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JF

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Problem 79

The equilibrium constant for the reaction

$$2 \mathrm{Fe}^{3+}(a q)+\mathrm{Hg}_{2}^{2+}(a q) \rightleftharpoons 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{Hg}^{2+}(a q)$$

is $K_{c}=9.1 \times 10^{-6}$ at 298 $\mathrm{K}$

(a) What is $\Delta G^{\circ}$ at this temperature?

(b) If standard-state concentrations of the reactants and products are mixed, in which direction does the reaction proceed?

(c) Calculate $\Delta G$ when $\left[\mathrm{Fe}^{3+}\right]=0.20 M,\left[\mathrm{Hg}_{2}^{2+}\right]=0.010 M,$ $\left[\mathrm{Fe}^{2+}\right]=0.010 M,$ and $\left[\mathrm{Hg}^{2+}\right]=0.025 M$ . In which direction will the reaction proceed to achieve equilibrium?

Answer

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## Discussion

## Video Transcript

okay to start this question off, we have our equation here. You have our equation here, and then we have the givens here. So we know Casey is equal to 9.1 times 10 to the negative six at 298. And the money I want to find the Delta G standard. So we're gonna use this equation right here, and we can just plug Alvar knowns. And so we have Casey, that'll plug in right here. And then we have our is a constant. It's 8.314 Would you see right here and then you have to 98 Kelvin and then our case c So that's just a plug and chug through. You wanna positivity on do that? Calculations. The answer to that comes out to be 28 75 seven Jules. Sorry. That's a little messy. Seven. This isn't eight. Okay, So be asks us which way this reaction is going to go. And we can just think about the Delta G. So we know that a negative delta G means that the reaction is spontaneous. So we know that we have say we have a product or we ever reactant is here and our products here. We know a spontaneous reaction is going to proceed forward because it requires no additional energy. So it'll happen on its own, and reactions will form products. However, we have a positive Delta G, which means it's non spontaneous. He's gonna put non s, which means that if we have our reactions here are reacting is here and our products here, it's going to proceed to the left. So based on our Delta G value, we can say that the reaction at this temperature with the standard state concentrations will proceed to the left. Let me destroyed that here left. Great. All right. Moving on to part C. So we have we want to find our Delta G. And this is from our This is different from our delta g standard of the reaction. So this is going to be at specific concentrations that were given so in the question, were given certain concentrations, and we want to plug those into find Q. Since this is what we don't have in our equation. So we know this We just calculated this are again is a constant T is temperature. So if we're able to find Cube. We can put this back in and get our Delta G. So I wrote out our equation to find que accused the reaction quotient. So you're going to take products, overreact INTs and then use the coefficients. So here are the coefficients and, um, used those as the power. Put those to the power of each of the products and then react INTs, these air, all twos, they're a little messy. Perfect. And then we need to find that we were given the concentrations for each of these. So we're gonna plug those in right here. I set up a little skeleton, so we're told that f e two plus is 20.10 h g two plus is point 025 f e three plus is point 20 and, uh, h g 22 plus is point 010 again. All right, so we're gonna solve out for that. If you want to pause the video and do that quick calculation, you should get about 1.5 six times. Sorry. Times 10 to the negative fourth. Okay, So now that we have our cue, our reaction quotient we can use this number and plug it into this equation in order to get our final answer for Delta G. So I have again the skeleton. So this was the Delta G standard that we calculated at the very beginning. Here we have our our this is the temperature. And then we're gonna take the natural log of the reaction question, which was 1.56 times tended in any good Ford and plug it in right there. Remember that you're taking the natural log of this number and then multiplying it by r and t. All right, so you want a pause the video and do that quick calculation? You should get 739 Jules. Or if you need to put it in Kila, Jules, you're just gonna divide that by 1000 to get seven point 039