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300. K Determine the value of the thermodynamic equilibrium constant K, at euch temperature At 20X8. K,AG, = 5.85 kJ mol-! What is K at that temperature?Kat 2000.K...

Question

300. K Determine the value of the thermodynamic equilibrium constant K, at euch temperature At 20X8. K,AG, = 5.85 kJ mol-! What is K at that temperature?Kat 2000.K =At 30X. K, AG; ~50.23 kJ mol What is K atthat temperature'Kat 30N) K =

300. K Determine the value of the thermodynamic equilibrium constant K, at euch temperature At 20X8. K,AG, = 5.85 kJ mol-! What is K at that temperature? Kat 2000.K = At 30X. K, AG; ~50.23 kJ mol What is K atthat temperature' Kat 30N) K =



Answers

The change in enthalpy $$\left(\Delta H_{\mathrm{rn}}^{\circ}\right)$$ for a reaction is $$
-25.8 \mathrm{kJ} / \mathrm{mol}$$ The equilibrium constant for the reaction is $$
1.4 \times 10^{3} \text { at } 298 \mathrm{K}$$ What is the equilibrium constant for the reaction at
$$655 \mathrm{K} ?$$

All right. So for this one, we're trying to find an equilibrium Constant K Ah, at 6 55 Kelvin for some reactions that we looked at earlier in problem 74. And so we'll start with the first reaction which is to And there, too going Tonto for And so the first thing I would do is I think back to how do we calculate the equilibrium, Constant K? And so you look at this formula Delta G. He goes, Don't the Jeannot plus r t ln okay, and so we can calculate Delta Do not. And we can't estimate Delta G if we know that the age not indulge us night and our is a constant and then t is 6 55 So from there, once we found Delta G, not in Delta G, we can get what K is by solving the algebra, and so that's what we'll do. So find a G night. You do Delta G A formation of the products might have still to g information of the reactant ce accounting for the molar ratios so you can find these values in your textbook. I'm just gonna write them down 99 eight minus two comes 51.3, and that equals minus 2.8. Killer Jules. So it's fine. Delta H not. He's the same process of non 0.16 Minus two terms. 33 queen too, equals minus 57.24 killed Jules. And we'll do. That s up here. Oh, quick. Don't. That s not equals Korea. Four 0.4 minus two times to 40.1. And that comes out to be, um, if you convert to kill a Jules, it's minus 0.175 A kill Jules per coven of values so we can plug in and find out estimate what Delta G is. So don't thingy is approximately still the age nine minus 6 55 which is the temperature comes that the s not. And so, if you plug those values in, you'll get approximately 57.9. And so from here we can solve the equation. The fine, the equilibrium constant K 77.9. Finessing killer Jules, he cools. Might is two point eight, plus, the constant are which in killer Joe lt's point 008 314 killed. Jules promote Kevin terms 6 55 times the natural log. Okay? And so we could just solve for this. And so me enough getting 60.7 equals 5.45 natural log. Okay? And so if you raise both powers to e k equals 66171.2. So that's reporting. RV was held the same way. Ah, little tricky part in the middle. So this is a grooming gas going to chlorine gas with chlorine gas going to through the e r c e o. It's a gas. So they give you Delta G, not a formation. Ah, just be our CEO. So if you multiply that by to account for the moles, you get minus two curdles, don't age not is also given for permission from B r c e o in delta h for B R. Two unsealed to above zero. So it's just two times that constant they give you, which is 14.6. And so you get 29.2. Killer Jules, don't as they didn't give you. But you can solve for it using the Gibbs equation. And since this is it standard temperature, you can do to 98 comes off the s not. And so you just plug in these values and you can sell for Delta s on Delta Ass night. Turns out to be and kill Jules 0.1, uh, killed Jules per Kelvin. And so again, you can take all these numbers in approximate what? Delta G at 6 55 Calvin is 29.2, minus 60 of times, dear. And so you get approximately minus 39.6 killer Jules and then completing this offer to equilibrium Constant K. So minus 39.6 equals minus two plus zero point. Uh uh, 831834 co jewels for Calvin terms 6 50 Mentor log. Okay. And so then you have you solved through the algebra you get minus 6.95 equals natural log of K. Raise both sides to e in K equals 0.1 And that's how you do this problem.

In this question we've been given to conditions. So a condition one, we are 298. Kill them. and condition # two, we are 655 kevin. So we've been asked to determine the equilibrium constant at condition took say kato given the equilibrium constant under hey one. So if we are to relate these two conditions, we can tell that Lynn K two Of AK one is equal to the standard entropy change of the reaction divided by art negative. This is going to be one over T 2 -1 over T one. So at the end we just want to make our K2 subject of the formula. And for us to remove this localism We say okay to over K one. We raise everything by an exponent. This is equal job exponent of negative delta eight standard divided by are multiplied by one over 2: -1 over T one. So If we are to make this K2 subjects of the formula, we just have to take this to the other side. So I start K two is equal to K one exponent of the standard and probably change divided by RT what are Multiplied by one over T 2 -1 over 81. So all we have to do is to substitute our values into this formula for us to then determine them. K 86 55 killed. So our K two is going to be equal to 1.4. Stand to the poetry multiplied by the exponent. Uh huh negative. This is going to be To 5.8 Multiplied by 10 to the par three jobs. For more, Divided by r. Then we multiply this by 1/6 55 minus one over two 98. So I would hate to this is going to be equal to 4.7.

