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4. (20): We have solid steel containing Ti and €. Ti and € can easily make stable compound called TiC which can im- prove the strength of steel.When pur...

Question

4. (20): We have solid steel containing Ti and €. Ti and € can easily make stable compound called TiC which can im- prove the strength of steel.When pure Fe is in equilibrium with pure € at [2000C. the equilibrium C content in solid Fe is 0.036 mole fraction. Assume that C shows the Henrian behavior in solid Fe until this solubility When Fe is equilibrated with 50% CO and 50% CO: mixture at 12009C, the solubility of € in solid Fe is 2.0E-05 mole fraction (iii) Ti(s) + C(s) TiC(s): AG&#x

4. (20): We have solid steel containing Ti and €. Ti and € can easily make stable compound called TiC which can im- prove the strength of steel. When pure Fe is in equilibrium with pure € at [2000C. the equilibrium C content in solid Fe is 0.036 mole fraction. Assume that C shows the Henrian behavior in solid Fe until this solubility When Fe is equilibrated with 50% CO and 50% CO: mixture at 12009C, the solubility of € in solid Fe is 2.0E-05 mole fraction (iii) Ti(s) + C(s) TiC(s): AG' = -164262.3 Jmol at 1200PC The Henrian activity coefficient of Ti(s) in solid Fe 5.1789E-02 Calculate what is the composition of gas mixture of CO and COz to achieve this C content (in above question) As- sume no oxidation reaction occurs_ When Ti solubility in Fe is 0.001 mole fraction; what is the minimum content to form TiC phase in solid Fe at 1200"C 249 #



Answers

A $1.362 \mathrm{~g}$ sample of an iron ore that contained $\mathrm{Fe}_{3} \mathrm{O}_{4}$ was dissolved in acid and all of the iron was reduced to $\mathrm{Fe}^{2+} .$ The solution was then acidified with $\mathrm{H}_{2} \mathrm{SO}_{4}$ and titrated with $39.42 \mathrm{~mL}$ of $0.0281 \mathrm{M} \mathrm{KMnO}_{4}$, which oxidized the iron to $\mathrm{Fe}^{3+}$. The net ionic equation for the reaction is $5 \mathrm{Fe}^{2+}+\mathrm{MnO}_{4}^{-}+8 \mathrm{H}^{+} \longrightarrow 5 \mathrm{Fe}^{3+}+\mathrm{Mn}^{2+}+4 \mathrm{H}_{2} \mathrm{O}$ (a) What was the percentage by mass of iron in the ore? (b) What was the percentage by mass of $\mathrm{Fe}_{3} \mathrm{O}_{4}$ in the ore?

So this is the given reaction. For the first part, we need to find expression for the thermodynamic equilibrium Constant. So it'll be K is equal stools. He no products that 53 or four Onda It's too the bar for because it has before over here and divided by the extend that his f e for the bar three hi ale has tools to the power four Just the girl Stop Pay off to Gazprom, the bar for to the field Still four have to the power but we don't have anything so can't be I am for the be part we need to explain why the partial pressure off which too is independent or the mount off Half e And if it was three present Mm, So, uh, Sueno be no FC Is it close to one and peace p off effort towards trees. It's, uh, sorry. There will be if he three or four is it in one So cake and written as one in tow. The off a stool which took gas to the bar four divided by Did they really no one on the B next door to depart for and the partial pressure off the hydrogen is independent, Damonte off if he and if three or four present. And for the sleep part. Yeah, it's a yes, because the production off each to NH two or could be accomplished regardless of those Proposition's off A P and A three or four. Because, uh, because the benefit three or four are in solid phase, where the students tools are in gashes faced as solid fell does not show appreciable change during the equilibrium version. It is independent off F E N f e two or four.

