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Revie Jopics[Ratcronccel following tharmodynamic prorxrtics appropriate Dutnerical sign for thc followingWithout dowg calculations match #rutnermicIcachOn2CHo(g) 701(g)4CO_(g) 6HzO(g)Clear AllAHxn4 SrnAGxnWaouhigh0 low T, > 0 hich' PrevousNoASuei9>

Revie Jopics [Ratcronccel following tharmodynamic prorxrtics appropriate Dutnerical sign for thc following Without dowg calculations match #rutnermicIcachOn 2CHo(g) 701(g) 4CO_(g) 6HzO(g) Clear All AHxn 4 Srn AGxn Waou high 0 low T, > 0 hich ' Prevous No ASuei9>



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Calculate $E^{\circ}$ for the following cells: (a) $\mathrm{Mn}\left|\mathrm{Mn}^{2+} \| \mathrm{H}^{+}\right| \mathrm{H}_{2} \mid \mathrm{Pt}$ (b) $\mathrm{Au}\left|\mathrm{AuCl}_{4}^{-} \| \mathrm{Co}^{3+}, \mathrm{Co}^{2+}\right| \mathrm{Pt}$ (c) $\mathrm{Pt}\left|\mathrm{S}^{2-}\right| \mathrm{S} \| \mathrm{NO}_{3}^{-}|\mathrm{NO}| \mathrm{Pt} \quad$ (basic medium)

One question is a match type cushion. And we know that delta G is given as delta H minus T delta S. So from here, if delta G is less than zero is less than zero, then the reaction would be spontaneous. Or if I say delta edge is less than T delta as is less than T deltas. So this implies DELTA G will be less than zero. So in both the cases the reaction would be spontaneous. So I can say that the option a option A matches with B and S. Matches with P and S. And if delta G is equal to zero, that means the reaction is spontaneous. Sorry that the reaction is in equilibrium. So it represents equilibrium condition equilibrium. So in an option day it matches with cuba. And now if if delta S. Is less than zero, then we can say T delta as will be negative. If it is negative, that means uh delta edge that will be greater than T delta S. Delta edge that will be resident T. Delta is. So I can say in option B. The option are matches B matches with our. Now if delta edge is equal to delta A, then delta G. That can be written as delta minus T. Delta as. So delta at minus T. Deltas can be written as delta E by T. So from here we can write that delta G comes out to be zero. So it represents equilibrium condition. That means C represents, see matches with Q. C matches with cuba. So these are the matching A, matches with P and S. D. matches with q b matches with r and C matches with Q.

All right, So each one of our problems have this space function. Four X squared, minus four X plus one. Oh, nine. So, uh huh. We're going to evaluate this. I'm going to find the Vertex completing the square. Mhm. Yeah. Mhm. Mhm. Let me get four times x squared minus X plus one on nine times are over four mhm and a complete this square. We need X squared minus x plus half of our coefficient, which is one half just because it's minus one times X for B then minus another one half squared +19 came over for Yeah, yeah. Mhm, Yeah, yeah. So we get four times quantity of X minus one half squared, and now our r minus one half square goes to minus 1/4. So we're just left with plus one away over four. After we distribute are for we get X minus one half squared. I just wanna wait. So a vertex is that X equals one half and normally would go to wanna wait, but it won't for this case. So our first function, f x it's gonna be the square root of this base function, which we're gonna rewrite as X minus one half square was going. So if we plug in are very text 0.1 half you get a square room of one half minus one half squared plus one away or just the square root of 108 Yeah, mhm. Which is equal? Oh, two approximately equal to I should say 10.39 approximately now for our next function. Dfx, we get mhm. Three are the Cube group of our X minus one half squared plus one Oh eight Mhm. Mhm. So and then, if we just plug in our one half Uh huh. We get okay, no one has canceled. Once again we get and we're left with the cube root of one away, which is approximately equal to 4.76 Mhm. Lastly, for our h of x h of X is a little different. Yeah, we do have kind of the same base of four X squared, minus four x plus one on nine. But instead we have four x to the fourth minus four x squared plus one. Oh, nine a notice. It's the same equation that we have, except with an X squared in place of our X. Yeah. So that means after the same analysis will get X squared minus one half squared plus one. Oh, eight meaning? Uh huh. That we're gonna get Yeah, yeah, X minus one over. Radical two times X plus one over. Radical two. It's one of a radical to is just the same as radical to over two. Mm. But either way, we plug each of those values in so h of plus or minus one divided by radical to is gonna give us zero for this term. And then just to wanna wait left over. So h of X as men's at one, divided by radical to want to wait and one negative one over. Radical two. Wow. Can't wait. Yeah, Mhm. So slightly different from our g of X, which has a one half 4.76 and er fx, which has a one. Yeah, one seconds. Yeah. Okay. One half 10.39 Mhm. Although they all have the same general face equations. But those are three minimum values. There are three minimum values for R three functions


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