Here. We have to calculate equal from constant when were provided. But certain other wild was like the ancient. Just my next 25 months. Pete, tell the truth. We have can want to be 1.4 and to turn to the power Klay it's 1400. The equable temperature is still 90. Calvin and equilibrium Constant got me after find its temperature is six with 35 killing. So we're gonna use the formula. You'll learn que two I came on. It was equal to lying This tell the age by our wanted by the by t two my name's won't divided by t one. So we know all of the values here except for K two. So let's just put in the wild use and see Get so Ellen don't know K two is we know. Okay, one is voting hard. Delta H is minus 25.8. They already have a minus years of the minus minus. We have plus 25.8 kill jewels. But our artisan jeweled so converting the killer jewels to Jules. We hit When you're 5 100 you're added, right? Three point dreams. War times one divided by 6 55 Linus one covers the park to my cake. So solving for K Okay too. We have the while. You trip 84.6.

In this question I've been asked to determine the equilibrium question K. And since we are dealing with state functions, thermodynamic state functions we can use the expression standard keeps energy change is equal to negative Paracin Lynn K. And this is our equilibrium constant that we're looking. So making K substitute formula we get cape being equal to the exponent of negative and it gives energy change divided by our routine. So the main goal here in the first part of the question is to just remind this standard gives energy change and we know this to be and that gives energy change can be calculated from standard and they will be changed minus T. Multiplied by standard entropy change. So since we are dealing with state functions for example for these two we can use this expression to say for example the standard entropy change is equal to the sum of the entropy changes of formation of the reactions of the product minus the sum of and that entropy change of formation of the reactions. And we always have to make sure that we multiply by the respective strict geometric coefficient because these expressions or these parameters are always given in Permal of substance. So we always have to make sure that we multiply by the respective documentary coefficient. Now applying this, we can use the same expression on the standard entropy change. So are playing this would get this from our data booklets all appendices. This is going to be one, one More of product, multiplied by 9.16 Multiple miners to multiplied by three 3.2. So this gives us a standard entropy change of negative 57 point 24 and the season tell a joke. Then we can do the same for the standard entropy change. This is equal to one more. Multiplied by The entropy change which is equal to 304 0.4 minus two moles. Multiplied by 240.1. And this is going to be equal to negative 175 .8. And this is in Joel's pair. No. Now that we have our standard entropy change and our standard entropy change. We can then use this formula to take your mind there. Standard keeps energy change and we take the standard gives energy change and plug it in here to finally get our equilibrium constant. So the standard keeps energy change to achieve standard is equal to negative five 7.25. This is in college also. We multiply by 10 to the poetry to get it in jewels because our standard entropy changes also in job. So this multiplied by there should be minus our temperature which is 655 Kelvin Multiplied by the entropy change which is negative. one point Okay, so our deal turkey standard. It's going to be equal to 5.7 Times 10 to the powerful. Sure what? This tells us. We have a standard mm Then that keeps energy change. That is greater than zero. So it tells us that under standard conditions this reaction is not spontaneous. It needs an external force or external source of energy for it to kicks that all to initially get it, get a drink. So now that we have our delta G standard. We then use this formula, this initial formula here to determine our equilibrium constant K. So our K. is going to be equal to the exponent of negative 5.7 to extend to the powerful divided by Uh which is 8.314. Multiplied by the temperature of 655 Children. So our K here is going to be equal to 2.41 multiplied by 10 to the power negative what? So we do the same for remaining part of the question that is we calculate the standard and then change this is equal to two, multiplied by wonderful 26 -1. 30.9 When there's one multiplied by zero, this is zero. Because understand that conditions for a pure element this standard and they'll be changing formation is zero because all of these are referenced under Few elements. eight standard condition This is going to be equal to negative 1.7. So for this one to calculate our standard, let's first of all calculate our standard standard gives energy change. If we use this formula we're going to get to Want to play it by -1 one, multiplied by 3.1 -1, multiplied by zero To get a negative 5.1 killer job. And for us to then get delta is the standard entropy change. This is going to be the entropy change -1.7 times 20 poetry Miners. The standard keeps energy change off negative 5.1 times 10 to the power three divided by two nine. was These are standard conditions at 25° sources here. What we're doing we are using this formula. Yeah. To data mine our standard entropy chain. So now that we have our standard entropy change, this is equal to standard entropy change is equal trump 11.404 in Joel's pair. Sure. So now that we have this you can then use this formula again to say to achieve is equal to delta age standard minus t daughter is standard. Now this is now going to be evaluated at a temperature of six. Quite fine. Remember all this what we're doing here. We're evaluating these under standard conditions of 25 Degrees sources. So now we want to account for the temperature that we've been given Which is 255 kills. So we can then say it all to change standard is equal to -1.7. to understand to the poetry -655 multiplied by 1 1.40. Sure. So our delta chief standard he is going to be equal to negative 9.1 from stand to the power trade in job. Now that we have our don't Turkey, we then use this formula to get our equilibrium constant, so our equilibrium constant K is going to be the exponents of negative Gibbs, which is negative 9.1 times 10 to the power train, divided by our great point 314 Times 655. So our K is going to be equal to five point then.


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