Yeah. Okay, so this is a equilibrium question. So the equation chemical equation are given here, which is iron oxide act with hydrogen to produce the iron metal and water vapor. It also gives the entropy of this reaction. As we can see, the entropy is positive. So it's a and or systemic reaction direction will be accompanied by absorbing the heat. So the first question is right. The expression for the equitable constant. So we can work on that. The equation constant in this problem is equal to the concentration of the water vapor Power three over the concentration of the hydrogen gas power three. We don't have to involve iron or iron oxide because they are all solids. So for the solids we usually regard them as one in the equivalent constant expressions. So now we can move to the same question, What will happen to the concentration of each reactant and product equipment If more iron is added? So we can first because when we determine whether react the reaction move forward or backwards, we compare the reaction cogent with the queen constant. So again first right down the expression of the reaction cogent, which is actually saying as a queen constant. But this time the concentration is at any time any case not in the equipment. So you'll find the reaction cogent actually has not seen to do with iron because iron is solid. Which means by changing the mass of the island, we're not influenced change influence the direction Colton's. So the Q. C. Well remain constant and it will be still equals to the K. C. Their reaction equipment constant. In this case the requirement will not chance. So the concentration of the hydrogen and water will remain the same will be the same. It does not change. So now looking at the question, see what if what will happen to the concentration of each reactant and product a queen. But if water is removed, so them right on again, the cartoons of this reaction. So in the initial case we know the Q. C. Equal to the K. C. Right So it's in equipment state. But once it says we remove the water which means the concentration of the water were actually goes down. So instantly the newly uh uh reaction cogent well goes on. And this case it will be smaller than the K. C. Which means in this case through action would actually move right. Words move forwards. So in this case the hydrogen will be consumed. So the hydrogen concentration will be reduced and you are mainly remove the water. So definitely the water. The concentration of the water would be also removed. And now we can go to the question, what will happen to the concentration of each reactant and product equivalent brim? Ive hydrogen gas is added so we can treat it similar with the question. See we write down the reaction Collins expression again. Okay, and if we you see if we increase the month of the hydrogen, then the newly reaction cogent which actually goes down and initially it's equal to K. C. But after you remove the hydrogen actually would be smaller than the reaction um the queen constant and in this case it will be same through action will move forward, which means the water will increase and you are deliberately manly increase the concentration of hydrogen. So definitely hydrogen concentration of hydrogen will also increase. So now the question is what will happen to the concentration of each reactant and product at queen bee? Um If the volume of the reaction vessel is decreased. So this case you have considered the volume right? Yeah. So when you think about volume, you have to say the value change before and after the reaction you will find for the gas finish here, the reaction has three more molecules which is three more is hydrogen and also for the product that's also three more the um water. So which means for the reaction volume does not change, which means the value we have no influence on the equilibrium. So in this case the volume will not change the queue. He remains the same and the concentration of hydrogen and water does not change. And finally, yeah, is what will happen to the concentration of each reactant and product is the temperature of system is increased when you increase the temperature. So remember in the book, why says you can actually regard the heat as a reaction or product based on whether it's endoscopic or exhaust summit. So you see the delta H entropy is positive. So it's and atomic reaction, which means actually will absorb heat during the reaction. So we can add heat in the reaction site. In this case when you increase the temperature, which means to increase the concentration in the heat so definitely the reaction will move right. Words move forwards. In this case the reactant hydrogen would be consumed so the concentration will go down and the product award as water will be generated so the concentration will go up and this is the answer for the whole question.

