of negative 0.12 t. Applying the initial condition of acts of zero is equal to Europe, where five Thio we can end up with C is equal to native to So therefore, we can write our final answer as X if t is equal to 2.5 minus two e to the power of negative 0.12 teeth

So this question wants us to calculate their um uh they're tfl operation off meth. No giving that. Methanol evaporates. Hearts five degrees Celsius. So meth, no C three h h. And now we have really good state going T o Guess your state re absolutely history. Whole age gas. Okay, so we need to calculate the delta g of the reaction. And, you know, the data g stand at a reaction. Wouldn't be questions. So mission. And which is the number of mole off cronuts? Much applied by the gotcha G off information off products. But that's its products. Minus So, Misha, hand number of mole of reactors wanted by by death case than that Off formation. Hot reactor. Okay, so in this case, our product is the methanol gas. So we have one more locates, but that's more. One more if it's multiplied by the delta G. A permission off methanol gas and the G A formation of methanol gases. My nose wants 62 points. Uh, three kill Jos. Sure Look, too. So mission son. Yeah, and, uh, mine us. The reactant in this case is methanol down. We have warm alof. It multiplied by data. Jia formation of methanol. Equated minus wants its two steaks, boys. Uh, six, just more. This is a secure. Just one more. So this would give us what's it's to give us, uh, 4.3 here. They're yours. And that is the key reaction. So we have a hospital to calculate the doubt G hot, various nonstandard conditions. The first no stand. That condition is when we have the pasha pressure hopeful methanol. TB wants to 1 51 0 millimeters off Nick. Yuri. So how do we go about this? We need to understand that the, uh, Dr G off reaction on the delta Just under four. Reaction our religion by the expression Dr G. Reaction is a question, Dr G. Stand Dad off Reaction lost. Hearty link. You okay? We have Q. It was a partial pressure. Methanol gas. I guess. In this case now, no Indians, we can go ahead and, uh, on the calculation on the difference. No. Stand that conditions. So the first no standard condition. Is there p pressure pressure off 1 50 millimeters mercury so down we can calculate its cue. Thank you. Would then be wa skewed. Um, Another pressure of water to make until make you're so cute. Demi across to want you TV, Let me tell. Make Yuri. You got it by the hot, most very pressure with your cell in 60 minutes. Make Yuri and this would give us provided by several 60 this week. It was at a 600.91 night 74 Andi. If we know that, then we can put that into these equations. Since we know how we no see to be 25 degrees Celsius with Ruby 2 98.15 Calvin's, we know us. What General can stay there to g Reaction Noticing gf reaction. It's a question that's understand that for the reaction we calculate sets to before 0.3 villagers. So this is the 4.3 killed Joe's Woz harm these big ass constant and that is each 0.314 Yeah, it's 1314 The unit is Jules for Calvin, but since we had dinner with killer jersey, it's wise that we just come. That's that's to Cuba just by much of my my terrace, Part three minus three. Now give us given deals with Calvin much applied by temperature, which is 25 degree. So she is if you come by, That's a careful. You must unite to hate my one like Calvin. Uh, multiply by link you a queue here. He still went. One nice 74 So natural law greedy, negative value. What's applied that by June they hate won't lie. And what you find out by 8.3 Wonderful time stairs by minus three. So we will have Ah, that's gene reaction will be across the 4.3 kilos. Jos minus four Points out. You Ah! What is there? A two kilo jos? And now leave us zero fines. Jew 78 little 0.27 h um, just make it. Okay. That point too. This is a 0.27 to 8. She goes Okay, so, um, the next condition is, uh, When, uh he is, um one p is unready. Minimum, make Ewing. Please 100 wriggling. It's on the curing, dear. Full here. He wants to 100,000,000. Make Yumi by 7 60 Maybe I'm a cure. And that would be 102 by 7 16 Delevingne's 0.13 Cheers. Okay, Now Delta Jiri out. You know you'd be 4.3 Cure Jos Waas. Each 0.314 times stands by my history just for Calvin. What's a live likes you? 98.15 Caroline Lane zero much want to reach you, what with this? Give us. So this would give us my nose. Little 0.7 to 4 here does. And the next condition is when p methanol. Uh uh damn points. You don't know that it's something Curie so doubtful you be waas Thio implies there on the neck, Yuri divided by cell 16 minutes. Make Yuri and down. He bust tend to grab a cell. 60. These little planes, you know, 13 Thio Andi way Can't go ahead and, uh, said that Dr. G Reaction was It was the 4.3 killed Gilles minus 8.314 Time stands for minus three. Give Joe spot. Calvin much fly bites. United hate point won't buy Lian 0.13 Chu Then they should give us once should plus yeah, so this should give us minus 6.44 Kill a judge. Okay, so they evaporate in open air 25 decreased Alice years. So as we can see the pasha pressure for methanol this low? Um, yeah. The partial pressure from that annoys, you know, whenever the partial pressure for meth annoys No, I hear the dirty value on the negative value since the, uh, in Q is GTO. So whatever. You gotta do bodies negative. Like, you know, previously we know that's, uh the reaction is spontaneous. We never doubted you use negative. So negative Doubting too, whenever I see a license. You Yeah. Want Timmy s reaction? So that happens whenever the pressure. Now that the predicated the pasha fridge of mechanized milk whenever I doubt he's negative, you have a spontaneous reaction. And that's a stuffed paladin of Kali. Uh, the agreeable peaceable.


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