Good question says that pure iron metal could be produced by the reaction of iron three oxide with hydrogen gas and part ay asks us. Right? The expression for the equilibrium. Constant Casey for the reversible reaction. Never had that reaction here. Effie. Two of three trioxide with each to gas forms, iron solid and gashes water. So the equilibrium constant For this reaction, it's going to be the concentration of products over reacting ts. And for these problems we exclude Pierre solids in pure liquids. And so we're going to exclude iron. But water in this case is a gas, not pure liquid. It's not a solvent, so it is going to be in this if you see H two a liquid, usually a solvent, and you excluded but in this case is included. So H 20 That's cubed because of this three here and same thing for the reactant ce iron three oxide is a solid pierce. Also, it's excluded, but hydrogen gas is included, and it is also cute. So then this is now the equilibrium constant equation, and so now we know any time for the remaining parts. If it tells us we're going to change the amounts of the solids. Those aren't even included in the equal react equilibrium, constant equation. So any changes to solids will have no effect on equilibrium so that we know that. So let's go through each of these and see what happens when we start perturbing the system, he says. What will happen to the concentration of the rackets and products if more F G is added? Like we said, this is a solid. It's not even included in the equilibrium constant. Therefore, no change here, right and see ceases What will happen if each to it was removed. If we remove H 20 we're gonna shift this reaction to the right. Therefore then after we remove, it will get more H 20 and less each too, he says. What will happen if each to has added again? This will also shifted to the right so we will have more h 20 and last age too. And this is what will happen if the pressure on the system is increased by reducing the volume and how you determine this is whether or not one side of the reaction has fewer moles of gas on the other side. Both of these have three most of gas on either side, so changing volumes and pressures will have no effect on the system. If one side had fewer moles of gas, increasing pressure shifts towards the side with fewer miles of gas. That's not the case here. Finally, F says, what will happen if the temperature on the system's increased? It tells us that Delta H is 98.7 Killer Jules, this is a positive number, meaning that he is required for this reaction. You can think of the heat as a reactant so you can put it on the left side here. So if you increase heat, it's like increasing the amount of reactive. So we're gonna shift this to the right as well. That will give us more H 20 and bless each, too.

To solve this problem will use the density off C six a 14 to find the mask and the most off C six a 14 in volatile. This is the majority off C six F 14, which is then used to find the majority off oxygen. Our auto, from its small traction, will then use Henry's law that could be used to find K H R Henry's Law constant in Bobby. Using Henry's law, we'll find a celebrity off accident and that given temperature, let's first assume one letter off pal through Rohack scene, which is C 6 14. Mama's off off. This is 3 38 grounds for more density. Given as 1.674 g per Emily, the density is equal to mass. Divided by volume, we can calculate the mass using the density and volume. So the moles in one letter off part floor Oh heck sane will be 4.95 moles per liter to find out the moles off oxygen dissolved in one litter per floor. Oh Hussain, more affection off oxygen is 4.28 multiplied by 10 part minus three at 2 98 K and 1013 to 5. Paschal. Our one atmosphere Poor flora Taxin is articulate brain with the oxygen and more fraction off oxygen is already given as reject above therefore, articulate blame. The number off World's off oxygen dissolved in a little off C six at 14 will be 4.28 multiplied by 10. Power Ministry is equal to moles off boxes. Um, dreaded by most off oxygen plus molds off power flora hugs in solving it for moles off boxes. Um, we get most off oxygen at 0.212 moles per liter off solution. This will be the majority off solution multi off oxygen in this solution. As for Henry's law, as gas is equal to K H multiplied by PKS solving this for Henry's Law Constant cage for Oxygen and Part Flora Hexen we get catch as 0.212 moles per liter atmosphere. So the Henry's law states that the concentration of dissolved gas is directly proportional to the partial pressure of the gas about the solution. The cage for oxygen is 7 56.7 moles per liter atmosphere now using the equation P gas is your a k p c h c a r k p c h is you'll be gas by sea. Ever see a is the concentration off the especies in that Equus phase on celebrity and pig s is a partial pressure off that species in the gas phase under equilibrium conditions, KPC it is handy is constant and pressure Equus freeze concentration terms with unit as atmosphere later, but more as a percentage of oxygen in air is 20.9. The partial pressure off oxygen at one atmosphere will be 0.209 atmosphere. So the celebrity off oxygen will be 2.76 multiplied Vibe 10 power minus for most polyta at 25 C and one atmosphere calculating the mask we get as 8.838 multiplied by 10 per monastery grams per liter converting it into pp. Um, we get 8.84 ppm oxygen in the water at 25 degrees, integrate and one atmosphere in support. See, in descending out off pH. We have C 6 14 is greater than C six at 14 is greater than ethanol is greater than water toe dissolved oxygen in a solvent. The solvent molecules must be moved apart. Toe make room for the gas. The stronger the inter molecular forces in the solvent, the more difficult it is to separate solvent particles on the lower the scalability of the gas. Both C 6 14 and see six x 14 have weak discretion. Forces with C 6 14 having the vicar force due to the electoral negative. Floren atoms rippling each other in both internal and water. The molecules are held together by strong hydrogen bonds, with those bonds being stronger in water at the boiling point indicates.


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